ไฟล์ course syllabi - คณะวิทยาศาสตร์ มหาวิทยาลัยมหิดล - Mahidol ...

sc.mahidol.ac.th

ไฟล์ course syllabi - คณะวิทยาศาสตร์ มหาวิทยาลัยมหิดล - Mahidol ...

Mathematics Course Syllabi

for Courses Offered by

Department of Mathematics

Faculty of Science, Mahidol University

2006 Revision


Table of Contents

Ç·¤³ 110 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Ç·¤³ 113 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Ç·¤³ 115 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Ç·¤³ 116 á¹Ç¤Ô´àªÔ§¤³ÔµÈÒʵÌÊÒÁÑ-áÅСÒûÃÐÂØ¡µŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Ç·¤³ 117 ¤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Ç·¤³ 136 àâҤ³ÔµáººÂؤÅÔ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Ç·¤³ 141 »¯ÔºÑµÔ¡ÒäÍÁ¾ÔÇàµÍÃŒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Ç·¤³ 145 ¡ÒûÃÐÁǿމÍÁÙÅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Ç·¤³ 160 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Ç·¤³ 161 ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Ç·¤³ 162 á¤Å¤ÙÅÑÊáÅÐÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ-¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Ç·¤³ 163 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Ç·¤³ 170 ¤³ÔµÈÒʵÌáÅÐÊÔµÔÈÒʵ̾×é¹°Ò¹·Õè㪉䴉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Ç·¤³ 180 ÊÔµÔÈÒʵÌ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33

Ç·¤³ 181 ÊÔµÔÈÒʵÌÊíÒËÃѺÇÔ·ÂÒÈÒʵÌ¡ÒÃá¾·ÂŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39

Ç·¤³ 182 ÊÔµÔÈÒʵÌÊíÒËÃѺÇÔ·ÂÒÈÒʵÌÊØ¢ÀÒ¾ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42

Ç·¤³ 183 ÊÔµÔÈÒʵÌ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Ç·¤³ 203 ·ÄɮդÇÒÁ¹ˆÒ¨Ð໓¹ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Ç·¤³ 204 ¡ÒÃÍ͡Ẻ¡Ò÷´Åͧ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Ç·¤³ 205 ¡ÒÃÇÔà¤ÃÒÐËŒËÅÒµÑÇá»Ã (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51

Ç·¤³ 209 ·ÄɮաÒä³¹Ò (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Ç·¤³ 213 á¤Å¤ÙÅÑÊËÅÒµÑÇá»Ã . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

Ç·¤³ 214 á¤Å¤ÙÅÑÊ¢Ñé¹ÊÙ§. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60

Ç·¤³ 216 á¤Å¤ÙÅÑÊ¢Ñé¹ÊÙ§. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62

Ç·¤³ 222 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸Œ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Ç·¤³ 226 µÑÇá»ÃàªÔ§«‰Í¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66

Ç·¤³ 234 ¡ÒÃÇÔà¤ÃÒÐËŒàÇ¡àµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

Ç·¤³ 235 àâҤ³ÔµÇÔà¤ÃÒÐËŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Ç·¤³ 236 àâҤ³Ôµ¹Í¡áººÂؤÅÔ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Ç·¤³ 237 ¡ÒÃÇÔà¤ÃÒÐËŒàÇ¡àµÍÃŒáÅÐà·¹à«ÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

Ç·¤³ 241 ¡ÒÃà¢Õ¹â»Ãá¡ÃÁ¤ÍÁ¾ÔÇàµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Ç·¤³ 263 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒáÅл’-ËÒ¤ˆÒ¢Íº . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Ç·¤³ 266 ·Äɮմ͡àºÕé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Ç·¤³ 273 â¤Ã§ÊÉҧàªÔ§¤³ÔµÈÒʵÌáÅСÒþÔÊÙ¨¹Œ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84

Ç·¤³ 275 ·ÄÉ®Õ૵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Ç·¤³ 283 ¤ÇÒÁ¹ˆÒ¨Ð໓¹áÅÐÊÔµÔÈÒʵÌ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90

Ç·¤³ 284 ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Ç·¤³ 285 ¡Ãкǹ¡ÒÃÊâ·á¤ÊµÔ¡¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95

Ç·¤³ 290 ËÑÇ¢‰Í¾ÔàÈÉ㹤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Ç·¤³ 291 ËÑÇ¢‰Í¤Ñ´ÊÃà 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Ç·¤³ 292 ËÑÇ¢‰Í¤Ñ´ÊÃà 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Ç·¤³ 300 ·ÄÉ®Õ૵ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

i


Ç·¤³ 301 ·ÄɮաÃÒ¿¢Ñé¹á¹Ð¹íÒ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103

Ç·¤³ 302 ·ÄɮաÃØ» (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Ç·¤³ 303 ·Äɮըíҹǹ 2 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Ç·¤³ 304 ·ÄÉ®Õà¡Á (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Ç·¤³ 305 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸ŒáÅСÒÃÇÔà¤ÃÒÐˌ෹à«ÍÃŒ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Ç·¤³ 306 ÊÁ¡ÒÃÍÔ¹·Ô¡ÃÑÅ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115

Ç·¤³ 307 »’-ËÒ¤ˆÒ¢Íº (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118

Ç·¤³ 308 ¼Å¡ÒÃá»Å§àªÔ§¤³ÔµÈÒʵÌ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Ç·¤³ 309 ·ÄÉ®ÕÃËÑÊ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Ç·¤³ 321 ¤³ÔµÇÔà¤ÃÒÐËŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Ç·¤³ 325 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§¨ÃÔ§ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

Ç·¤³ 326 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§«‰Í¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Ç·¤³ 336 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸Œàº×éͧµ‰¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Ç·¤³ 342 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§µÑÇàÅ¢ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Ç·¤³ 350 ·Äɮըíҹǹ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Ç·¤³ 351 ¾Õª¤³ÔµàªÔ§àʉ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Ç·¤³ 352 ¾Õª¤³Ôµ¹ÒÁ¸ÃÃÁ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Ç·¤³ 356 ·ÄɮաÃØ» . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Ç·¤³ 362 ¤³ÔµÈÒʵÌã¹ÇÔ·ÂÒÈÒʵÌ¡ÒÂÀÒ¾ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Ç·¤³ 363 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÂˆÍ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Ç·¤³ 364 ÊÁ¡ÒÃÍÔ¹·Ô¡ÃÑÅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Ç·¤³ 365 ¿’§¡ŒªÑ¹¾ÔàÈÉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151

Ç·¤³ 366 ¤³ÔµÈÒʵÌ»ÃСѹªÕÇÔµ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Ç·¤³ 367 ·ÄÉ®Õà¡Á . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

Ç·¤³ 368 ¼Å¡ÒÃá»Å§àªÔ§¤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Ç·¤³ 369 ÇÔ¸ÕàªÔ§¤³ÔµÈÒʵÌ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159

Ç·¤³ 370 ÇÔÂص¤³Ôµ¢Ñé¹á¹Ð¹íÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160

Ç·¤³ 372 ·ÄÉ®ÕÃËÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162

Ç·¤³ 373 µÃáÈÒʵÌàªÔ§¤³ÔµÈÒʵÌ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Ç·¤³ 374 ·ÄɮաÃÒ¿¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

Ç·¤³ 376 ¤³ÔµÈÒʵÌàªÔ§¡ÒèѴ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168

Ç·¤³ 380 ·ÄɮդÇÒÁ¹ˆÒ¨Ð໓¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170

Ç·¤³ 382 ¡ÒÃÍ͡Ẻ¡Ò÷´Åͧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172

Ç·¤³ 383 ÇÔ¸ÕàªÔ§ÊÔµÔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174

Ç·¤³ 384 ÊÔµÔäɾÒÃÒÁÔàµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Ç·¤³ 386 ·Äɮբͧ¡ÒèѴáÇ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180

Ç·¤³ 387 ·ÄÉ®ÕÊÔ¹¤‰Ò¤§¤Åѧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182

Ç·¤³ 391 ËÑÇ¢‰Í¾ÔàÈÉ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Ç·¤³ 392 ËÑÇ¢‰Í¾ÔàÈÉ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185

Ç·¤³ 396 ÊÑÁÁ¹Ò 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Ç·¤³ 397 ÊÑÁÁ¹Ò 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Ç·¤³ 401 ËÑÇ¢‰Í¾ÔàÈÉ 1 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

Ç·¤³ 402 ËÑÇ¢‰Í¾ÔàÈÉ 2 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Ç·¤³ 403 ËÑÇ¢‰Í¾ÔàÈÉ 3 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

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Ç·¤³ 404 ËÑÇ¢‰Í¾ÔàÈÉ 4 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

Ç·¤³ 410 »ÃÐÇѵԤ³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196

Ç·¤³ 430 ·Í¾ÍâÅÂÕ·ÑèÇä» . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .199

Ç·¤³ 433 ·Í¾ÍâÅÂÕàªÔ§¾Õª¤³Ôµàº×éͧµ‰¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201

Ç·¤³ 435 àâҤ³Ôµ¡ÒÃá»Å§. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .203

Ç·¤³ 436 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸ŒáÅСÒÃÇÔà¤ÃÒÐˌ෹à«ÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Ç·¤³ 448 ¡ÒûÃÐÂØ¡µŒ¤ÍÁ¾ÔÇàµÍÃŒã¹ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Ç·¤³ 449 ·ÄɮաÒä³¹Ò . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .209

Ç·¤³ 450 ·Äɮըíҹǹ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Ç·¤³ 452 ¾Õª¤³Ôµ¹ÒÁ¸ÃÃÁ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Ç·¤³ 456 â¤Ã§ÊÉҧ¾Õª¤³Ôµ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Ç·¤³ 460 ÃкºàªÔ§¾ÅÇѵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Ç·¤³ 462 ÊÁ¡ÒÃ͹ؾѹ¸ŒàªÔ§¼ÅµˆÒ§. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219

Ç·¤³ 464 »’-ËÒ¤ˆÒ¢Íº . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Ç·¤³ 465 ·ÄɮբͧÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Ç·¤³ 466 ¤³ÔµÈÒʵÌ»ÃСѹªÕÇÔµ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Ç·¤³ 467 ·ÄɮաÒäǺ¤ØÁ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227

Ç·¤³ 468 á¤Å¤ÙÅÑÊ¡ÒÃá»Ã¼Ñ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229

Ç·¤³ 473 ¡ÒÃÇԨѴíÒà¹Ô¹¡Òà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

Ç·¤³ 474 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒõѴÊԹ㨠. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233

Ç·¤³ 480 ÇÔ¸Õ¡ÒÃÊ؈ÁµÑÇ͈ҧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235

Ç·¤³ 481 ¡ÒÃÇÔà¤ÃÒÐˌ͹ءÃÁàÇÅÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .239

Ç·¤³ 483 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒôÍÂàªÔ§àʉ¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .241

Ç·¤³ 484 ¡ÒÃÇÔà¤ÃÒÐËŒËÅÒµÑÇá»Ã . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Ç·¤³ 486 ¡ÒèíÒÅͧàÅÕ¹Ẻ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

Ç·¤³ 491 ËÑÇ¢‰Í¾ÔàÈÉ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

Ç·¤³ 492 ËÑÇ¢‰Í¾ÔàÈÉ 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .251

Ç·¤³ 493 â¤Ã§¡ÒÃÇԨѠ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .252

Ç·¤³ 494 â¤Ã§¡ÒÃÇԨѠ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .253

Ç·¤³ 496 ÊÑÁÁ¹Ò 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Ç·¤³ 497 ÊÑÁÁ¹Ò 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

Ç·¤³ 603 ·ÄɮբͧÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

Ç·¤³ 607 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§¿’§¡ŒªÑ¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .258

Ç·¤³ 608 ¾Õª¤³ÔµÊÁÑÂãËÁˆ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260

Ç·¤³ 630 ¡ÒÃÇԨѴíÒà¹Ô¹¡Òà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

Ç·¤³ 631 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒõѴÊԹ㨠. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264

Ç·¤³ 633 ¡Ãкǹ¡ÒÃÊâ·á¤ÊµÔ¡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

Ç·¤³ 643 ¡ÒÃÇÔà¤ÃÒÐˌ͹ءÃÁàÇÅÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268

Ç·¤³ 645 Ẻ¨íÒÅͧàªÔ§àʉ¹·ÑèÇä». . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .270

Ç·¤³ 673 ÃкºàªÔ§¾ÅÇѵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Ç·¤³ 688 ¡ÒÃ͹ØÁÒ¹àªÔ§ÊÔµÔ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274

Ç·¤³ 110 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

SCMA 110 Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .278

Ç·¤³ 113 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

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SCMA 113 Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284

Ç·¤³ 115 á¤Å¤ÙÅÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

SCMA 115 Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290

Ç·¤³ 116 á¹Ç¤Ô´àªÔ§¤³ÔµÈÒʵÌÊÒÁÑ-áÅСÒûÃÐÂØ¡µŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294

SCMA 116 Simple Mathematical Concepts and Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297

Ç·¤³ 117 ¤³ÔµÈÒʵÌ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .300

SCMA 117 Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303

Ç·¤³ 136 àâҤ³ÔµáººÂؤÅÔ´. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306

SCMA 136 Euclidean Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

Ç·¤³ 141 »¯ÔºÑµÔ¡ÒäÍÁ¾ÔÇàµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

SCMA 141 Computer Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Ç·¤³ 145 ¡ÒûÃÐÁǿމÍÁÙÅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312

SCMA 145 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

Ç·¤³ 160 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

SCMA 160 Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

Ç·¤³ 161 ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

SCMA 161 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

Ç·¤³ 162 á¤Å¤ÙÅÑÊáÅÐÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ-¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

SCMA 162 Calculus and Introduction to Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Ç·¤³ 163 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

SCMA 163 Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

Ç·¤³ 170 ¤³ÔµÈÒʵÌáÅÐÊÔµÔÈÒʵ̾×é¹°Ò¹·Õè㪉䴉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

SCMA 170 Applicable Basic Mathematics and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

Ç·¤³ 180 ÊÔµÔÈÒʵÌ¢Ñé¹á¹Ð¹íÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .343

SCMA 180 Introduction to Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

Ç·¤³ 181 ÊÔµÔÈÒʵÌÊíÒËÃѺÇÔ·ÂÒÈÒʵÌ¡ÒÃá¾·ÂŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

SCMA 181 Statistics for Medical Science. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .358

Ç·¤³ 182 ÊÔµÔÈÒʵÌÊíÒËÃѺÇÔ·ÂÒÈÒʵÌÊØ¢ÀÒ¾. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360

SCMA 182 Statistics for Health Sciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

Ç·¤³ 183 ÊÔµÔÈÒʵÌ¢Ñé¹á¹Ð¹íÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .364

SCMA 183 Introduction to Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

Ç·¤³ 203 ·ÄɮդÇÒÁ¹ˆÒ¨Ð໓¹ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

SCMA 203 Probability Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

Ç·¤³ 204 ¡ÒÃÍ͡Ẻ¡Ò÷´Åͧ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

SCMA 204 Experimental Design (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

Ç·¤³ 205 ¡ÒÃÇÔà¤ÃÒÐËŒËÅÒµÑÇá»Ã (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .378

SCMA 205 Multivariate Analysis (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

Ç·¤³ 209 ·ÄɮաÒä³¹Ò (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

SCMA 209 Theory of Computation (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

Ç·¤³ 213 á¤Å¤ÙÅÑÊËÅÒµÑÇá»Ã. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .391

SCMA 213 Calculus of Several Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

Ç·¤³ 214 á¤Å¤ÙÅÑÊ¢Ñé¹ÊÙ§ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

SCMA 214 Advanced Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Ç·¤³ 216 á¤Å¤ÙÅÑÊ¢Ñé¹ÊÙ§ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

iv


SCMA 216 Advanced Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Ç·¤³ 222 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸Œ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

SCMA 222 Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

Ç·¤³ 226 µÑÇá»ÃàªÔ§«‰Í¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .407

SCMA 226 Complex Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Ç·¤³ 234 ¡ÒÃÇÔà¤ÃÒÐËŒàÇ¡àµÍÃŒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .415

SCMA 234 Vector Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Ç·¤³ 235 àâҤ³ÔµÇÔà¤ÃÒÐËŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421

SCMA 235 Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423

Ç·¤³ 236 àâҤ³Ôµ¹Í¡áººÂؤÅÔ´ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .425

SCMA 236 Non-Euclidean Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

Ç·¤³ 237 ¡ÒÃÇÔà¤ÃÒÐËŒàÇ¡àµÍÃŒáÅÐà·¹à«ÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .429

SCMA 237 Vector and Tensor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

Ç·¤³ 241 ¡ÒÃà¢Õ¹â»Ãá¡ÃÁ¤ÍÁ¾ÔÇàµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

SCMA 241 Computer Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

Ç·¤³ 263 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒáÅл’-ËÒ¤ˆÒ¢Íº . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

SCMA 263 Differential Equations and Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

Ç·¤³ 266 ·Äɮմ͡àºÕé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

SCMA 266 Theory of Interests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

Ç·¤³ 273 â¤Ã§ÊÉҧàªÔ§¤³ÔµÈÒʵÌáÅСÒþÔÊÙ¨¹Œ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443

SCMA 273 Mathematical Structures and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

Ç·¤³ 275 ·ÄÉ®Õ૵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .449

SCMA 275 Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

Ç·¤³ 283 ¤ÇÒÁ¹ˆÒ¨Ð໓¹áÅÐÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

SCMA 283 Probability and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

Ç·¤³ 284 ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

SCMA 284 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

Ç·¤³ 285 ¡Ãкǹ¡ÒÃÊâ·á¤ÊµÔ¡¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

SCMA 285 Introduction to Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

Ç·¤³ 290 ËÑÇ¢‰Í¾ÔàÈÉ㹤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .469

SCMA 290 Special Topics in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

Ç·¤³ 291 ËÑÇ¢‰Í¤Ñ´ÊÃà 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .471

SCMA 291 Selected Topics I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

Ç·¤³ 292 ËÑÇ¢‰Í¤Ñ´ÊÃà 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .473

SCMA 292 Selected Topics II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

Ç·¤³ 300 ·ÄÉ®Õ૵ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

SCMA 300 Set Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

Ç·¤³ 301 ·ÄɮաÃÒ¿¢Ñé¹á¹Ð¹íÒ (¾ÔÊÔ°ÇÔ¸Ò¹). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .481

SCMA 301 Introduction to Graph Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

Ç·¤³ 302 ·ÄɮաÃØ» (¾ÔÊÔ°ÇÔ¸Ò¹). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .485

SCMA 302 Group Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

Ç·¤³ 303 ·Äɮըíҹǹ 2 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

SCMA 303 Number Theory II (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

Ç·¤³ 304 ·ÄÉ®Õà¡Á (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

v


SCMA 304 Game Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

Ç·¤³ 305 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸ŒáÅСÒÃÇÔà¤ÃÒÐˌ෹à«ÍÃŒ (¾ÔÊÔ°ÇÔ¸Ò¹). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .499

SCMA 305 Differential Geometry and Tensor Analysis (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .502

Ç·¤³ 306 ÊÁ¡ÒÃÍÔ¹·Ô¡ÃÑÅ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .505

SCMA 306 Integral Equations (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

Ç·¤³ 307 »’-ËÒ¤ˆÒ¢Íº (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .511

SCMA 307 Boundary Value Problems (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

Ç·¤³ 308 ¼Å¡ÒÃá»Å§àªÔ§¤³ÔµÈÒʵÌ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .517

SCMA 308 Mathematical Transforms (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

Ç·¤³ 309 ·ÄÉ®ÕÃËÑÊ (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523

SCMA 309 Coding Theory (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

Ç·¤³ 321 ¤³ÔµÇÔà¤ÃÒÐËŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .529

SCMA 321 Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

Ç·¤³ 325 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§¨ÃÔ§. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .535

SCMA 325 Real Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

Ç·¤³ 326 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§«‰Í¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .539

SCMA 326 Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

Ç·¤³ 336 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸Œàº×éͧµ‰¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

SCMA 336 Elementary Differential Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545

Ç·¤³ 342 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§µÑÇàÅ¢ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

SCMA 342 Numerical Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .549

Ç·¤³ 350 ·Äɮըíҹǹ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

SCMA 350 Number Theory I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

Ç·¤³ 351 ¾Õª¤³ÔµàªÔ§àʉ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555

SCMA 351 Linear Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .556

Ç·¤³ 352 ¾Õª¤³Ôµ¹ÒÁ¸ÃÃÁ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

SCMA 352 Abstract Algebra I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

Ç·¤³ 356 ·ÄɮաÃØ» . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

SCMA 356 Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

Ç·¤³ 362 ¤³ÔµÈÒʵÌã¹ÇÔ·ÂÒÈÒʵÌ¡ÒÂÀÒ¾ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

SCMA 362 Mathematics in Physical Sciences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .567

Ç·¤³ 363 ÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÂˆÍÂ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .569

SCMA 363 Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

Ç·¤³ 364 ÊÁ¡ÒÃÍÔ¹·Ô¡ÃÑÅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

SCMA 364 Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

Ç·¤³ 365 ¿’§¡ŒªÑ¹¾ÔàÈÉ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577

SCMA 365 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

Ç·¤³ 366 ¤³ÔµÈÒʵÌ»ÃСѹªÕÇÔµ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

SCMA 366 Life Actuarial Mathematics I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .584

Ç·¤³ 367 ·ÄÉ®Õà¡Á . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .586

SCMA 367 Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .588

Ç·¤³ 368 ¼Å¡ÒÃá»Å§àªÔ§¤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

SCMA 368 Mathematical Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

Ç·¤³ 369 ÇÔ¸ÕàªÔ§¤³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

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SCMA 369 Mathematical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

Ç·¤³ 370 ÇÔÂص¤³Ôµ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596

SCMA 370 Introduction to Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .598

Ç·¤³ 372 ·ÄÉ®ÕÃËÑÊ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

SCMA 372 Coding Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

Ç·¤³ 373 µÃáÈÒʵÌàªÔ§¤³ÔµÈÒʵÌ¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .604

SCMA 373 Introduction to Mathematical Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606

Ç·¤³ 374 ·ÄɮաÃÒ¿¢Ñé¹á¹Ð¹íÒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .608

SCMA 374 Introduction to Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610

Ç·¤³ 376 ¤³ÔµÈÒʵÌàªÔ§¡ÒèѴ¢Ñé¹á¹Ð¹íÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .612

SCMA 376 Introduction to Combinatorial Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

Ç·¤³ 380 ·ÄɮդÇÒÁ¹ˆÒ¨Ð໓¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .616

SCMA 380 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

Ç·¤³ 382 ¡ÒÃÍ͡Ẻ¡Ò÷´Åͧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620

SCMA 382 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622

Ç·¤³ 383 ÇÔ¸ÕàªÔ§ÊÔµÔ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .624

SCMA 383 Statistical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .627

Ç·¤³ 384 ÊÔµÔäɾÒÃÒÁÔàµÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .631

SCMA 384 Nonparametric Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .634

Ç·¤³ 386 ·Äɮբͧ¡ÒèѴáÇ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637

SCMA 386 Queuing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639

Ç·¤³ 387 ·ÄÉ®ÕÊÔ¹¤‰Ò¤§¤Åѧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .641

SCMA 387 Inventory Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643

Ç·¤³ 391 ËÑÇ¢‰Í¾ÔàÈÉ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .645

SCMA 391 Special Topics I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

Ç·¤³ 392 ËÑÇ¢‰Í¾ÔàÈÉ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .647

SCMA 392 Special Topics II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648

Ç·¤³ 396 ÊÑÁÁ¹Ò 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649

SCMA 396 Seminar I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650

Ç·¤³ 397 ÊÑÁÁ¹Ò 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

SCMA 397 Seminar II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .652

Ç·¤³ 401 ËÑÇ¢‰Í¾ÔàÈÉ 1 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

SCMA 401 Special Topics I (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

Ç·¤³ 402 ËÑÇ¢‰Í¾ÔàÈÉ 2 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

SCMA 402 Special Topics II (Distinction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .658

Ç·¤³ 403 ËÑÇ¢‰Í¾ÔàÈÉ 3 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

SCMA 403 Special Topics III (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661

Ç·¤³ 404 ËÑÇ¢‰Í¾ÔàÈÉ 4 (¾ÔÊÔ°ÇÔ¸Ò¹) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

SCMA 404 Special Topics IV (Distinction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

Ç·¤³ 410 »ÃÐÇѵԤ³ÔµÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .665

SCMA 410 History of Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .668

Ç·¤³ 430 ·Í¾ÍâÅÂÕ·ÑèÇä». . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .671

SCMA 430 General Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673

Ç·¤³ 433 ·Í¾ÍâÅÂÕàªÔ§¾Õª¤³Ôµàº×éͧµ‰¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

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SCMA 433 Elementary Algebraic Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677

Ç·¤³ 435 àâҤ³Ôµ¡ÒÃá»Å§ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

SCMA 435 Transformation Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .681

Ç·¤³ 436 àâҤ³ÔµàªÔ§Í¹Ø¾Ñ¹¸ŒáÅСÒÃÇÔà¤ÃÒÐˌ෹à«ÍÃŒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683

SCMA 436 Differential Geometry and Tensor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

Ç·¤³ 448 ¡ÒûÃÐÂØ¡µŒ¤ÍÁ¾ÔÇàµÍÃŒã¹ÊÔµÔÈÒʵÌ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687

SCMA 448 Computer Applications in Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

Ç·¤³ 449 ·ÄɮաÒä³¹Ò. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .691

SCMA 449 Theory of Computation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .693

Ç·¤³ 450 ·Äɮըíҹǹ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695

SCMA 450 Number Theory II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697

Ç·¤³ 452 ¾Õª¤³Ôµ¹ÒÁ¸ÃÃÁ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

SCMA 452 Abstract Algebra II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

Ç·¤³ 456 â¤Ã§ÊÉҧ¾Õª¤³Ôµ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703

SCMA 456 Algebraic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705

Ç·¤³ 460 ÃкºàªÔ§¾ÅÇѵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .707

SCMA 460 Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

Ç·¤³ 462 ÊÁ¡ÒÃ͹ؾѹ¸ŒàªÔ§¼ÅµˆÒ§ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

SCMA 462 Difference Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

Ç·¤³ 464 »’-ËÒ¤ˆÒ¢Íº . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715

SCMA 464 Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717

Ç·¤³ 465 ·ÄɮբͧÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719

SCMA 465 Theory of Ordinary Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .721

Ç·¤³ 466 ¤³ÔµÈÒʵÌ»ÃСѹªÕÇÔµ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723

SCMA 466 Life Actuarial Mathematics II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

Ç·¤³ 467 ·ÄɮաÒäǺ¤ØÁ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .727

SCMA 467 Control Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729

Ç·¤³ 468 á¤Å¤ÙÅÑÊ¡ÒÃá»Ã¼Ñ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .731

SCMA 468 Calculus of Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733

Ç·¤³ 473 ¡ÒÃÇԨѴíÒà¹Ô¹¡Òà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .735

SCMA 473 Operations Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737

Ç·¤³ 474 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒõѴÊÔ¹ã¨. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .739

SCMA 474 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741

Ç·¤³ 480 ÇÔ¸Õ¡ÒÃÊ؈ÁµÑÇ͈ҧ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .743

SCMA 480 Sampling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747

Ç·¤³ 481 ¡ÒÃÇÔà¤ÃÒÐˌ͹ءÃÁàÇÅÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .751

SCMA 481 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

Ç·¤³ 483 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒôÍÂàªÔ§àʉ¹ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755

SCMA 483 Linear Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .759

Ç·¤³ 484 ¡ÒÃÇÔà¤ÃÒÐËŒËÅÒµÑÇá»Ã . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

SCMA 484 Multivariate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .766

Ç·¤³ 486 ¡ÒèíÒÅͧàÅÕ¹Ẻ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769

SCMA 486 Simulation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771

Ç·¤³ 491 ËÑÇ¢‰Í¾ÔàÈÉ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .773

viii


SCMA 491 Special Topics III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774

Ç·¤³ 492 ËÑÇ¢‰Í¾ÔàÈÉ 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .775

SCMA 492 Special Topics IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776

Ç·¤³ 493 â¤Ã§¡ÒÃÇԨѠ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .777

SCMA 493 Research Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778

Ç·¤³ 494 â¤Ã§¡ÒÃÇԨѠ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .779

SCMA 494 Research Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 780

Ç·¤³ 496 ÊÑÁÁ¹Ò 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781

SCMA 496 Seminar III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782

Ç·¤³ 497 ÊÑÁÁ¹Ò 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783

SCMA 497 Seminar IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784

Ç·¤³ 603 ·ÄɮբͧÊÁ¡ÒÃàªÔ§Í¹Ø¾Ñ¹¸ŒÊÒÁÑ- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785

SCMA 603 Theory of Ordinary Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .787

Ç·¤³ 607 ¡ÒÃÇÔà¤ÃÒÐËŒàªÔ§¿’§¡ŒªÑ¹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .789

SCMA 607 Functional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791

Ç·¤³ 608 ¾Õª¤³ÔµÊÁÑÂãËÁˆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794

SCMA 608 Modern Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796

Ç·¤³ 630 ¡ÒÃÇԨѴíÒà¹Ô¹¡Òà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .798

SCMA 630 Operations Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800

Ç·¤³ 631 ¡ÒÃÇÔà¤ÃÒÐËŒ¡ÒõѴÊÔ¹ã¨. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .802

SCMA 631 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804

Ç·¤³ 633 ¡Ãкǹ¡ÒÃÊâ·á¤ÊµÔ¡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .806

SCMA 633 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 808

Ç·¤³ 643 ¡ÒÃÇÔà¤ÃÒÐˌ͹ءÃÁàÇÅÒ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .810

SCMA 643 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812

Ç·¤³ 645 Ẻ¨íÒÅͧàªÔ§àʉ¹·ÑèÇä» . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814

SCMA 645 Generalized Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816

Ç·¤³ 673 ÃкºàªÔ§¾ÅÇѵ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .818

SCMA 673 Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 820

Ç·¤³ 688 ¡ÒÃ͹ØÁÒ¹àªÔ§ÊÔµÔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822

SCMA 688 Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824

ix


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 110 Course Title Calculus

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions NS, NR, TT, OT, PO and TD

8. Course Description

Functions, limits, continuity, derivatives of algebraic functions, logarithmic functions, exponential functions,

and trigonometric functions, implicit differentiation, higher-order derivatives, differentials, applications of

differentiation, indeterminate forms and l’ Hospital’s rule, functions of several variables and partial derivatives,

total differentials and total derivatives; antiderivatives and integration, techniques of integration, applications

of integration.

9. Course Objective(s)

After succesful completion of this course, students will be able to

1. describe the essential ideas, concepts and theories of calculus.

2. apply knowledge in calculus to everyday life and related disciplines.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Functions and concept of limits and 4 - - Assigned instructor(s)

continuity

for the semester.

3 Concept of derivatives

Rules for derivatives: focus on

formulas

4–5 Chain rule

Power rule

Implicit differentiation

Higher-order derivatives

Differentials

5–7 Application of derivatives and differentials:

- Approximation

- Rate of change

- Related rates

- Graph sketching

- Relative extrema and absolute extrema

- l’ Hospital’s rule

2 - -

3 - -

5 - -

8 Mid-term Examination -

SCMA 110 (1/2) 1 Calculus


9–10 Function of several variables

- Partial derivatives

- Total differentials and total

derivatives

10–11 Antiderivatives and indefinite integrals

of one-variable functions

- Rules of integration

- Evaluation of antiderivatives using

formulas and technology

12–13 - Integration by parts and by partial

fractions

3 - -

3 - -

4 - -

14 Definite integrals and their properties 2 - -

15 Applications of integration: areas under

curves and areas of regions between

curves

Activity for application of integration

Review

2 - -

16 Final Examination -

11. Teaching Method(s)

Lecture, in-class activities and problem-solving practice.

12. Teaching Media

Transparencies, whiteboards, blackboards, computerized presentations and occasionally distributed sheets.

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by

1. the ability in describing the essential ideas, concepts and theories of calculus.

2. the ability in applying knowledge in calculus to everyday life and related disciplines.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

1 Assignments 10%

2 Mid-term examination 45%

3 Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Anton H, Bivens I, Davis S. Calculus 7th ed. New York: Wiley; 2002.

2. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ͹ؾѹ¸ŒáÅСÒûÃÐÂØ¡µŒ. ¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2545.

3. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ÍÔ¹·Ô¡ÃÑÅáÅСÒûÃÐÂØ¡µŒ.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

16. Instructor(s)

Instructors of department of Mathematics

SCMA 110 (2/2) 2 Calculus


17. Course Coordinator

Dr. Kornkanok Bunwong

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: sckbw@mahidol.ac.th

SCMA 110 (3/2) 3 Calculus


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 113 Course Title Calculus

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions SC, SC-Kan, EN, RT and PT

8. Course Description

Limits, continuity, definition and properties of derivatives, derivatives of algebraic functions, logarithmic

functions, exponential functions, trigonometric functions, inverse trigonometric functions, hyperbolic functions

and inverse hyperbolic functions, implicit differentiation, higher-order derivatives, differentials, applications of

differentiation, indeterminate forms and l’ Hospital’s rule, functions of several variables and partial derivatives,

total differentials and total derivatives, antiderivatives and integration, techniques of integration, improper

integrals, applications of integration, numerical evaluation of derivatives and integrals.

9. Course Objective(s)

This course is designed to introduce the students to the essential ideas of calculus and its applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Concept and the importance of limit

- Left and right limits

- Infinite limits and limits at infinity

- Techniques for finding limits

- Zeno paradox

- Delta-epsilon arguments (optional)

2 - - Assigned instructor(s)

for the semester.

2–4 Continuity

Secant lines and tangent lines

Review of definition of derivatives and

properties

Derivatives of polynomial functions,

logarithmic functions, exponential

functions, trigonometric functions,

inverse trigonometric functions,

hyperbolic functions and inverse

hyperbolic functions

4–5 Chain Rule

Power Rule

Implicit differentiation

Higher-order derivatives

Differential

5 - -

2 - -

SCMA 113 (1/3) 4 Calculus


5–7 Application of derivatives and differentials:

- Approximation

- Rate of change

- Related rates

- Graph sketching

- Relative extrema and absolute extrema

- l’ Hospital’s rule and Newton’s

method

5 - -

8 Mid-term examination -

9–10 Function of several variables

- Partial derivatives

- Total differentials and total

derivatives

10–12 Concept of antiderivatives and indefinite

integrals of one-variable functions

- Rules of integration

- Evaluation of antiderivatives using

formulas

- Introductory substitution method

12–13 - Integration by parts and by partial

fractions

14 Concept and idea of definite integrals

- Properties of definite integrals

- Frequent mistakes in applying substitution

method

3 - -

4 - -

3 - -

2 - -

15

Improper integrals

Applications of integration: areas under

curves and areas of regions between

curves

Review

2 - -

16 Final examination 2 -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

SCMA 113 (2/3) 5 Calculus


13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Anton H, Bivens I, Davis S. Calculus 7th ed. New York: Wiley; 2002.

2. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ͹ؾѹ¸ŒáÅСÒûÃÐÂØ¡µŒ. ¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2545.

3. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ÍÔ¹·Ô¡ÃÑÅáÅСÒûÃÐÂØ¡µŒ.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Pairote Satiracoo

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scpsc@mahidol.ac.th

SCMA 113 (3/3) 6 Calculus


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 115 Course Title Calculus

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions EG

8. Course Description

Limits; continuity; derivatives of algebraic functions, logarithmic functions, exponential functions,

trigonometric functions, inverse trigonometric functions and hyperbolic functions; applications of differentiation;

indeterminate forms, techniques of integration; improper integrals; applications of integration; numerical

evaluation of derivatives and integrals; calculus of real-valued functions of two variables; algebra of vectors in

three-dimensional space; calculus of vector-valued functions and applications; straight lines; planes and surfaces

in three-dimensional space.

9. Course Objective(s)

This course is designed to introduce the students to the essential ideas of calculus and its applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Limits and Continuity

Definition of a Derivative

Finding the derivative from the

definition

3 - - Assigned instructor(s)

for the semester.

2 Rules of Differentiation:

- Power and Sum Rules

- Product and Quotient Rules

The Chain Rule

Derivative of Logarithmic Functions

Derivative of Exponential Functions

3 Derivative of Trigonometric Functions

Derivative of the Inverse Trigonometric

Functions

Derivative of Hyperbolic Functions

Derivative of the Inverse Hyperbolic

Functions

4 Implicit Differentiation

Higher - Order Derivatives

Differentials

Applications of Derivatives

- Related Rates , Rate of Change

3 - -

3 - -

3 - -

SCMA 115 (1/3) 7 Calculus


5 - Sketching the graph of a function

from the derivative

- I’Hospital’s rule

6 Functions of Several Variables

Partial Derivatives

Total Differentials and Total Derivatives

Antiderivatives

Indefinite Integral

- Basic Integration Rules

Definite Integrals

- Properties of the Definite Integrals

Integration by u-Substitution

7 Integration by Trigonometric Substitutions

√ When Integrands Contains:

- a 2 − b 2 u 2


- a 2 + b 2 u 2


- b 2 u 2 − a 2

Integration by Parts

3 - -

3 - -

3 - -

8 Midterm -

9 Integration of Powers of Trigonometric

∫ Functions:

- sin m u cos n

∫ u du

- tan m u sec n

∫ u du

- cot m u csc n u du


Integrals of the form (a + bx) p/q dx

Integration by Partial Fractions

10 Improper integral

Applications of Integration:

- Areas under curves

- Area of a region between two

curves

- Approximate Integration

- Arc Length

11 Vectors in R 2 and R 3

- Rectangular Coordinate System in

Three Dimensions R 3

- Vector Addition

- Scalar Multiplication of a Vector

- Unit Vector

- Angle Between Two Vectors

- Projection of a vector on another

vector

3 - -

3 - -

3 - -

SCMA 115 (2/3) 8 Calculus


12 Products Between Vectors

- Dot Product of two Vectors

- Cross Product of two Vectors

Equation of Lines in R 2 and R 3

Equation of Planes

13 Vector-Valued Functions

- Limits and Continuity

- Differentiation and Integration of

Vector-Valued Functions

- Unit Tangent Vector

14 Unit Normal Vector and Curvature

- Velocity and Acceleration Vectors

- Gradient Vectors

- Divergence and Curl

15 Double Integrals and Applications

Definition of a Double Integral

Iterated Integrals and Area in the

Plane

Use Double Integrals to find Volumes

3 - -

3 - -

3 - -

3 - -

16 Final examination -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Anton H, Bivens I, Davis S. Calculus 7th ed. New York: Wiley; 2002.

2. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ͹ؾѹ¸ŒáÅСÒûÃÐÂØ¡µŒ. ¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2545.

SCMA 115 (3/3) 9 Calculus


3. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ÍÔ¹·Ô¡ÃÑÅáÅСÒûÃÐÂØ¡µŒ.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Pallop Huabsomboon

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scphc@mahidol.ac.th

SCMA 115 (4/3) 10 Calculus


Course Syllabus

1. Program of Study General Education Courses in Faculty of Science

Science for Other Majors

2. Course Code SCMA 116 Course Title Simple Mathematical Concepts and

Applications

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course General education course in science for other majors

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Applications of concepts in numbers and numerals, geometry, logic, number theory and probability.

9. Course Objective(s)

- For students to be able to apply mathematical knowledge learnt in class in problem solving.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 Applications of concepts in numbers

and numerals

- Representing numbers by numerals

and applications

- Magic and games on numbers

- Use of symbols for numbers and

applications in problem solving by

equations

6 - - Assigned instructor(s)

for the semester.

4–6 - Applications of concepts in geometry

- The history of geometry: attempts

to measure the size of earth and

the distances between earth and

sun/moon

- The symbol π

- Similar triangles

- Applications of similar triangles

(field study)

7–9 Logic and logic problems

- Truth tables

- Validity of reasoning and test of

validity by truth tables

- Solving logic problems

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

SCMA 116 (1/3) 11 Simple Mathematical Concepts and Applications


10–12 Applications of concepts in number

theory

- Primes, composites and applications

- Greatest common divisors, least

common multipliers and applications

- Relatively prime numbers and applications

- Congruence and applications

13–15 Applications of concepts in probability

- Probability, random variables and

expected values

- Application of probability in decision

problems

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

- Lecture.

- In-class activities.

- Problem-solving practice.

12. Teaching Media

- Transparencies/whiteboards/blackboards/computerized presentations

- Occasionally distributed sheets

13. Measurement and Evaluation of Student Achievement

Ability to apply mathematical knowledge learnt in class in problem solving.

Grade assignment is carried out according to the faculty and university regulations, using t-score

norm-referenced evaluation method to assign letter grades as follows:

91–100 assign A

81–90 assign B+

71–80 assign B

61–70 assign C+

51–60 assign C

34–50 assign D+

18–33 assign D

0–17 assign F

Ratio of types of assessment:

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

1. Evaluate students’ performance according to the criterion in 12 above.

2. Evaluate students’ satisfactory in course management.

SCMA 116 (2/3) 12 Simple Mathematical Concepts and Applications


15. Reference(s)

1. David M. Burton, The History of Mathematics an Introduction, Wm.C.Brown Publishers.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Lect. Pariwat Pacheenburawana

SCMA 116 (3/3) 13 Simple Mathematical Concepts and Applications


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 117 Course Title Mathematics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions SS

8. Course Description

Basic knowledge in mathematics; practice of computation skills; reasoning; practice of solving problems in

evaluation of limits, continuity, differentiation of logarithmic functions, exponential functions, trigonometric

functions and inverse functions; differentials; applications of derivatives; derivatives of order greater than one;

implicit differentiation; l’Hospital’s rule; integrals; integration by substitution; integration by parts; integration

by partial fractions; partial derivatives; introduction to ordinary differential equations; solving separable

differential equations and linear first order differential equations.

9. Course Objective(s)

This course is designed to introduce the students to the essential ideas of calculus and its applications.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Limits and Continuity 3 - - Assigned instructor(s)

for the semester.

2 Definition of a Derivative

Finding the derivative from the

definition

3 Rules of Differentiation:

- Power and Sum Rules

- Product and Quotient Rules

4 The Chain Rule

Derivative of Logarithmic Functions

Derivative of Exponential Functions

5 Derivative of Trigonometric Functions

Derivative of the Inverse Trigonometric

Functions

Implicit Differentiation

Higher - Order Derivatives

6 Differentials

Applications of Derivatives

- Related Rates , Rate of Change

- Sketching the graph of a function

from the derivative

3 - -

3 - -

3 - -

3 - -

3 - -

SCMA 117 (1/3) 14 Mathematics


7 - I’Hospital’s rule

- Functions of Several Variables, Partial

Derivatives

3 - - Assigned instructor(s)

for the semester.

8 Midterm examination -

9 Antiderivatives

Indefinite Integral

Basic Integration Rules

Integration by u-Substitution

3 - -

3 - -

10 Integration by Trigonometric Substitutions

√ When Integrands Contains:

- a 2 − b 2 u 2

- a 2 + b 2 u 2

- b 2 u 2 − a 2

11 Integration by Parts 3 - -

12 Integration by Partial Fractions 3 - -

13 Improper integral 3 - -

14 Applications of Integration:

- Areas under curves

- Area of a region between two

curves

15 First order ordinary differential equations

- Separation of variables method

- Linear first order differential

equations

3 - -

3 - -

16 Final examination - -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

SCMA 117 (2/3) 15 Mathematics


14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Anton H, Bivens I, Davis S. Calculus 7th ed. New York: Wiley; 2002.

2. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ͹ؾѹ¸ŒáÅСÒûÃÐÂØ¡µŒ. ¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2545.

3. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ÍÔ¹·Ô¡ÃÑÅáÅСÒûÃÐÂØ¡µŒ.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

4. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. Differential equations.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Chontita Rattanakul

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: sccrt@mahidol.ac.th

SCMA 117 (3/3) 16 Mathematics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 136 Course Title Euclidean Geometry

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Properties of geometric figures; parallel lines; geometric constructions; theorems on angles, straight lines,

circles, triangles, quadrilaterals and polygons.

9. Course Objective(s)

To brighten the students’ brain by exploring the basic and challenging problems in plane geometry.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction and historical notes

- High school geometry: a quick review

- Euclidean geometry versus noneuclidean

geometry

3 - - Assigned instructor(s)

for the semester.

2 - The Euclidean tools and their

equivalence to the modern tools

- Concurrency and colinearity

3 - Properties of triangles

- Centroids, orthocenters, circumcircles,

inscribed circles and escribed

circles and their properties

4 - Internal and external division of

line segments

- Harmonic division

- Stewart’s theorem

5 - Menelaus’ theorem and its converse

- Ceva’s theorem and its converse

6 - Ptolemy’s theorem and its converse

- The radii of circumcirles, inscribed

circles and escribed circles

- Heron’s formula

7 - Euler’s theorem

- Euler lines

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 136 (1/2) 17 Euclidean Geometry


8 - Simson lines

- Pedal triangles

3 - - Assigned instructor(s)

for the semester.

9 - The nine-point circles 3 - - Assigned instructor(s)

for the semester.

10 - The nine-point circles and Feuerbach’s

theorem

3 - - Assigned instructor(s)

for the semester.

11 - Archimedes’ theorem 3 - - Assigned instructor(s)

for the semester.

12 - Gergonne points

- Nagel points

3 - - Assigned instructor(s)

for the semester.

13 - Isogonal lines and points 3 - - Assigned instructor(s)

for the semester.

14 - Properties of quadrilaterals and

polygons

3 - - Assigned instructor(s)

for the semester.

15 - Properties of triangles in connection

with parabolas

for the semester.

3 - - Assigned instructor(s)

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A, B + , B, C + , C, D + , D and F.

15. Reference(s)

1. Euclid’s elements

2. Geometry: Ancient and Modern

3. New Plane Geometry.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 136 (2/2) 18 Euclidean Geometry


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 141 Course Title Computer Laboratory

3. Number of Credits 2(0-4) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 1

8. Course Description

Computer applications on any mathematical problems depending on the interest of the students and

instructor.

9. Course Objective(s)

For students to practise the use of computer in solving mathematical problems.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–16 Computer applications on any mathematical

problems depending on

lab.

for the semester.

32 Related computer 32 Assigned instructor(s)

the interest of students and the

instructor.

11. Teaching Method(s)

Students work on given problems using computers.

12. Teaching Media

1. One set of personal computer for each student

13. Measurement and Evaluation of Student Achievement

1. Term project and oral presentation 50%

2. Assignments 20%

3. Final examination 30%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)


16. Instructor(s)


17. Course Coordinator


SCMA 141 (1/1) 19 Computer Laboratory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 145 Course Title Data Processing

3. Number of Credits 3(2-2) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Computer systems; data structure; number and data representation; steps of program development; system

flow chart; computer languages; compilation.

9. Course Objective(s)

For students to have knowledge on concepts of data processing.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

2 - Computer systems 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

3 - Computer systems 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

4 - Data structure 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

5 - Data structure 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

6 - Number and data representation 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

7 - Number and data representation 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

8 - Steps of program development 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

9 - Steps of program development 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

10 - System flow chart 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

11 - System flow chart 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

12 - Computer languages 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

SCMA 145 (1/2) 20 Data Processing


13 - Computer languages 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

14 - Compilation 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

15 - Compilation 2 Corresponding lab 2 Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. One set of personal computer for each student

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Term project 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 145 (2/2) 21 Data Processing


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 160 Course Title Ordinary Differential Equations

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

Second semester/2007

7. Course Conditions RT

8. Course Description

Complex variables; introduction to ordinary differential equations; linear first order differential equation;

nonlinear first order differential equations; applications of first order equations; linear second order equations;

applications of second order equations; high order linear equations.

9. Course Objective(s)

The objective of this course is to teach the students to understand the basic concepts, theory, methods and

applications of ordinary differential equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Differential equations

- Classification of differential equations

- Solutions of differential equations

- Initial value problems, boundary

value problems

- Existence of solutions

2 - - Assigned instructor(s)

for the semester.

2–6 First order differential equations

- Separable differential equations

- Exact differential equations

- Integrating factors

- Linear differential equations

- Bernoulli equations

- Homogeneous equations

7 Applications of first order differential

equations

12 - -

2 - -

8 Midterm examination -

SCMA 160 (1/2) 22 Ordinary Differential Equations


9-14 Higher order differential equations

- Basic theory of linear differential

equations

- Linear differential equations

- Solutions of homogeneous linear

differential equations with constant

coefficients

- The method of undetermined coefficients

- Variation of parameters

- The Cauchy-Euler equation

12 - -

15 Applications of higher order equations 2 - -

16 Final examination -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Ross RL. Introduction to ordinary differential equations. 4th ed. New York: Wiley; 1989.

2. Boyce WE. Elementary Differential Equations and Boundary Value Problem. 8th ed. New York: Wiley;

2006.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Dr. Meechoke Chuedoung

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scmcd@mahidol.ac.th

SCMA 160 (2/2) 23 Ordinary Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 161 Course Title Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions SI, RA, BM, PI, DT, PY, VS

8. Course Description

Probability; random variables and probability distributions; mathematical expectation; Binomial, Poisson,

Chi-square, T and F probability distributions; sampling distributions; point estimation; interval estimation;

hypothesis test.

9. Course Objective(s)

The objective of this course is to provide a comprehensive course of calculus and to teach the students to

understand the basic concepts, theory, methods and applications of systems of ordinary differential equations,

with adequate practice through problem solving with the aid of computer softwares.

10. Course Outline

Week

Topic

Lecture/Seminar Hours Lab Hours

Instructor

1 Review of differential calculus

Chain rule and derivatives of inverse

2 Introduction 2 Assigned instructor(s)

for the semester.

functions

2 Derivatives of trigonometric, inverse

2 Software introduction 2

trigonometric, exponential and logarithmic

functions

Implicit differentiation and related

rates

3 Applications of derivatives

2 Software introduction 2

l’ Hospital’s rule of type 0 0

Other applications

4 Review of integral calculus

2 Tutorial problems 2

Definite and indefinite integrals

Fundamental Theorems of Calculus

5 Techniques of integrations

2 Tutorial problems 2

Example of an improper integral: a

prelude for lab

6 Techniques of integrations

2 Tutorial problems 2

Applications of antiderivatives

7 Applications of antiderivatives 2 Tutorial problems 2

8 Mid-term examination -

SCMA 161 (1/2) 24 Statistics


9 Introduction to differential equations

and systems of ordinary differential

equations

Systems of ordinary differential equations

of two variables

10 Solutions for special cases by separation

of variables

Direction fields

11 Phase portraits

Stationary solutions

Matrix representation

12–13 Solutions to systems of linear ordinary

differential equations by eigenvalue

method

Linear independence and Wronskian

14–15 Applications and case analysis of

solutions

2 Tutorial problems

Self-investigation

2 Tutorial problems

Self-investigation

2 Tutorial problems

Self-investigation

4 Seminar on application

of calculus

and differential

equations

4 Seminar on application

of calculus

and differential

equations

2

2

2

4

4

16 Final examination -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Neuhauser C. Calculus for biology and medicine. 2th ed. Upper Saddle River, N.J.: Prentice Hall;2004.

2. Zill DG, Cullen MR. Differential equations. 6th ed. Thomson; 2005.

3. Stewart J. Calculus, 5th edition, Thomson; 2003

SCMA 161 (2/2) 25 Statistics


16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Asst. Prof. Dr. Chaiwat Maneesawarng

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: tecmn@mahidol.ac.th

SCMA 161 (3/2) 26 Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

3. Number of Credits 3(3-0) (Lecture-Lab)

2. Course Code SCMA 162 Course Title Calculus and Introduction to Ordinary

Differential Equations

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions MT, PH

8. Course Description

Review of limits and continuity; derivatives; applications of derivatives; integration; techniques of integration;

applications of integration; linear first order differential equations; nonlinear first order differential equations:

separation of variables, exactness and substitution; applications of first order equations; linear second order

equations; applications of second order equations.

9. Course Objective(s)

The objective of this course is to introduce the students to the essential ideas of calculus and its applications

as well as basic concepts, theory, methods and applications of ordinary differential equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Review of limits and continuity 2 - - Assigned instructor(s)

for the semester.

1–2 Derivatives: definition and direct

evaluation

Interpretation of derivatives: rate of

change, slope, speed

Rules of differentiation: power, sum,

product and quotient rules

2–3 Chain rule and derivatives of inverse

functions

Derivatives of trigonometric, inverse

trigonometric, exponential and logarithmic

functions

3 - -

3 - -

SCMA 162 (1/3) Calculus 27 and Introduction to Ordinary Differential Equations


3–6 Applications of derivatives related to

students’ discipline

- Implicit differentiation and related

rates

- Differentials

- Sketching the graph of a function

from the derivative

Functions of several variables

- Partial derivatives

- Total differentials and total

derivatives

7 Antiderivatives

Definite and indefinite integrals

Fundamental Theorems of Calculus

Basic integration rules

9 - -

4 - -

8 Mid-term Examination -

9–10 Techniques of integrations: substitution

and integration by parts

10–11 Applications of integration related to

students’ discipline

12–13 Differential equations

- Classification of differential equations

- Solutions of differential equations

- Initial value problems, boundary

value problems

First order equations:

- Existence and uniqueness of solutions

- Methods: separation of variables,

linear equations and change of

variables

14 - Methods: exact equations and integrating

factors

15 - Applications of first order equations

related to students’ discipline

4 - -

5 - -

6 - -

3 - -

3 - -

16 Final examination -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

SCMA 162 (2/3) Calculus 28 and Introduction to Ordinary Differential Equations


3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ͹ؾѹ¸ŒáÅСÒûÃÐÂØ¡µŒ. ¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2545.

2. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. ÍÔ¹·Ô¡ÃÑÅáÅСÒûÃÐÂØ¡µŒ.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

3. ÃÈ.´Ã.¨Ô¹´Ò ÍÒ¨ÃÔÂСØÅ. Differential equations.¡Ãا෾: ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ ¤³ÐÇÔ·ÂÒÈÒʵÌ ÁËÒÇÔ·ÂÒÅÑÂ

ÁËÔ´Å; 2544.

4. Anton H, Bivens I, Davis S. Calculus 7th ed. New York: Wiley; 2002.

5. Ross RL. Introduction to ordinary differential equations. 4th ed. New York: Wiley; 1989.

6. Boyce WE. Elementary Differential Equations and Boundary Value Problem. 8th ed. New York: Wiley;

2006.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Pairote Satiracoo

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scpsc@mahidol.ac.th

SCMA 162 (3/3) Calculus 29 and Introduction to Ordinary Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 163 Course Title Ordinary Differential Equations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

Second semester/2007

7. Course Conditions SC, SC-Kan, EN, EG

8. Course Description

Complex variables; introduction to ordinary differential equations; linear first order differential equations;

nonlinear first order differential equations; applications of first order equations; second order linear equations;

applications of second order equations; high order linear equations; systems of linear equations; matrices;

determinants; vector spaces; linear transformations; solving linear algebraic problems by numerical methods;

applications in science and engineering.

9. Course Objective(s)

The objective of this course is to teach the students to understand the basic concepts, theory, methods and

applications of single ordinary differential equations. Furthermore, the students should know how to solve and

apply the system of linear differential equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Differential equations

- Classification of differential equations

- Solutions of differential equations

- Initial value problem, boundary

value problem

- Existence of solutions

3 - - Assigned instructor(s)

for the semester.

2–4 First order differential equations

- Separable differential equations

- Exact differential equations

- Integrating factors

- Linear differential equations

- Bernoulli equations

- Homogeneous equations

- Differential equations with linear

coefficients in 2 variables

- Substitution methods

5 Applications of first order differential

equations

9 - -

3 - -

SCMA 163 (1/3) 30 Ordinary Differential Equations


6–7 Higher order differential equations

- Basic theory of linear differential

equations

- Linear differential equations

- Solutions of homogeneous linear

differential equations with constant

coefficients

6 - -

8 Midterm examination -

9–10 Higher order differential equations

- The method of undetermined coefficients

- Variation of parameters

- Cauchy-Euler equations

- Differential operators

10 Applications of higher order differential

equations

11 Linear algebra

System of linear differential equations

- Homogeneous linear system and

Nonhomogeneous linear system

- Consistent solutions and inconsistent

solutions

- Row-reduced echelon form

- Linearly independent and linearly

dependent of vectors

12–13 Vector spaces

- Properties of vector space

- n dimensional Euclidean space

- Subspace

- Basis and dimension

- Orthogonal basis and Orthonormal

basis

- Gram-Schmidt process

13-15 Linear transformations

- Matrices and linear transformations

- Algebra of linear transformations

- Rank and nullity of linear transformations

- Null space of linear transformations

- Important theory of linear

transformations

4 - -

2 - -

3 - -

5 - -

6 - -

15 Eigenvalues and Eigenvectors 1 - -

SCMA 163 (2/3) 31 Ordinary Differential Equations


16 Final examination -

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Ross RL. Introduction to ordinary differential equations. 4th ed. New York: Wiley; 1989.

2. Boyce WE. Elementary Differential Equations and Boundary Value Problem. 8th ed. New York: Wiley;

2006.

3. Anton H. Elementary linear algebra 9th ed. N.J.: Wiley; 2005.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Somsak Orankitjaroen

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scsok@mahidol.ac.th

SCMA 163 (3/3) 32 Ordinary Differential Equations


Course Syllabus

1. Program of Study General Education Courses in Faculty of Science

Science for Other Majors

2. Course Code SCMA 170 Course Title Applicable Basic Mathematics and

3. Number of Credits 2(2-0) (Lecture-Lab)

Statistics

4. Prerequisite None

5. Type of Course General education course in science for other majors

6. Session/Academic Year

Second semester/2007

7. Course Conditions 0

8. Course Description

Mathematical and statistical concepts, skills and techniques applicable in everyday life: systems of linear

equations, matrices, linear programming, sets and counting priciples, probability and decision.

9. Course Objective(s)

To enable students to have quantitative concepts, skills and techniques applicable in everyday life. This

course covers both theory and applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Straight lines and linear functions

- Coordinates plane and linear functions

- Simple mathematical models by

linear functions and applications

3 - - Assigned instructor(s)

for the semester

2–4 Systems of linear equations and matrices

- Matrix operations

- Solving systems of linear equations

and applications

4–6 Linear programming

- Linear inequalities of two variables

and applications

- Linear programming and applications

6–8 Sets and counting principles

- Fundamental concepts and definitions

- Sum and product principles and

applications

9 Probability

- Sample spaces and events

- Definition and properties of probability

- Forms of probability

4 - -

4 - -

5 - -

2 - -

SCMA 170 (1/3) 33 Applicable Basic Mathematics and Statistics


10 - Laws of probability

- Baye’s law

11 Decision

- Meaning and techniques used for

decision

- Mathematical expectation and decision

- Return table

12 - Decision under certain situation

- Decision under risky situation

2 - -

2 - -

2 - -

13 - Decision under uncertain situation 2 - -

14 - Decision under competitive

situation

2 - -

15 - Decision trees 2 - -

11. Teaching Method(s)

- Lecture.

- In-class activities.

- Problem-solving practice.

12. Teaching Media

- Transparencies/whiteboards/blackboards/computerized presentations

- Occasionally distributed sheets

13. Measurement and Evaluation of Student Achievement

Knowledge in concepts and ability to apply quantitative techniques.

Grade assignment is carried out according to the faculty and university regulations, using t-score

norm-referenced evaluation method to assign letter grades as follows:

91–100 assign A

81–90 assign B+

71–80 assign B

61–70 assign C+

51–60 assign C

34–50 assign D+

18–33 assign D

0–17 assign F

Ratio of types of assessment:

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

1. Evaluate students’ performance according to the criterion in 12 above.

2. Evaluate students’ satisfactory in course management.

SCMA 170 (2/3) 34 Applicable Basic Mathematics and Statistics


15. Reference(s)

1. Ernest Haeussler et. al., Introductory Mathematical Analysis for Business, Economics and the Life and

social Sciences.

2. Soo T. Tan, Finite Mathematics for the Managerial, Life and Social Sciences.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Lect. Thitikom Puapansawas

SCMA 170 (3/3) 35 Applicable Basic Mathematics and Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 180 Course Title Introduction to Statistics

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions SC, SC-Kan

8. Course Description

Probability; random variables and probability distributions; mathematical expectation; special probability

distributions; descriptive statistics; sampling distributions; point estimation; interval estimation; hypothesis

testing; elementary use of statistical software.

9. Course Objective(s)

After taking this course the students

1. have knowledge about and understand elementary statistics,

2. can apply the knowledge in statistics to related disciplines,

3. have basic knowledge for advanced study in statistics.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

1–2 Chapter 1 Probability

4 -

- Section 1 Problems leading to the

study of statistics

- Section 2 Sample spaces and events

- Topic 1 Sample spaces

- Topic 2 Events

- Section 3 Probability

- Topic 1 Definition

- Topic 2 Axioms

- Topic 3 Theory of probability of

events

- Section 4 Conditional probability

- Section 5 Product law of probability

- Section 6 Independent events

- Section 7 Baye’s theorem

- Topic 1 Sum law of probability

- Topic 2 Baye’s theorem

Instructor

SCMA 180 (1/6) 36 Introduction to Statistics


3 Chapter 2 Random variables and

probability distributions

- Section 1 Random variables

- Topic 1 Discrete random variables

- Topic 2 Continuous random variables

- Section 2 Probability distributions

- Topic 1 Discrete probability distributions

- Topic 2 Continuous probability

distributions

- Section 3 Discrete and continuous

cumulative probability distributions

- Topic 1 Discrete cumulative

probability distributions

- Topic 2 Continuous cumulative

probability distributions

4 Chapter 3 Mathematical expectation

- Section 1 Expected values of random

variables

- Topic 1 Definition

- Topic 2 Properties of expected

values

- Section 2 Expected values of functions

of random variables

- Section 3 Variances of random variables

- Topic 1 Definition

- Topic 2 Properties

- Section 4 Standard deviations of

random variables

- Topic 1 Definition

- Topic 2 Properties

2 -

2 -

SCMA 180 (2/6) 37 Introduction to Statistics


5–6 Chapter 4 Special probability distributions

- Section 1 Binomial distributions

- Topic 1 Binomial experiments

- Topic 2 Definition of binomial

distributions

- Topic 3 Expected values

- Topic 4 Variances

- Section 2 Hyper-geometric distributions

- Topic 1 Definition of hypergeometric

distributions

- Topic 2 Expected values

- Topic 3 Variances

- Section 3 Poisson distributions

- Topic 1 Definition of Poisson distributions

- Topic 2 Expected values

- Topic 3 Variances

- Section 4 Normal distributions

- Topic 1 Definition of normal distributions

- Topic 2 Expected values

- Topic 3 Variances

6–7 Chapter 5 Descriptive statistics

- Section 1 Measures of center:

means, medians and modes

- Section 2 Measures of variability:

Ranges, variances, and standard

deviations

- Section 3 Measures of relative

standing: z-scores, percentiles,

quartiles

- Section 4 Some selected graph presentation:

dot plot, box plot, stemand-leaf

plot, etc.

- Section 5 Statistical software and

demonstration

3 -

3 -

8 Midterm examination -

SCMA 180 (3/6) 38 Introduction to Statistics


9–10 Chapter 6 Sampling distributions

- Section 1 Populations and samples

- Section 2 Sampling methods

- Topic 1 Simple random sampling

- Topic 2 Systematic sampling

- Topic 3 ¡ÒêѡµÑÇ͈ҧẺẈ§

໓¹ªÑé¹

- Topic 4 ¡ÒêѡµÑÇ͈ҧẺà¡ÒÐ

¡Å؈Á

- Section 3 Sample mean distributions

- Topic 1 One population

- Topic 2 Two populations

- Section 4 Central limit theorem

- Section 5 Proportion distribution

- Topic 1 One population

- Topic 2 Two populations

- Section 6 T distributions

- Topic 1 T distribution form

- Topic 2 T distribution table usage

- Section 7 Chi-square distributions

- Topic 1 Chi-square distribution

form

- Topic 2 Chi-square distribution

table usage

- Section 8 F distributions

- Topic 1 F distribution form

- Topic 2 F distribution table

usage

4 -

SCMA 180 (4/6) 39 Introduction to Statistics


11–12 Chapter 7 Estimation

- Section 1 Estimation of means

- Topic 1 Point estimation

- Topic 2 Interval estimation

- Topic 3 Sample size determination

- Section 2 Estimation of mean differences

- Topic 1 Point estimation

- Topic 2 Interval estimation

- Section 3 Estimation of proportions

- Topic 1 Point estimation

- Topic 2 Interval estimation

- Topic 3 Sample size determination

- Section 4 Estimation of proportion

differences

- Topic 1 Point estimation

- Topic 2 Interval estimation

- Section 5 Estimation of variances

- Topic 1 Point estimation

- Topic 2 Interval estimation

- Section 6 Estimation of variance

ratios

- Topic 1 Point estimation

- Topic 2 Interval estimation

13-15 Chapter 8 Tests of hypotheses

- Section 1 Concepts and definitions

- Topic 1 Hypotheses for testing

- Topic 2 Errors of test of hypotheses

- Topic 3 p-values of tests

- Topic 4 Steps of hypothesis testing

- Section 2 Test of means

- Section 3 Test of mean differences

- Section 4 Test of proportions

- Section 5 Test of proportion differences

- Section 6 Test of variances

- Section 7 Test of variance ratios

4 -

6 -

16 Final examination -

SCMA 180 (5/6) 40 Introduction to Statistics


11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software, rally-type activities, group

working, problem-based learning, computer-aided instructions

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Weiss NA. Introductory statistics. 4th ed. Addison-Wesley; 1995.

2. Johnson RA. Statistics: principles and methods. 3rd. ed. John Wiley & Sons; 1992.

3. Hogg RV. Probability and statistical inference. 5th ed. Prentice=Hall; 1997.

4. Mendenhall W. Probability and statistics. 11th ed. Brooks/Cole; 2003.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Assoc. Prof. Taweeratana Siwadune

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: sctsw@mahidol.ac.th

SCMA 180 (6/6) 41 Introduction to Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 181 Course Title Statistics for Medical Science

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 0

8. Course Description

Concepts and applications of probability and probability distributions in various events; interpretation

of statistical values; descriptive statistics; sampling for good representatives of populations and its use in

estimation and hypothesis testing; presentation of article or published research depending on groups of students

by statistical methods.

9. Course Objective(s)

After taking this course the students

1. have knowledge about and understand elementary statistics,

2. can apply the knowledge in statistics to everyday life and related disciplines,

3. can use basic statistical softwares.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Probability of everyday events

Problems leading to the study of

statistics

Sample spaces and events

Applications of theory of probability

of events and applications of Baye’s

Theorem

3 - - Assigned instructor(s)

for the semester.

2–4 Concepts and applications of random

variables and probability

distributions

4.5 - -

4–6 Special probability distributions 3.5 - -

6–7 Data description by statistical values 2.5 - -

8 Midterm examination -

9–12 Concepts and methods for finding

population values by sampling

method

12–15 Test of hypothesis as an aid for decision

in real events

7 - -

7.5 - -

SCMA 181 (1/3) 42 Statistics for Medical Science


16 Presentation of articles or research in 2 - -

statistics depending on groups of

students.

11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software

12. Teaching Media

1. Distributed sheets

2. Statistical software

13. Measurement and Evaluation of Student Achievement

1. knowledge about elementary statistics.

2. Ability to apply the knowledge in statistics to everyday life and related disciplines.

3. Ability to use basic statistical softwares.

Grade assignment is carried out according to the faculty and university regulations, using t-score

norm-referenced evaluation method to assign letter grades as follows:

91–100 assign A

81–90 assign B+

71–80 assign B

61–70 assign C+

51–60 assign C

34–50 assign D+

18–33 assign D

0–17 assign F

Ratio of types of assessment:

1. Midterm Examination 45%

2. Final Examination 45%

3. Assigned work 10%

14. Course Evaluation

1. Evaluate students’ performance according to the criterion in 12 above.

2. Evaluate students’ satisfactory in course management.

15. Reference(s)

1. Neil A. Weiss, Introductory Statistics, 4th (1995), Addison-Wesley

2. Richard A. Johnson, Statistics: Principles and Methods, 3rd edition (1992), John wiley & Sons.

3. Robert V. Hogg, Probability and Statistical Inference, 5th edition (1997), Prentice-Hall.

4. William Mendenhall, Probability and Statistics, 11th edition (2003), Brooks/cole.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Asst. Prof. Jirakul Sujaritkul

SCMA 181 (2/3) 43 Statistics for Medical Science


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 182 Course Title Statistics for Health Sciences

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course

6. Session/Academic Year

First and second semesters/2007

7. Course Conditions 0

8. Course Description

Concepts and applications of probability and probability distributions in various events; interpretation

of statistical values; descriptive statistics; sampling for good representatives of populations and its use in

estimation and hypothesis testing.

9. Course Objective(s)

After taking this course the students

1. have knowledge about and understand elementary statistics,

2. can apply the knowledge in statistics to everyday life and related disciplines,

3. can use basic statistical softwares.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Probability of everyday events

Problems leading to the study of

statistics

Sample spaces and events

Applications of theory of probability

of events and applications of Baye’s

Theorem

3 - - Assigned instructor(s)

for the semester.

2–4 Concepts and applications of random

variables and probability

distributions

4.5 - -

4–6 Special probability distributions 3.5 - -

6–7 Data description by statistical values 2.5 - -

8 Midterm examination -

9–12 Concepts and methods for finding

population values by sampling

method

12–15 Test of hypothesis as an aid for decision

in real events

16 Presentation of articles or research in

statistics depending on groups of

students.

7 - -

7.5 - -

2 - -

SCMA 182 (1/2) 44 Statistics for Health Sciences


11. Teaching Method(s)

Lecture, discussion and problem solving with the aid of computer software

12. Teaching Media

1. Distributed sheets

2. Statistical software

13. Measurement and Evaluation of Student Achievement

1. Mid-term examination 45%

2. Final examination 45%

3. Assigned work 10%

14. Course Evaluation

Students performance is graded assigning letter grades of A, B + , B, C + , C, D + , D and F.

15. Reference(s)

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Instructors of department of Mathematics

SCMA 182 (2/2) 45 Statistics for Health Sciences


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 183 Course Title Introduction to Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Probability; random variables and probability distributions; some important probability distributions;

sampling distributions; estimation of parameters; statistical hypothesis test.

9. Course Objective(s)

1. à¾×èÍãˉ¹Ñ¡ÈÖ¡ÉÒä´‰àÃÕ¹ÃÙ‰Ö§·ÄÉ®ÕáÅÐÇÔ¸Õ¡Ò÷ҧÊÔµÔàº×éͧµ‰¹ ·Õè㪉㹡ÒÃÇÔà¤ÃÒÐËŒ¢‰ÍÁÙÅ áÅÐÊÒÁÒùíÒä»»ÃÐÂØ¡µŒãª‰

ä´‰

2. à¾×èÍ໓¹¾×鹤ÇÒÁÃى㹡ÒÃàÃÕ¹ÇÔªÒÊÔµÔ¢Ñé¹ÊÙ§

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Probability of event , Rules of

Probability

- Conditional probability , Independent

events , Bayes’ Rule

3 - - Assigned instructor(s)

for the semester.

2–3 - Random variable , Probability distribution

- Cumulative probability distribution

, Joint distribution

- Marginal distribution , Conditional

distribution , Independence

-

4–5 - Expected value , Moment of random

variable

- Variance

- Chebyshev ’ Inequality

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

SCMA 183 (1/3) 46 Introduction to Statistics


6–7 - (discrete) Uniform distribution ,

Bernoulli distribution

6 - - Assigned instructor(s)

for the semester.

- Binomial distribution , Hypergeometric

distribution

- Poisson distribution , Negative Binomial

distribution

- Geometric distribution , (continuous)

Uniform distribution

- Normal distribution , Exponential

distribution

- Chi-square distribution , t distribution

, F distribution

8 Mid-term examination 3 - - Assigned instructor(s)

for the semester.

9–10 - Population and sample , Sampling

distribution

6 - - Assigned instructor(s)

for the semester.

- Sampling distribution of x, Sampling

distribution of ̂p

- Sampling distribution of (n−1)s2

σ 2 ,

Sampling distribution of x 1 − x 2

- Sampling distribution of ̂p 1 − ̂p 2 ,

Sampling distribution of s2 1 /σ2 1

s 2 2 /σ2 2

11–12 - Estimation Estimator and Its properties

6 - - Assigned instructor(s)

for the semester.

- Methods to finding estimator Interval

Estimation

- Confidence interval of µ, Confidence

interval of p

- Confidence interval of σ 2 , Confidence

interval of µ 1 − µ 2

- Confidence interval of p 1 − p 2 , Confidence

interval of σ1/σ 2 2

2

- Sample size for Estimation

13–15 - Hypothesis Testing

- Type 1 Error and Type 2 Error

9 - - Assigned instructor(s)

for the semester.

- General steps of Hypothesis Testing

- Testing of µ, Testing of p

- Testing of σ 2

- Testing of µ 1 − µ 2 , Testing of p 1 −

p 2

- Testing of σ 2 1/σ 2 2

- P-value of the test

SCMA 183 (2/3) 47 Introduction to Statistics


16 Review 3 - - Assigned instructor(s)

11. Teaching Method(s)

Lecture and participation

12. Teaching Media

Lecture note and power-point

13. Measurement and Evaluation of Student Achievement

1. Mid-term Exam 30%

2. Pop Quiz 15%

3. Homework 15%

4. Final Exam 40%

14. Course Evaluation

There are 8 grades : A, B + , B, C + , C, D + , D áÅÐ F ( using t - score )

15. Reference(s)

for the semester.

1. Richard A. Johnson, Statistics: Principles and Methods, 3rd edition (1992), John wiley & Sons.

2. Robert V. Hogg, Probability and Statistical Inference, 5th edition (1997), Prentice-Hall.

3. William Mendenhall, Probability and Statistics, 11th edition (2003), Brooks/cole.

16. Instructor(s)

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

17. Course Coordinator

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

SCMA 183 (3/3) 48 Introduction to Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 203 Course Title Probability Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 213 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 380:

Probability spaces; random variables; probability distributions; special distributions; law of large numbers;

limiting distributions.

9. Course Objective(s)

At the completion of this course students should be able to

1. have a knowledge and understand probability theory

2. explain probability theory

3. solve problems of probability theory

4. apply probability theory to solve some real problems

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 -Probability spaces

8 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

3–4 Random variables

- Rigorous discussion on challenging

problems and selected topics for

independent study

5–7 Probability distributions

- Rigorous discussion on challenging

problems and selected topics for

independent study

8–11 Special distributions

- Rigorous discussion on challenging

problems and selected topics for

independent study

14–15 Limiting distributions

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

16 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

SCMA 203 (1/2) 49 Probability Theory (Distinction)


11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out.

13. Measurement and Evaluation of Student Achievement

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

15. Reference(s)

1. Cramer H. (1955). The Elements of Probability Theory and Some of Its Applications, John Wiley and

Sons, Inc., New York.

2. Feller, W. (1957). An Introduction to Probability Theory and Its Applications, 2nd edition, John Wiley

and Sons, Inc., New York.

3. Parzen, E. (1960). Modern Probability and Its Applications, John Wiley and Sons, Inc., New York.

4. Ross, S. (1976). A First Course in Probability, Macmillian Publishing Co., Inc., New York.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 203 (2/2) 50 Probability Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 204 Course Title Experimental Design (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 382:

Basic principles of experimental design; colmpletely randomized design; randomized block design; Latin square

design; factorial experiments; confounding; split-plot experiment.

9. Course Objective(s)

At the completion of this course students should be able to

1. have a knowledge and understand experimental design

2. design experiment and explain the experiment

3. analyze data and write a mathematical model and interprete the result from each experiment

4. use experimental design and apply to real problem.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Basic principles of experimental design

for the semester.

8 - - Assigned instructor(s)

- Rigorous discussion on challenging

problems and selected topics for

independent study

3–4 Completely randomized design

- Rigorous discussion on challenging

problems and selected topics for

independent study

5–6 Randomized block design

- Rigorous discussion on challenging

problems and selected topics for

independent study

7–8 Latin square design

- Rigorous discussion on challenging

problems and selected topics for

independent study

9–11 Factorial experiments

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

16 - - Assigned instructor(s)

for the semester.

SCMA 204 (1/2) 51 Experimental Design (Distinction)


12–13 Confounding

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

14–15 Split-plot experiment

- Rigorous discussion on challenging

problems and selected topics for

independent study

11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out.

13. Measurement and Evaluation of Student Achievement

8 - - Assigned instructor(s)

for the semester.

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

15. Reference(s)

1. ¨ÃÑ- ¨Ñ¹·ÅÑ¡¢³Ò (2523) ÊÔµÔÇÔ¸ÕÇÔà¤ÃÒÐËŒáÅÐÇҧἹ§Ò¹ÇԨѠÊíҹѡ¾ÔÁ¾Œä·ÂÇѲ¹Ò¾Ò¹Ôª ¡Ãا෾ÁËÒ¹¤Ã

2. ÊØþŠÍØ»´ÔÊÊ¡ØÅ (2536) ÊÔµÔ¡ÒÃÇҧἹ¡Ò÷´Åͧ àňÁ 1 ÊËÁÔµÃÍÍ¿à«· ¡Ãا෾ÁËÒ¹¤Ã

3. Box, G.E.P.; Hunter, W.G. and Hunter, J.S. (1978). Statistics for experiments: An Introduction to design,

data analysis, and model building. John Wiley and Sons, Inc., New York.

4. Cochran, W.G. and Cox, G.M. (1957). Experimental designs. 2nd edition, John Wiley and Sons, Inc.,

New York.

5. Cox, D.R.(1958). Planning of Experiments. John Wiley and Sons, Inc., New York.

6. John, P.W.M. (1971). Statistical design and analysis of experiments. Macmillan Company, New York.

7. Kempthorne, O. (1983). Design and analysis of experiments. Robert E. Krieger Publishing Company,

Florida.

8. Montgomery, D.C. (1991). Design and analysis of experiments. 3rd edition, John Wiley and Sons, Inc.,

New York.

9. Snedecor, G.W. and Cochran, W.G. (1967). Statistical Methods. 6th edition, the Iowa State University

Press, Iowa.

10. Steel, R.G.D. and Torrie, J.H. (1960). Principles and procedures of statistics. McGraw-Hill Book Co.,

Inc., New York.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 204 (2/2) 52 Experimental Design (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 205 Course Title Multivariate Analysis (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 283 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 484:

Multivariate normal distribution; multiple and partial correlation; Wishart distribution; Hotelling’s T

distribution; multivariate analysis of variance; discriminant analysis; factor analysis.

9. Course Objective(s)

à¾×èÍãˉ¹Ñ¡ÈÖ¡ÉÒÁÕ¤ÇÒÁÃÙ‰áÅФÇÒÁࢉÒã¨à¡ÕèÂǡѺ¡ÒÃÇÔà¤ÃÒÐËŒ¢‰ÍÁÙÅ·ÕèÁÕËÅÒµÑÇá»Ã áÅÐÊÒÁÒùíÒ¤ÇÒÁÃى任ÃÐÂØ¡µŒãª‰

¡Ñº»’-ËÒ¨Ãԧ䴉

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Aspects of Multivariate Analysis

- The organization of Data

- Matrix and Vector Algebra

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

2

- Random Vectors and Matrices

- Mean Vectors and covariance Matrices

-

- Matrix Inequalities and Maximization

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

SCMA 205 (1/4) 53 Multivariate Analysis (Distinction)


3–4 - Random Samples

- Expected Values of the sample

mean and covariance matrix

-

- Generalized Variance

- Sample values of Linear combinations

- Rigorous discussion on challenging

problems and selected topics for

independent study

5–7 - Multivariate Normal Density and

its properties

- sampling from a Multivariate Normal

Distribution

- Maximum Likelihood Estimation

- Sampling distribution of x and S

- Large-sample behavior of x and S

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

8 Mid-Term Examination 4 - - Assigned instructor(s)

for the semester.

9–10 - Inference about a mean vector

- Hotelling ’ s T 2 and Likelihood Ratio

Tests

- Confidence interval and simultaneous

comparisons of mean

- Large-sample Inferences 0f mean

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–13 - Paired Comparisons áÅÐ Repeated

Measures Design

- Comparing Mean Vectors from two

populations

- One-Way MANOVA

- Simulatneous Confidence Intervals

ÊíÒËÃѺ treatment effects

- Two-Way MANOVA

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

SCMA 205 (2/4) 54 Multivariate Analysis (Distinction)


14–15 - Separation and Classification for

two populations

- Classification with two multivariate

normal populations

- Evaluating classification functions

- Fisher ’ s Discriminant Function

- Classification with several populations

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

16 Present Report 4 - - Assigned instructor(s)

11. Teaching Method(s)

Lecture and participation

12. Teaching Media

Lecture note and power-point

13. Measurement and Evaluation of Student Achievement

1. Mid-term Exam 30%

2. Pop Quiz 10%

3. Homework 15%

4. Report 15%

5. Final Exam 30%

14. Course Evaluation

There are 8 grades : A, B + , B, C + , C, D + , D áÅÐ F ( using t - score )

15. Reference(s)

for the semester.

1. Richard A. Johnson , Applied Multivariate Statistical Analysis , 4th edition (1998) , Prentice-Hall

2. Donald F. Morrison , Multivariate Statistical Methods , 3rd edition (1990) , McGraw-Hill

3. T.W. Anderson , An introduction to Multivariate Statistical Analysis , 3rd edition (2003 ) , John Wiley &

Sons.

16. Instructor(s)

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

17. Course Coordinator

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

SCMA 205 (3/4) 55 Multivariate Analysis (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 209 Course Title Theory of Computation (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 449:

Formal language; finite automata; nondeterminism; pushdown automata; Turing machines; post machines;

Minsky’s Theorem; limits of language acceptence; universal Turing machines; unsolvable problems;

computability; recursive function theory.

9. Course Objective(s)

The objective of this course is to familiarize students with foundations and basic principles of abstract

models of computers.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Mathematical notation and Techniques

- Basic mathematical definitions

- Mathematical induction and recursive

definitions

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

2–5 Regular languages and finite automata

- Regular expressions and regular

languages

- Finite automata

- Nondeterminism

- Kleen’s theorem

- Minimal finite automata

- Regular languages and nonregular

languages

- Rigorous discussion on challenging

problems and selected topics for

independent study

16 - - Assigned instructor(s)

for the semester.

SCMA 209 (1/3) 56 Theory of Computation (Distinction)


6–10 Context-free languages and Pushdown

automata

- Context-free languages

- Derivation trees and ambiguity

- Simplified forms and normal forms

- Pushdown automata

- The equivalence of CFGs and

PDAs

- Parsing

- CFLs and Non-CFLs

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–16 Turing machines, their languages, and

computation

- Variation of Turing machines

- Recursively enumerable languages

- More general grammars

- Unsolvable decision problems

- Computability: Primitive recursive

functions

- Computability: µ-Recursive functions

- Rigorous discussion on challenging

problems and selected topics for

independent study

20 - - Assigned instructor(s)

for the semester.

24 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture, homework and presentation.

12. Teaching Media

Computer

13. Measurement and Evaluation of Student Achievement

- Take home assignment 10

- Class assignment 15 %

- Midterm examination 30

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. John C. Martin., Introduction to languages and the theory of computation.omputation.

2. John E. Hopcroft and Jeffrey D. Ullman., Introduction to automata theory languages and computation.

3. Michael Sipser., Introduction to the theory of computation.

4. Peter Linz., An introduction to formal languages and automata.

SCMA 209 (2/3) 57 Theory of Computation (Distinction)


16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 209 (3/3) 58 Theory of Computation (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 213 Course Title Calculus of Several Variables

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Quadric surfaces; functions of several variables; limits; continuity; partial derivatives; Jacobians; maxima

and minima; Lagrange multipliers; Taylor series; line integrals; double integrals; multiple integrals; multiple

integrals by cylindrical coordinates and spherical coordinates; surface integrals.

9. Course Objective(s)

- To understand continuity of functions of several variables.

- To understand and know how to find partial derivatives of functions of several variables.

- To understand and know how to find the difference types of multiple integrals of functions of several variables.

- The partial derivatives and multiple integration can be applied.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 1.Quadric surface

3 - - Assigned instructor(s)

2.Functions of several variables

for the semester.

- Functions of two variables

2 - Functions of more than two variables

3.Limits

3 4.Continuity

5.Partial derivatives

- Partial derivatives of function of 2

variables

- Partial derivatives of function of

more than 2 variables and higher

derivatives

4 - Tangent planes and differentials

- The chain rule

5 - Implicit differential 6.Maxima and

minima

6 7.Lagrange multipliers

8.Taylor series

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

7–9 9.Double integrals 9 - - Assigned instructor(s)

for the semester.

SCMA 213 (1/2) 59 Calculus of Several Variables


10–12 10.Triple integrals 9 - - Assigned instructor(s)

for the semester.

13 11.Triple integrals by cylindrical coordinates

12.Triple integrals by spherical

coordinates

14 13.Multiple integration

14.Jacobians

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

15 15.Line integrals

16.Surface integrals

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture in class and home assignment are given.

12. Teaching Media

-

13. Measurement and Evaluation of Student Achievement

1. Two class tests 50%

2. Final exam 50%

14. Course Evaluation

Grading scale is

85–100 A

80–85 B +

74–79 B

68–73 C +

62–67 C

56–61 D +

50–55 D

0–49 F

15. Reference(s)

1. Calculus, Early Transcendentals, 5th. Ed., J. Stewart, Brooks/Cole, Publishers.

2. Advance calculus of several variables, C.H. Edwards,JR., Dover Publications, inc., New York.

16. Instructor(s)

Dr. Boriboon Novaprateep

17. Course Coordinator

Dr. Boriboon Novaprateep

SCMA 213 (2/2) 60 Calculus of Several Variables


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 214 Course Title Advanced Calculus

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Sequences; series; functions; limits; continuity; uniform continuity; differentiability; Intermediate Value

Theorem; Rolle’s Theorem; Mean Value Theorem; l’Hospital’s rule; Fundamental Theorems of Calculus;

functions of several variables.

9. Course Objective(s)

The Objective of the course is to teach the students to understand the basic concepts and definitions and

theories advanced calculus.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 Sets and Functions

- R and R n

- Functions

- Topological Terminology

- Sequences

- Compact Sets

7 - - Assigned instructor(s)

for the semester.

3–6 Continuity

- Basic Definitions

- Uniform Continuity

- Limits of Functions

- Discontinuities

9 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

6–9 Differentiation

- Derivatives for Functions on R n

- The Derivative

- The Mean Value Theorem

- L’Hospital’s Rule

for the semester.

9–12 Integration

- The Definite Integral

- Substitution in Multiple Integrals

12–14 Series

- Infinit Series

- Conditionally Convergent Series

9 - - Assigned instructor(s)

for the semester.

7 - - Assigned instructor(s)

for the semester.

SCMA 214 (1/2) 61 Advanced Calculus


14–16 Uniform Convergence

7 - - Assigned instructor(s)

- Series and Sequence of Functions

for the semester.

- Power Series

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. R. Creighton Buck, Advanced Calculus

2. Steven R. Lay, Analysis an Introduction to Proof.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 214 (2/2) 62 Advanced Calculus


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 216 Course Title Advanced Calculus

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Functions of several variables; graphs of functions of several variables and contour diagrams; derivatives

of functions of several variables; partial derivatives; directional derivatives; gradients of functions of several

variables; differentials; optimization problems; integration of functions of several variables.

9. Course Objective(s)

The Objective of the course is to teach the students to understand the basic concepts and definitions and

theories advanced calculus.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–11 Differential Calculus of Functions of

Several variables

- Function of Several Variables

- Domain and Regions

- Contour Diagram

- Partial Derivatives

- Differential

- The Directional Derivatives

- Maxima and Minima of Functions

of Several variables

22 - - Assigned instructor(s)

for the semester.

12–16 Integral Calculus of Functions of Several

variables

- The Definite Integral

- Double Integrals

- Triple Integral and Multiple Integrals

in General

10 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

SCMA 216 (1/2) 63 Advanced Calculus


- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. Kaplan W., Advanced Calculus

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 216 (2/2) 64 Advanced Calculus


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 222 Course Title Differential Equations

3. Number of Credits 2(2-0) (Lecture-Lab)

4. Prerequisite SCMA 160, SCMA 161, SCMA 162 or SCMA 163

5. Type of Course Core course/basic professional course/specialized course

6. Session/Academic Year

First and second semesters/2007

7. Course Conditions None

8. Course Description

Theory of ordinary differential equations; series solutions to ordinary differential equations; Laplace

transforms; systems of differential equations; Fourier series; elementary partial differential equations.

9. Course Objective(s)

For students to have knowledge on concepts and theory of differential equations and be able to apply them in

their professional areas.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Theory of ordinary differential

4 - - Assigned instructor(s)

equations

for the semester.

3–5 Series solutions to ordinary differential

equations

6 - -

6–7 Laplace transforms 4 - -

8 Midterm examination -

9 Laplace transforms (cont.) 2 - -

10–11 Systems of differential equations 4 - -

12–13 Fourier series 4 - -

14–15 Elementary partial differential

equations

4 - -

16 Final examination -

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

3. Computer software

13. Measurement and Evaluation of Student Achievement

Student achievement is measured and evaluated by the ability in using the essential ideas of calculus and its

applications.

Students achievement will be graded according to the faculty and university standard using the symbols: A,

B + , B, C + , C, D + , D and F.

SCMA 222 (1/2) 65 Differential Equations


Evaluation criteria

Assignments 10%

Mid-term examination 45%

Final examination 45%

14. Course Evaluation

1. Evaluate as indicated in number 13 above.

2. Evaluate student’satisfaction towards teaching and learning of the course using a questionnaire

15. Reference(s)

1. Boyce WE. Elementary Differential Equations and Boundary Value Problem. 8th ed. New York: Wiley;

2006.

16. Instructor(s)

Instructors of department of Mathematics

17. Course Coordinator

Dr. Gumpon Sritanratana

Faculty of science, Mahidol University

Telephone: 0-2201-5000 ext. 5340

E-mail: scgst@mahidol.ac.th

SCMA 222 (2/2) 66 Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 226 Course Title Complex Variables

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Complex numbers; analytic functions; Cauchy-Riemann equations; conformality; analytic continuation;

Cauchy’s Theorems; maximum modulus principle; Liouville’s Theorem; Residue Theorems and evaluation of

real integrals; principle of arguments; Rouche’s Theorem.

9. Course Objective(s)

The objective of this course is to teach the students to understand the basic concepts and definitions and

theories of Complex Variables.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Complex Numbers

- Sums and Products

- Algebraic Properties

- Moduli and Conjugates

- Triangle Inequality

- Polar Coordinates and Euler’s Formula

- Products and Quotients in Exponential

Form

- Roots of Complex Numbers

- Regions in the Complex Plane

6 - - Assigned instructor(s)

for the semester.

SCMA 226 (1/4) 67 Complex Variables


3–5 Analytic Functions

- Functions of a Complex Variable

- Mappings

- Limits

- Theorems on Limits

- Limits Involving the Point at Infinity

- Continuity

- Derivatives

- Differentiation Formulas

- Cauchy-Riemann Equations

- Sufficient Conditions for Differentiability

- Polar Coordinates

- Analytic Functions

- Reflection Principle

- Harmonic Functions

6–7 Elementary Functions

- The Exponential Function

- Trigonometric Functions

- Hyperbolic Functions

- The Logarithmic Function and Its

Branches

- Some Identities Involving Logarithms

- Complex Exponents

- Inverse Trigonometric and Hyperbolic

Functions

8–9 Integrals

- Complex-Valued Functions w(t)

- Contours

- Contour Integrals

- Antiderivatives

- Cauchy-Goursat Theorem

- Proof of the Theorem

- Simply and Multiply Connected

Domains

- Cauchy Intergral Formula

- Derivatives of Analytic Functions

- Liouville’s Theorem and the fundamental

Theorem of Algebra

- Maximum Moduli of Functions

7 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

SCMA 226 (2/4) 68 Complex Variables


10–11 Series

- Convergence of Sequences and Series

- Taylor Series

-

- Absolute and Uniform Convergence

of Power Series

- Integration and Differentiation of

Power Series

- Uniqueness of Series Representations

- Multiplication and Division of

Power Series

- Analytic Continuation

12–13 Residues and Poles

- Residues

- Residue Theorems

- The Three Types of Isolated Singular

Points

- Residues at Poles

- Zeros and Poles of Order m

- Conditions under Which f(z) ≡ 0

- Behavior of f Near Removable and

Essential Singular Points

14–15 Applications of Residues

- Evaluation of Improper Integrals

- Improper Integrals Involving Sines

and Cosines

- Definite integrals Involving Sines

and Cosines

- Indented Paths

- Integration along a Branch Cut

- Argument Principle and Rouche’s

Theorem

- Inverse Laplace Transforms

16 Conformal Mapping

- Preserving of Angles

- Further Properties

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media

Computer

SCMA 226 (3/4) 69 Complex Variables


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. James Ward Brown and Ruel V.Churchill, Complex Variables and Applications.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 226 (4/4) 70 Complex Variables


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 234 Course Title Vector Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Algebra of vectors; vectors in rectangular coordinate system; vector differential calculus; vector integral

calculus; curvilinear coordinates; surface integrals of vector-valued functions; Divergence Theorem; Green’s

Theorem; Stokes’ Theorem.

9. Course Objective(s)

- Can find Sum of vector quantity.

- Can find the several types of product of vectors.

- Can find the several types of derivatives both of vector functions and scalar functions.

- Can find the several types of integrals.

- Understand and can apply the theory that relates with calculus of vector.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 1.Algebra of vectors

2.Vector in rectangular coordinate

system

3 - - Assigned instructor(s)

for the semester.

2

3

3–4

4

4–5

5–6

6–7

- Scalar Product

- Vector product

- Triple product

- Reciprocal set of vector

3.Vector differential calculus

- Vector differentiation

- Gradient

- Divergence

3 - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

SCMA 234 (1/3) 71 Vector Analysis


7–8

8

9

10

11

- Curl

4. Vector integral calculus

- Ordinary integrals of vectors

- Line integrals

- Surface integrals

- Volume integrals

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

? - - Assigned instructor(s)

for the semester.

12 5.Surface integrals of vector-valued

functions

? - - Assigned instructor(s)

for the semester.

12–13 6.Divergence Theorem ? - - Assigned instructor(s)

for the semester.

13 7. Greens Theorem ? - - Assigned instructor(s)

for the semester.

14 8. StokesTheorem ? - - Assigned instructor(s)

for the semester.

14–15 9. Curvilinear coordinates ? - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture in class and home assignment are given.

12. Teaching Media

-

13. Measurement and Evaluation of Student Achievement

1. Two class tests 50%

2. Final exam 50%

14. Course Evaluation

Grading scale is

85–100 A

80–85 B +

74–79 B

68–73 C +

62–67 C

56–61 D +

50–55 D

0–49 F

15. Reference(s)

1. Calculus, Early Transcendentals, 5th. Ed., J. Stewart, Brooks/Cole, Publishers.

2. Advance calculus of several variables, C.H. Edwards,JR., Dover Publications, inc., New York.

3. Vector analysis, M.R.Spiegel, Schaum Outline Series, McGraw-Hill Book Co.

SCMA 234 (2/3) 72 Vector Analysis


16. Instructor(s)

Dr. Boriboon Novaprateep

17. Course Coordinator

Dr. Boriboon Novaprateep

SCMA 234 (3/3) 73 Vector Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 235 Course Title Analytic Geometry

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 1

8. Course Description

Conic sections; coordinate systems in R 3 ; graphs in R 3 ; change of coordinates; planes and surfaces in R 3 .

9. Course Objective(s)

- Can draw and write the equations of lines and conic sections in rectangular coordinate.

- Can draw and write the equations of lines, planes and surfaces in rectangular coordinate.

- Can draw and write the equations of graphs in polar coordinate.

- Can draw and write the equations of graphs in parametric form.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 1.Fundamental concepts 6 - - Assigned instructor(s)

for the semester.

3–4 2.Conic sections 6 - - Assigned instructor(s)

for the semester.

5 3.Simplification of equation by rotations

and translations

4.Space coordinates and surfaces

6 - Coordinate system in R 3 and graph

of an equation

- General linear equation

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

7 - Surface of revolution 2 - - Assigned instructor(s)

for the semester.

7–8 - Second-degree equations 2 - - Assigned instructor(s)

for the semester.

8 - Quadric surfaces

5.Polar coordinates

2 - - Assigned instructor(s)

for the semester.

9 - Change of coordinate 1 - - Assigned instructor(s)

for the semester.

9–10 - Graphs of polar coordinate

equations

3 - - Assigned instructor(s)

for the semester.

11 - Polar equations of lines and circles 3 - - Assigned instructor(s)

for the semester.

SCMA 235 (1/2) 74 Analytic Geometry


12 - Polar equations of conics

- Trigonometric equations

13 - Intersections of polar coordinate

graphs

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

14 6.Parametric Equations 3 - - Assigned instructor(s)

for the semester.

15 7.Planes and surfaces in R 3 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture in class and home assignment are given.

12. Teaching Media

-

13. Measurement and Evaluation of Student Achievement

1. Two class tests 50%

2. Final exam 50%

14. Course Evaluation

Grading scale is

85–100 A

80–85 B +

74–79 B

68–73 C +

62–67 C

56–61 D +

50–55 D

0–49 F

15. Reference(s)

1. Calculus, Early Transcendentals, 5th. Ed., J. Stewart, Brooks/Cole, Publishers.

2. Analytic geometry,5th.Ed.,G.Fuller, Addison-Wesley Publishing Co.

16. Instructor(s)

Dr. Boriboon Novaprateep

17. Course Coordinator

Dr. Boriboon Novaprateep

SCMA 235 (2/2) 75 Analytic Geometry


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 236 Course Title Non-Euclidean Geometry

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Projective geometry; elliptic geometry; hyperbolic geometry; linear method in geometry; geometry of straight

lines; geometry of quadratic curves; projective spaces.

9. Course Objective(s)

To impose the students to all kinds of non-euclidean geometry, their properties and applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction and historical notes

- Euclidean geometry: a quick review

3 - - Assigned instructor(s)

for the semester.

- Euclid’s fifth postulate

2 - Projective geometry 3 - - Assigned instructor(s)

for the semester.

3 - Projective geometry 3 - - Assigned instructor(s)

for the semester.

4 - elliptic geometry 3 - - Assigned instructor(s)

for the semester.

5 - elliptic geometry 3 - - Assigned instructor(s)

for the semester.

6 - hyperbolic geometry 3 - - Assigned instructor(s)

for the semester.

7 - hyperbolic geometry 3 - - Assigned instructor(s)

for the semester.

8 - linear method in geometry 3 - - Assigned instructor(s)

for the semester.

9 - linear method in geometry 3 - - Assigned instructor(s)

for the semester.

10 - geometry of straight lines 3 - - Assigned instructor(s)

for the semester.

11 - geometry of straight lines 3 - - Assigned instructor(s)

for the semester.

12 - geometry of quadratic curves 3 - - Assigned instructor(s)

for the semester.

SCMA 236 (1/2) 76 Non-Euclidean Geometry


13 - geometry of quadratic curves 3 - - Assigned instructor(s)

for the semester.

14 - projective spaces 3 - - Assigned instructor(s)

for the semester.

15 - projective spaces 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 236 (2/2) 77 Non-Euclidean Geometry


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 237 Course Title Vector and Tensor Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 234 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Algebra and calculus of tensor quantities; invariance under coordinate transformations; contravariant,

covariant and mixed tensors; Christoffel symbols; covariant and intrinsic differentiation; generalized products

and operations of vector analysis; basic equations of differential geometry; dynamics; electromagnetic field

theory; elasticity and fluids in generalized coordinates

9. Course Objective(s)

To provide an introduction to vector and tensor analysis with some discussion of important applications in

theoretical physics.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Review of vector analysis 3 - - Assigned instructor(s)

for the semester.

2 - Curvilinear coordinate systems 3 - - Assigned instructor(s)

for the semester.

3 - Contravariant and covariant vectors 3 - - Assigned instructor(s)

for the semester.

4 - Metric tensor 3 - - Assigned instructor(s)

for the semester.

5 - Transformation properties of

tensors

3 - - Assigned instructor(s)

for the semester.

6 - Christoffel’s symbols 3 - - Assigned instructor(s)

for the semester.

7 - Covariant and intrinsic derivatives

of tensors

8 - Introduction to differential geometry

- Frenet-Serret formulae

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 - Geodesics 3 - - Assigned instructor(s)

for the semester.

10 - Riemannian curvature 3 - - Assigned instructor(s)

for the semester.

SCMA 237 (1/2) 78 Vector and Tensor Analysis


11 - Space of constant curvature 3 - - Assigned instructor(s)

for the semester.

12 - Tensors in Euclidean geometry 3 - - Assigned instructor(s)

for the semester.

13 - Dynamics 3 - - Assigned instructor(s)

for the semester.

14 - Special relativity 3 - - Assigned instructor(s)

for the semester.

15 - Electromagnetic field theory 3 - - Assigned instructor(s)

for the semester.

16 - Elasticity 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the applications of vector and tensor analysis to problems in theoretical

physics

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Tensor Calculus, D. Kay, McGraw Hill (Schaum Outline Series)

2. Tensor Calculus, J. L. Synge and A. Schild, Dover.

3. Vector Analysis, M. R. Spiegel, McGraw Hill (Schaum Outline Series)

16. Instructor(s)

To be arranged.

17. Course Coordinator

Attend all classes. Complete all assignments without copying.

SCMA 237 (2/2) 79 Vector and Tensor Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 241 Course Title Computer Programming

3. Number of Credits 3(2-2) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Solving mathematical problems using computer or computer language depending on the interest of the

instructor.

9. Course Objective(s)

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–16 Computer programming in any computer

language depending on the

puter lab

for the semester.

32 Practice in com-

32 Assigned instructor(s)

interest of the instructor.

11. Teaching Method(s)

Instructor gives lecture 32 hours and students work on given problems using computers 32 hours.

12. Teaching Media

1. Personal computer 1 set / 1 student

2. LCD projector 1 set

3. Powerpoint presentation

13. Measurement and Evaluation of Student Achievement

On successful completion of this unit, student should be able to

1. write with good style well-documented computation programs,

2. design computer algorithms for solving the mathematical problem as given by instructor,

3. implement any algorithms on computers using the language that instructor is interested in.

14. Course Evaluation

1. Two assignments 20%

2. Two short test during week 6 and week 14 20%

3. End of semester two-hour(?) examination 60%

To pass the unit, the student must obtain an overall mark of at least 50 percent.

15. Reference(s)

16. Instructor(s)

1. Lect. Benchawan Wiwatanapataphee

2. Lect. Meechoke choodaung

3. Lect. Somkid Amorsamankul

17. Course Coordinator

Head of Department and undergraduate committee.

SCMA 241 (1/1) 80 Computer Programming


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 263 Course Title Differential Equations and Boundary

Value Problems

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 163 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Theory of ordinary differential equations; series solutions to ordinary differential equations; Laplace

transforms; system of differential equations; Fourier series; partial differential equations.

9. Course Objective(s)

For students to have knowledge on concepts and theory of differential equations and be able to apply them in

their professional areas.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Theory of ordinary differential

equations

3 - Theory of ordinary differential

equations

- Series solutions to ordinary differential

equations

4 - Series solutions to ordinary differential

equations

5 - Series solutions to ordinary differential

equations

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 - Laplace transforms 3 - - Assigned instructor(s)

for the semester.

7 - Laplace transforms 3 - - Assigned instructor(s)

for the semester.

8 - Systems of differential equations 3 - - Assigned instructor(s)

for the semester.

9 - Systems of differential equations 3 - - Assigned instructor(s)

for the semester.

10 - Fourier series 3 - - Assigned instructor(s)

for the semester.

SCMA 263 (1/2)

81 Differential Equations and Boundary Value Problems


11 - Fourier series 3 - - Assigned instructor(s)

for the semester.

12 - Partial differential equations 3 - - Assigned instructor(s)

for the semester.

13 - Partial differential equations 3 - - Assigned instructor(s)

for the semester.

14 - Partial differential equations 3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

1. William Boyce and Richard DiPrima, Elementary Differential Equations and Boundary Value Problems.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 263 (2/2)

82 Differential Equations and Boundary Value Problems


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 266 Course Title Theory of Interests

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 1

8. Course Description

Simple interest; compound interest; effective rate of interest; effective rate of discount; annuities; amortization

schedule and sinking funds; yield rates; bonds and other securities; installment loans.

9. Course Objective(s)

1. To understand the importance of interests, discounts, annuities and theoretical computation methods.

2. To understand and be able to apply computation of interests, annuities and methods for paying for debts,

computation of yield rates or the price of bonds and other securities, and monetary analysis.

3. To learn to use computer application programs for monetary computation and analysis.

4. To search and present interesting topics.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Computation of simple and compound 6 - - Assigned instructor(s)

interests and discounts

for the semester.

3 Cumulative functions, total money

function, present values, interest

rates, discounts, effective rate of

discounts and interests

4–5 Various types of comparison of interest

and discount measurement,

computation for nonconstant

interests

3 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6–7 Practical computation 6 - - Assigned instructor(s)

for the semester.

8 ordinary annuities and computation

methods

9–10 general annuities and computation

methods

11–12 Analysis of amortization schedule and

sinking funds

13–14 Yield rates and further investment

rates

3 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

SCMA 266 (1/2) 83 Theory of Interests


15 Bonds and other securities 3 - - Assigned instructor(s)

for the semester.

16 Practical applications and the EX- 3 - - Assigned instructor(s)

CEL program

for the semester.

11. Teaching Method(s)

Lecture and lab, with some self-study.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm examination 30%

2. Tests 10%

3. Report and class participation 10 %

4. Final examination 50%

14. Course Evaluation

t-score.

15. Reference(s)

1. Stephen G. Kellison, The Theory of Interest (second Edition), Irwin Inc.

2. Broverman, S.A., Mathematics of Investment and Credit (second Edition) 1996.

3. Parmenter M.M., The Theory of Interest and Life Contingencies with Pension Applications: A

Problem-Solving Approach, 1999.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 266 (2/2) 84 Theory of Interests


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 273 Course Title Mathematical Structures and Proofs

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Fundamentals of mathematical structures; introductory logic; mathematical proofs; application of definitions,

axioms, theorems and assumptions to reasoning; proofs of simple statements; proofs of compound statements;

proofs of statements with quantifiers; contrapositive proofs; proofs by contradiction; proofs of or-statement by

transforming into conditional form; proofs by weak and strong mathematical induction; proofs by exhaustion;

proofs of existence and uniqueness; proofs of well-definedness; proof of complicated statements.

9. Course Objective(s)

To teach the students how to learn mathematics and to provide them with the fundamental knowledge about

the philosophy of mathematics, the language of mathematics, mathematical structures, and the concept of

mathematical proofs with full practice.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction

- Variables, sets and logic: a quick

review

- Fundamental of mathematical

structures with historical notes

- Assignment 1 handed-out

3 - - Assigned instructor(s)

for the semester.

2 - Application of definitions, axioms,

theorems and assumptions

to reasoning

3 - Proof of simple statements

- Assignment 1 due

- Assignment 2 handed-out

4 - Proof of compound statements:

conjunctions, conditionals and biconditionals

- Assignment 1 returned

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 273 (1/3) 85 Mathematical Structures and Proofs


5 - Proof of compound statements: disjunctions

- Proof of statements with universal

quantifiers

- Quiz on fundamental of mathematical

structures

- Assignment 2 due

- Assignment 3 handed-out

6 - Proof of statements with existential

quantifier

- In-class practice

- Assignment 2 returned

- Assignment 3 due

7 - Proof techniques: contrapositive

proofs

- Proof techniques: proofs by contradiction

- Quiz on proofs of simple and compound

statements

- Assignment 3 returned

- Assignment 4 handed-out

8 - Proof techniques: proofs by contradiction

- Proof techniques: proofs by exhaustive

cases

9 - Proof techniques: proofs by exhaustive

cases

- Proof techniques: mathematical

induction

- Assignment 5 handed-out

10 - Proof techniques: strong mathematical

induction

- In-class practice

- Quiz on proof by contrapositivity/contradiction/exhaustive

cases

- Assignment 4 due

11 - Proof techniques: proofs of existence

and uniqueness

- Assignment 4 returned

- Assignment 5 due

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 273 (2/3) 86 Mathematical Structures and Proofs


12 - Proof techniques: negations and

well-defined definitions

- Proof of complicate statements

- Assignment 5 returned

13 - In-class practice

- Quiz on proof by induction and

strong induction

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

14 - In-class practice 3 - - Assigned instructor(s)

for the semester.

15 - In-class practice 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination (based on the material covered during the first 18 hours) 25%

4. Final Examination (based on the material covered during the semester) 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

1. Daniel J. Velleman, How To Prove It A Structured Approach, Cambridge University Press, 1994.

2. Daniel Solow, How To Read and Do Proofs An Introduction To Mathematical Thought Processes, John

Wiley & Sons, Inc., 2002.

3. Miklós Laczkovich, Conjecture and Proof, The Mathematical Association of America, 2001.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 273 (3/3) 87 Mathematical Structures and Proofs


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 275 Course Title Set Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Cardinality; countable sets; axioms of set theory; ordered pairs; relations; functions; cardinal numbers;

natural numbers; partially ordered sets; Axiom of Choice; ordinal numbers.

9. Course Objective(s)

The objective of the course is to teach the students to understand the basic concept and definitions and

theories of set theory.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Classes and Sets

- Building classes

- The algebra of classes

- Ordered pairs Cartesian products

- Graph

- Generalized union and intersection

- Sets

6 - - Assigned instructor(s)

for the semester.

3–4 Functions

- Fundamental concepts and definitions

- Properties of composite functions

and inverse functions

- Direct images and inverse images

under functions

- Product of a family of classes

- The axiom of replacement

5 - - Assigned instructor(s)

for the semester.

SCMA 275 (1/3) 88 Set Theory


4–5 Relations

- Fundamental concepts and definitions

- Equivalence relations and partitions

- Pre-image restriction and quotient

of equivalence relations

- Equivalence relations and functions

6–7 Partially Ordered Classes

- Fundamental concepts and definitions

- Ordered preserving functions and

isomorphism

- Distinguished elements. Duality

- Lattices

- Fully ordered classes. well-ordered

classes

- Isomorphism between well-ordered

classes

7–9 The Axiom of Choice Related Principles

- The axiom of choice

- An application of the axiom of

choice

- Maximal principles

- The well-ordering theorem

9–11 The Natural Numbers

- Elementary properties of the natural

numbers

- Finite recursion

- Arithmetic of natural numbers

11–13 Finite and Infinite Sets

- Equipotence of sets

- Properties of infinite sets

- Properties of denumerable sets

13–15 Arithmetic of Cardinal Numbers

- Operations on cardinal numbers

- Ordering of the cardinal Numbers

- Special properties of infinite cardinal

numbers

- Infinite sums and products of cardinal

numbers

4 - - Assigned instructor(s)

for the semester.

5 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

5 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

SCMA 275 (2/3) 89 Set Theory


15–16 Arithmetic of the Ordinal Numbers 5 - - Assigned instructor(s)

- Operations on ordinal numbers

for the semester.

- Ordering of the ordinal numbers

- The alephs and the continuum

hypothesis

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. Charles C. Pinter, Set Theory.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 275 (3/3) 90 Set Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 283 Course Title Probability and Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Random variables and probability distributions; moments and moment generating functions; vectors of

random variables; some important probability distributions; distributions of functions of random variables;

Central Limit Theorem; estimation of parameters and methods to determine estimators; statistical hypothesis

test.

9. Course Objective(s)

This course is required for all students majoring in mathematics. Every student is assumed to have taken

SCMA 183 before. In addition, a background in Advanced Calculus is a must. After taking this course the

students will have an adequate background for their further study in statistical inference or any other applied

courses in statistics.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Chapter 1 Discrete Distributions

- 1.1 A quick review on the following

topics:

- Random Variables of the Discrete

Type

- Mathematical Expectation

- The Mean, Variance, and Standard

deviation

- Binomial Distribution

3 - - Assigned instructor(s)

for the semester.

2 - 1.2 The Poisson Distribution

- 1.3 Generating Functions

3 Chapter 2 Continuous Distributions

- 2.1 Random Variables of the Continuous

Type

- 2.2 The Uniform and Exponential

Distributions

4 - 2.3 The Gamma and Chi-Square

Distributions

- 2.4 The Normal Distribution

5 - 2.5 Distributions of Functions of a

Random Variable

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 283 (1/3) 91 Probability and Statistics


6 Chapter 3 Multivariate Distributions

- 3.1 Multivariate Distributions

- 3.2 The Correlation Coefficient

7 - 3.3 Conditional Distributions

- 3.4 The Bivariate Normal Distribution

8 Chapter 4 Sampling Distribution

- 4.1 Independent Random Variables

- 4.2 Distributions of Sums of Independent

Random Variables

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 Midterm Examination 3 - - Assigned instructor(s)

for the semester.

10 - 4.3 Random Functions Associated

with Normal Distributions

- 4.4 The Central Limit Theorem

11 - 4.5 Approximations for Discrete

Distributions

- 4.6 The t and F Distributions

12 Chapter 5 Estimation

- 5.1 Point Estimation

13 - 5.2 Confidence Intervals for Means

- 5.3 Confidence Intervals for Difference

of Two Means

- 5.4 Confidence Intervals for Variances

- 5.5 Confidence Intervals for

Proportions

14 Chapter 6 Tests of Statistical Hypotheses

- 6.1 Tests about Proportions

- 6.2 Power and Sample Size

15 - 6.3 Tests about Mean

- 6.4 Tests about Variance

16 - 6.5 Chi-Square Tests

- 6.6 Contingency Tables

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instructor gives lecture weekly. Students can ask questions while the class is conducted. Students have to

submit homework assigned regularly by the instructor.

12. Teaching Media

A required textbook, chalk and board or any desired media such as an overhead projector or a visual

presentation.

13. Measurement and Evaluation of Student Achievement

- Homework 10%

SCMA 283 (2/3) 92 Probability and Statistics


- 2 Quizzes 20%

- Midterm Examination 35%

- Final Examination 35%

14. Course Evaluation

90–100 A

84–89 B +

78–83 B

72–77 C +

66–71 C

60–65 D +

54–59 D

0–53 F

15. Reference(s)

1. Probability and Statistical Inference. 6th edition. Robert V. Hogg and Allen T. Craig. Prentice-Hall

International, Inc.ger-Verlag).

2. Mathematical Statistics with Applications by Mendenhall, Scheaffer, and Wackerly.

16. Instructor(s)

A staff from mathematics department.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 283 (3/3) 93 Probability and Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 284 Course Title Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Probability; conditional probability; discrete and continuous random variables; discrete and continuous

probability distributions; functions of random variables; multivariate distributions; mathematical expectations;

sampling distributions; estimation; hypothesis testing.

9. Course Objective(s)

For students to have knowledge on concepts of statistics.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Probability 3 - - Assigned instructor(s)

for the semester.

3 - Conditional probability 3 - - Assigned instructor(s)

for the semester.

4 - Discrete and continuous random

variables

5 - Discrete and continuous probability

distributions

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 - Functions of random variables 3 - - Assigned instructor(s)

for the semester.

7 - Multivariate distributions 3 - - Assigned instructor(s)

for the semester.

8 - Mathematical expectations 3 - - Assigned instructor(s)

for the semester.

9 - Sampling distributions 3 - - Assigned instructor(s)

for the semester.

10 - Sampling distributions 3 - - Assigned instructor(s)

for the semester.

11 - Estimation 3 - - Assigned instructor(s)

for the semester.

12 - Estimation 3 - - Assigned instructor(s)

for the semester.

SCMA 284 (1/2) 94 Statistics


13 - Hypothesis testing 3 - - Assigned instructor(s)

for the semester.

14 - Hypothesis testing 3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Term project 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 284 (2/2) 95 Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 285 Course Title Introduction to Stochastic Processes

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 283 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Generating functions; recurrent event theory; Markov chain; stationary distribution for Markov chains;

Markov pure jump process.

9. Course Objective(s)

At the completion of this course students should be able to

1. have knowledge and understand Stochastic Processes

2. explain Stochastic Processes

3. apply Stochastic Process to solve problems

4. have basic knowledge on Stochastic Processes for advanced study in Mathematical Statistics

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Generating functions 6 - - Assigned instructor(s)

for the semester.

3–5 Recurrent event theory 9 - - Assigned instructor(s)

for the semester.

6–9 Markov chain 12 - - Assigned instructor(s)

for the semester.

10–13 Stationary distribution for Markov

chain

12 - - Assigned instructor(s)

for the semester.

14–16 Markov pure jump process 9 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out.

13. Measurement and Evaluation of Student Achievement

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

15. Reference(s)

1. Berger, M.A. (1993). An introduction to Probability and Stochastic Processes. Springer - Verlag, New

York, Inc., USA.

SCMA 285 (1/2) 96 Introduction to Stochastic Processes


2. Cox, D.R. and Miller, H.D. (1994). Theory of Stochastic Processes. Chapman & Hall, London, UK.

3. Feller, W. (1968). An Introduction to Probability Theory and Its Applications, 3nd edition, John Wiley &

Sons, New York, USA.

4. Narayan, B.U. (1972). Elements of Applied Stochastic Processes. John Wiley & Sons, Inc., USA.

5. Nelson, R. (1995). Probability, Stochastic Processes, and Queueing Theory. Springer - Verlag, New York,

Inc., USA.

6. Papoulis, A. (1991). Probability, Random Variables, and Stochastic Processes, 3nd edition, McGraw - Hill,

Inc., USA.

7. Pazen, E. (1960). Modern Probability Theory and Its Applications, Toppan Company, Ltd., Tokyo, Japan.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 285 (2/2) 97 Introduction to Stochastic Processes


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 290 Course Title Special Topics in Mathematics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topics of special interest to instructor.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 3 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 45 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 290 (1/1) 98 Special Topics in Mathematics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 291 Course Title Selected Topics I

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topics of special interest to instructor, approved by the department.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor, approved by the department.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 3 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor,

approved by the department

for the semester.

45 - - Assigned instructor(s)

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 291 (1/1) 99 Selected Topics I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 292 Course Title Selected Topics II

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topics of special interest to instructor, approved by the department.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor, approved by the department.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 3 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor,

approved by the department

for the semester.

45 - - Assigned instructor(s)

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 292 (1/1) 100 Selected Topics II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 300 Course Title Set Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 275:

Cardinality; countable sets; axioms of set theory; ordered pairs; relations; functions; cardinal numbers; natural

numbers; partially ordered sets; Axiom of Choice; ordinal numbers.

9. Course Objective(s)

The objective of the course is to teach the students to understand the basic concept and definitions and

theories of set theory.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Classes and Sets

- Building classes

- The algebra of classes

- Ordered pairs Cartesian products

- Graph

- Generalized union and intersection

- Sets

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

3–4 Functions

- Fundamental concepts and definitions

- Properties of composite functions

and inverse functions

- Direct images and inverse images

under functions

- Product of a family of classes

- The axiom of replacement

- Rigorous discussion on challenging

problems and selected topics for

independent study

6.6 - - Assigned instructor(s)

for the semester.

SCMA 300 (1/3) 101 Set Theory (Distinction)


4–5 Relations

- Fundamental concepts and definitions

- Equivalence relations and partitions

- Pre-image restriction and quotient

of equivalence relations

- Equivalence relations and functions

- Rigorous discussion on challenging

problems and selected topics for

independent study

6–7 Partially Ordered Classes

- Fundamental concepts and definitions

- Ordered preserving functions and

isomorphism

- Distinguished elements. Duality

- Lattices

- Fully ordered classes. well-ordered

classes

- Isomorphism between well-ordered

classes

- Rigorous discussion on challenging

problems and selected topics for

independent study

7–9 The Axiom of Choice Related Principles

- The axiom of choice

- An application of the axiom of

choice

- Maximal principles

- The well-ordering theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

9–11 The Natural Numbers

- Elementary properties of the natural

numbers

- Finite recursion

- Arithmetic of natural numbers

- Rigorous discussion on challenging

problems and selected topics for

independent study

5.3 - - Assigned instructor(s)

for the semester.

6.6 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

6.6 - - Assigned instructor(s)

for the semester.

SCMA 300 (2/3) 102 Set Theory (Distinction)


11–13 Finite and Infinite Sets

- Equipotence of sets

- Properties of infinite sets

- Properties of denumerable sets

- Rigorous discussion on challenging

problems and selected topics for

independent study

13–15 Arithmetic of Cardinal Numbers

- Operations on cardinal numbers

- Ordering of the cardinal Numbers

- Special properties of infinite cardinal

numbers

- Infinite sums and products of cardinal

numbers

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

15–16 Arithmetic of the Ordinal Numbers

- Operations on ordinal numbers

6.6 - - Assigned instructor(s)

for the semester.

- Ordering of the ordinal numbers

- The alephs and the continuum hypothesis

- Rigorous discussion on challenging

problems and selected topics for

independent study

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. Charles C. Pinter, Set Theory.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 300 (3/3) 103 Set Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 301 Course Title Introduction to Graph Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 374:

Fundamental concepts; connectedness of a graph; paths; trees; circuits; cutsets; matrix representations; planar

and dual graphs; domination; independence; chromatic numbers; transport network; Max-Flow Min-Cut

Theorem; complete matching; maximal matching.

9. Course Objective(s)

Students understand the fundamental concepts of graph theory and improve their ability to read and create

mathematical proofs.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Basic concepts and definitions

8 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

3–4 Tree and Distance

- Rigorous discussion on challenging

problems and selected topics for

independent study

5–6 Connectivity Paths and Digraphs

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 Adjacency matrix

- Counting walks, and triangles

in a graph, using power of the

adjacency matrix.

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

8 Midterm 4 - - Assigned instructor(s)

for the semester.

SCMA 301 (1/2) 104 Introduction to Graph Theory (Distinction)


9–10 Graph Coloring

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–12 Planar Graphs

- Rigorous discussion on challenging

problems and selected topics for

independent study

13–14 Ramsey Theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

15–16 Additional Topics depending on student

interest

8 - - Assigned instructor(s)

for the semester.

- Rigorous discussion on challenging

problems and selected topics for

independent study

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

There will be two regular exams: midterm test and final exam. Several homework are assigned and collected

for grading.

14. Course Evaluation

Grade will be based on: 20 % for the homework, 40 % for midterm, 40 % for the final. Course grades will be

determined roughly as :

85–100 A

81–84 B +

75–80 B

70–74 C +

60–69 C

55–59 D +

51–54 D

0–50 F

15. Reference(s)

1. Graphs and Digraphs, 3rd edition, G.Chartrand and L.Lesniak.

2. Graph an Introductory Approach, Robin J.Wilson and John J.Watkins.

16. Instructor(s)

Staff

17. Course Coordinator

Staff

SCMA 301 (2/2) 105 Introduction to Graph Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 302 Course Title Group Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 356:

Elements of group theory; concepts of homomorphy and groups with operators; structure and construction of

composite groups; cyclic groups; p-groups; Sylow p-groups.

9. Course Objective(s)

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Semigroups, Monoids and Groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

2 Homomorphisms and subgroups

- Rigorous discussion on challenging

problems and selected topics for

independent study

3 Cyclic groups, Cosets and counting

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 Normality, Quotient groups and homomorphisms

- Rigorous discussion on challenging

problems and selected topics for

independent study

5 Symmetric, alternating, and Dihedral

Groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 302 (1/3) 106 Group Theory (Distinction)


6 Categories and Functors, Products,

coproducts and Free objects

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 Direct products and direct sums of

groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 Free groups, Free products, Generators

and Relations

- Rigorous discussion on challenging

problems and selected topics for

independent study

9 Free abelian groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

10 Finitely generated abelian groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

11 The Krull-Schmidt Theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 The action of a group on a set

- Rigorous discussion on challenging

problems and selected topics for

independent study

13 The Sylow Theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

14 Classification of finite groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 302 (2/3) 107 Group Theory (Distinction)


15 Nilpotent and solvable groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

16 Normal and subnormal series of

groups

4 - - Assigned instructor(s)

for the semester.

- Rigorous discussion on challenging

problems and selected topics for

independent study

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 302 (3/3) 108 Group Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 303 Course Title Number Theory II (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 350 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 450:

Introduction to modern analytic and algebraic techniques used in the study of quadratic forms; distribution of

prime numbers; Diophantine approximations and other topics of classical number theory.

9. Course Objective(s)

Upon completion of this course students will be able to:

1. develop an ability to apply number theory in other subjects;

2. produce and appreciate imaginative and creative work arising from mathematical idea;

3. analyze a problem, select a suitable strategy and apply an appropriate technique to obtain its solution.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–4 - Introduction to modern analytic

and algebraic techniques used in

the study of quadratic forms

- Rigorous discussion on challenging

problems and selected topics for

independent study

16 - - Assigned instructor(s)

for the semester.

5–6 - Distribution of prime numbers

- Rigorous discussion on challenging

problems and selected topics for

independent study

7–15 - Diophanine approximations and

other topics of classical number

theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

36 - - Assigned instructor(s)

for the semester.

16 - Review 4 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

1. Lecture

2. Discussion

3. Presentation

SCMA 303 (1/2) 109 Number Theory II (Distinction)


12. Teaching Media

1. Text and handouts

2. Transparencies

13. Measurement and Evaluation of Student Achievement

Grades will be assigned according to the following point scale:

90–100 A

85–89 B +

80–84 B

75–79 C +

70–74 C

60–69 D +

50–59 D

0–49 F

14. Course Evaluation

- Graded homework, participation in class and group work 10%

- Exam I 20%

- Exam II 20%

- Quizzes 10%

- Final exam 40%

15. Reference(s)

1. Brown, Stephen I., On Prime Comparison, National Council of Teachers of Mathematics, 1978.

2. Hardy and Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford.

3. Niven, I. and Zuckerman, H. S., an Introduction to the Gauss by Applied Technical Systems in the $300

Range.

4. Shanks, Daniel, Solved and Unsolved Problems in Number Theory, Washington, D. C., Spartan Books,

1962.

5. Stein, M. L., et. al., a Visual Display of Some Properties of the Distribution of Primes, American

Mathematical Monthly, 71 (May 1964).

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 303 (2/2) 110 Number Theory II (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 304 Course Title Game Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 367:

Matrix games; extensive forms; game trees; mixed strategies; dominating strategies; bimatrix games; normal

forms; Nash equilibrium; repeated games.

9. Course Objective(s)

The student should know the basic concepts and theorems of game theory and be able to apply them.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Two-Person Zero-Sum Games:

- Matrix games

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

3 - Game trees

- Rigorous discussion on challenging

problems and selected topics for

independent study

4–5 - Utility theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

6–7 Two-Person Non-Zero-Sum Games:

- Nash Equilibrium

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - Prisoners’ Dilemma

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 304 (1/2) 111 Game Theory (Distinction)


9–10 - Evolutionary Game Theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–12 N-Person Games:

- Stable sets

- Rigorous discussion on challenging

problems and selected topics for

independent study

13–14 - The Core

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

8 - - Assigned instructor(s)

for the semester.

15–16 - Repeated Games

- Rigorous discussion on challenging

8 - - Assigned instructor(s)

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm Exam 50%

2. Final Exam 50%

14. Course Evaluation

Final course grades are assigned based on a 100-point total as follows:

90–100 A

86–89 B +

80–85 B

76–79 C +

70–75 C

66–69 D +

60–65 D

0–59 F

15. Reference(s)

1. Game Theory And Strategy, Philip Straffin, 1993, The Mathematical Association of America.

2. A Course In Game Theory, Osbourne and Rubinstein, 1994, Massachusetts Institute of Technology.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 304 (2/2) 112 Game Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 305 Course Title Differential Geometry and Tensor

Analysis (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 234 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 436:

Curvilinear coordinate systems; topological spaces; smooth manifolds; tangent vectors; curves; surfaces;

transformation groups; tensor fields; geodesics; curvature tensor; homology theory.

9. Course Objective(s)

To provide the students with concepts and theory of differential geometry and tensor analysis.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction and historical notes

- Review of geometry of curves and

surfaces in R 3

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

2 - Curvilinear coordinate systems

- Rigorous discussion on challenging

problems and selected topics for

independent study

3 - Topological spaces

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - Smooth manifolds

- Rigorous discussion on challenging

problems and selected topics for

independent study

5 - Tangent vectors and tangent bundles

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 305 (1/3) 113 Differential Geometry and Tensor Analysis (Distinction)


6 - Curves

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 - Surfaces

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - Transformation groups

- Rigorous discussion on challenging

problems and selected topics for

independent study

9 - Vector fields and integral curves

- Rigorous discussion on challenging

problems and selected topics for

independent study

10 - Tensor fields

- Rigorous discussion on challenging

problems and selected topics for

independent study

11 - Connections

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - Riemannian metrics

- Rigorous discussion on challenging

problems and selected topics for

independent study

13 - Geodesics

- Rigorous discussion on challenging

problems and selected topics for

independent study

14 - Curvature tensor

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

15 - Homology theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

11. Teaching Method(s)

4 - - Assigned instructor(s)

for the semester.

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

SCMA 305 (2/3) 114 Differential Geometry and Tensor Analysis (Distinction)


12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

1. Richard L. Bishop and Samuel I. Goldberg, Tensor Analysis on Manifolds, Dover Publications, Inc., 1980.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 305 (3/3) 115 Differential Geometry and Tensor Analysis (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 306 Course Title Integral Equations (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 363 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 364:

General properties of integral equations; Fredholm and Volterra equations; equations of the first and second

kinds; kernels; series solutions; orthogonalization; biorthogonal functions; Neumann series; solutions by integral

transforms; Hilbert-Schmidt theory; nonhomogeneous equations; Green’s functions.

9. Course Objective(s)

To provide an introduction to the analytical issues posed by integral equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction to integral equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

2 - Fredholm integral equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

3 - Volterra integral equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - Integral equations of the first and

second kinds

- Rigorous discussion on challenging

problems and selected topics for

independent study

5 - Existence of solutions

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 306 (1/3) 116 Integral Equations (Distinction)


6 - Review of Sturm-Liouville theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 - Kernels of integral equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - Series solutions

- Rigorous discussion on challenging

problems and selected topics for

independent study

9 - Orthogonalisation

- Rigorous discussion on challenging

problems and selected topics for

independent study

10 - Solutions via biorthogonal functions

- Rigorous discussion on challenging

problems and selected topics for

independent study

11 - Neumann series

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - Review of integral transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

13 - Solution of integral equations by

integral transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

14 - Hilbert-Schmidt theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

15 - Nonhomogeneous integral equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 306 (2/3) 117 Integral Equations (Distinction)


16 - Solutions via Green’s functions 4 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the properties and solutions of integral equations

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Integral Equations, F. Smithes, Cambridge.

2. Methods of Theoretical Physics, P. M. Morse and H. Feshbach, McGraw Hill.

3. Mathematical Methods for Physicists, G. Arfken and H. Weber, Harcourt/Academic

4. Introduction to Integral Equations with Applications, A. J. Jerri, Wiley.

5. A Course on Integral Equations, A. C. Pipkin, Springer-Verlag.

6. Integral Equations, H. Hochstadt, Wiley.

7. Integral Equations, B. L. Moiseiwitsch, Pitman.

16. Instructor(s)

To be arranged.

17. Course Coordinator

Attend all classes. Complete all assignments without copying.

SCMA 306 (3/3) 118 Integral Equations (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 307 Course Title Boundary Value Problems (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 464:

Linear partial differential equations; the wave equation; Green’s function and Sturm-Liouville problems; Fourier

series and Fourier transforms; the heat equation; Laplace’s equation and Poisson’s equation; problems in higher

dimensions.

9. Course Objective(s)

The primary aim of this course is to introduce junior and senior students to boundary value problems, with

related to partial differential equations and to teach the fundamental mathematical procedures for developing

solutions.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 - Boundary and Initial Conditions

- Classification of Partial Differential

Equations

- Boundary and Initial Conditions

- Implicit Boundary Conditions

- Examples of Boundary Value Problems

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - - Assigned instructor(s)

for the semester.

3–5 - Fourier Series

- Periodic Functions

- Fourier Series

- Determining Fourier Coefficients

- Fourier Series for Even and Odd

Functions

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - - Assigned instructor(s)

for the semester.

SCMA 307 (1/3) 119 Boundary Value Problems (Distinction)


6–8 - Technique of Separation of Variables

- The Method of Separation of Variables

- Nonhomogeneous Differential Equations

and Boundary Conditions

- Sturm-Liouville Theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

9–11 - Fourier Integral

- The Fourier Integral

- An Application of a Physical Problem

- Solving a Boundary Value Problem

Using a Fourier Transform

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–14 - Green’s Functions

- The Dirac Delta Function

- Green’s Function for the Laplace

Operator

- Some other Green’s Functions

- Direct Computation of Green’s

Function

- The Eigenfunction Method

- Rigorous discussion on challenging

problems and selected topics for

independent study

14–16 - The Laplace Transform

- The Laplace Transform

- Applications to the Heat Equations

- Applications to the Wave Equations

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - - Assigned instructor(s)

for the semester.

10 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

10 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture and biweekly assignment.

12. Teaching Media


SCMA 307 (2/3) 120 Boundary Value Problems (Distinction)


13. Measurement and Evaluation of Student Achievement

Homework 20%

Midterm Examinations 40%

Final Examinations 40%

14. Course Evaluation

Grade is evaluated from homework, midterm and final examinations in the form of A, B + , B, C + , C, D + , D

and F using normal curve.

15. Reference(s)

1. M. Humi, W. B. Miller, Boundary Value Problems and Partial Differential Equations, PWS-KENT

Publishing Company, 1992

2. M. A. Pinsky, Partial Differential Equations and Boundary Value Problems with Applications, McGRAW-

HILL, 1991

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 307 (3/3) 121 Boundary Value Problems (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 308 Course Title Mathematical Transforms (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 368:

Laplace transforms; Fourier transforms; cosine and sine transforms; finite transforms; Z-transforms; other

transforms.

9. Course Objective(s)

To provide an introduction to the subject of mathematical transforms, including their analytical properties

and applications.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction to the Laplace transform

for the semester.

4 - - Assigned instructor(s)

- Rigorous discussion on challenging

problems and selected topics for

independent study

2 - Existence of the Laplace transform

- Rigorous discussion on challenging

problems and selected topics for

independent study

3 - Convolution

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - Review of residue theory

- Rigorous discussion on challenging

problems and selected topics for

independent study

5 - Complex inversion formula

- Bromwich contour

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 308 (1/3) 122 Mathematical Transforms (Distinction)


6 - Applications of the Laplace transform

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 - Fourier integral theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - Fourier transform

- Rigorous discussion on challenging

problems and selected topics for

independent study

9 - Applications of the Fourier transform

- Rigorous discussion on challenging

problems and selected topics for

independent study

10 - Cosine and sine transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

11 - Finite Fourier transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - Fast Fourier transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

13 - Z transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

14 - Linear, time invariant systems

- Rigorous discussion on challenging

problems and selected topics for

independent study

15 - Hankel transforms

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 308 (2/3) 123 Mathematical Transforms (Distinction)


16 - Mellin transforms

4 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the properties and solutions of mathematical transforms

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Laplace Transforms, Schaum Outline Series, McGraw Hill.

2. Integral Transforms and Their Applications, L. Debnath, CRC Press.

3. Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw Hill.

4. Fourier Series and Boundary Value Problems, J. W. Brown and R. V. Churchill, McGraw Hill.

5. Operational Mathematics, R. V. Churchill, McGraw Hill.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 308 (3/3) 124 Mathematical Transforms (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 309 Course Title Coding Theory (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 372:

Introduction to coding theory; basic algebra; linear code; use of matrices in linear code; maximum likelihood;

extended code; cyclic code.

9. Course Objective(s)

To understand and can apply the several types of coding.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 1.Introduction to coding theory

- Entropy and Mutual information

- Rigorous discussion on challenging

problems and selected topics for

independent study

12 - - Assigned instructor(s)

for the semester.

4 - Rate-distortion function

- Rigorous discussion on challenging

problems and selected topics for

independent study

5 - Source coding theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

6 - Capacity-Cost function

- Rigorous discussion on challenging

problems and selected topics for

independent study

7 - Channel coding Theorem

- Rigorous discussion on challenging

problems and selected topics for

independent study

8 - Maximum likelihood

- Rigorous discussion on challenging

problems and selected topics for

independent study

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

SCMA 309 (1/3) 125 Coding Theory (Distinction)


9 2.Linear code

- Generator Parity-Check Matrices

- Rigorous discussion on challenging

problems and selected topics for

independent study

9–10 - Syndrome decoding

- Rigorous discussion on challenging

problems and selected topics for

independent study

10 - Hamming codes

- Rigorous discussion on challenging

problems and selected topics for

independent study

11 - Extended code

- Rigorous discussion on challenging

problems and selected topics for

independent study

11–12 - MacWilliams identities

- Rigorous discussion on challenging

problems and selected topics for

independent study

12–13 - Goppa codes

- Rigorous discussion on challenging

problems and selected topics for

independent study

13–14 3.Cyclic code

- BCH codes

- Rigorous discussion on challenging

problems and selected topics for

independent study

15 - Reed-Solomon codes

- Golay codes

- Rigorous discussion on challenging

problems and selected topics for

independent study

2.6 - - Assigned instructor(s)

for the semester.

2.6 - - Assigned instructor(s)

for the semester.

2.6 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

4 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture in class and home assignment are given.

12. Teaching Media

-

13. Measurement and Evaluation of Student Achievement

1. Two class tests 50%

2. Final exam 50%

SCMA 309 (2/3) 126 Coding Theory (Distinction)


14. Course Evaluation

Grading scale is

85–100 A

80–85 B +

74–79 B

68–73 C +

62–67 C

56–61 D +

50–55 D

0–49 F

15. Reference(s)

1. The Theory of Information and coding,R.J.McEliece, Addison-Wesley Publishing Co.

2. Basic Concepts in Information Theory and Coding, S.W.Golomb, Plenum Press, New York and London.

16. Instructor(s)

Dr. Boriboon Novaprateep

17. Course Coordinator

Dr. Boriboon Novaprateep

SCMA 309 (3/3) 127 Coding Theory (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 321 Course Title Mathematical Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 214 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Systems of real and complex numbers; basic topology; sequences and series; continuity; differentiation;

Riemann-Stieltjes integrals; sequences and series of functions.

9. Course Objective(s)

The objective of this course is to teach the students to understand the basic concepts and definitions and

theories of mathematical analysis.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 The Real and Complex Number Systems

- Ordered Sets

- Fields

- The Real Field

- The Extended Real Number System

- The Complex Field

- Euclidean Spaces

6 - - Assigned instructor(s)

for the semester.

3–5 Basic Topology

- Finite, Countable, and Uncountable

Sets

- Metric Spaces

- Compact Sets

- Perfect Sets

- Connected Sets

9 - - Assigned instructor(s)

for the semester.

SCMA 321 (1/3) 128 Mathematical Analysis


6–8 Numerical Sequences and Series

- Convergent Sequences

- Subsequences

- Cauchy Sequences

- Upper and Lower Limits

- Some Special Sequences

- Series

- Series of Nonnegative Terms

- The Root and Ratio Tests

- Power Series

- Summation-by parts

- Absolute Convergence

- Addition and Multiplication of Series

- Rearrangements

8–10 Continuity

- Limits of Functions

- Continuous Functions

- Continuity and Compactness

- Continuity and Connectedness

- Discontinuities

- Monotonic Functions

- Infinite Limits and Limits at

Infinity

10–12 Differentiation

- The Derivative of a Real Function

- Mean Value Theorems

- The Continuity of Derivatives

- L’Hospital’s Rule

- Derivatives of Higher Order

- Taylor’s Theorem

- Differentiation of Vector-valued

Functions

12–14 The Riemann-Stieltjes Integral

- Definition and Existence of Integral

- Properties of the Integral

-

- Integration of Vector-Valued Functions

- Rectifiable Curves

7 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

7 - - Assigned instructor(s)

for the semester.

SCMA 321 (2/3) 129 Mathematical Analysis


14–16 Sequences and Series of Functions

- Discussion of Main Problem

7 - - Assigned instructor(s)

for the semester.

- Uniform Convergence

- Uniform Convergence and Continuity

- Uniform Convergence and Integration

- Uniform Convergence and Differentiation

- Equicontinuous Families of Functions

- The Stone-Weierstrass Theorem

11. Teaching Method(s)

Lecture, homework and presentations.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. Rudin W., Principles of Mathematical Analysis,

2. George F.Simmons, Topology and Modern Analysis.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 321 (3/3) 130 Mathematical Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 325 Course Title Real Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 214 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Structure of real numbers; step functions; Lebesgue integrals; Convergence Theorem; Riemann integrals;

measurable functions; measurable sets; structure of measurable functions; integration over measurable sets;

Fundamental Theorems of Calculus; Hölder-Minkowski’s inequality; L p spaces; integration on R n ; iterated

integration; Fubini’s Theorem; transformations of integrals on R n .

9. Course Objective(s)

By the end of this course, students should:

1. understand the concepts of, and be able to prove results in measure theory and integral with respect to a

measure,

2. understand, and be able to prove and apply the convergence theorems,

3. understand the concepts of, and be able to prove results in the L p spaces.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 The real number system 3 - - Assigned instructor(s)

for the semester.

2–3 Lebesgue measure

- Outer measure

- Measurable sets and Lebesgue measure

- Measurable functions

4–5 Lebesgue Integral

- The Riemann integral

- The Lebesgue Integral

- Convergence theorems

6–7 General Measure and Integration

- Measure spaces

- Integration

- Convergence theorems

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

8–9 Differentiation and Integration 6 - - Assigned instructor(s)

for the semester.

SCMA 325 (1/2) 131 Real Analysis


10–12 The L p spaces

9 - - Assigned instructor(s)

- The Minkowski-Holder’s inequality

for the semester.

- Convergence and Completeness

- Bounded linear functionals on the

L p spaces

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

1. Royden, H. L.: Real Analysis, Third Edition, Macmillan Publishing Company (1988).

2. Rudin, W.: Real and Complex Analysis, McGraw-Hill Book Company (1987).

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 325 (2/2) 132 Real Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 326 Course Title Complex Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Specialized course/core course for Distinction Program

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 1

8. Course Description

Differentiation; integration; power series; conformal mapping; approximation theory; periodic functions;

elliptic functions; Riemann surface; analytic continuation.

9. Course Objective(s)

By the end of this course, students should:

1. understand the concepts of differentiation, integration and conformality, and be able to derive their

important properties;

2. understand the theory of approximation;

3. know general properties and significance of elliptic functions;

4. understand the nature and importance of analytic continuation.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Differentiation

3 - - Assigned instructor(s)

- Analytic functions

for the semester.

- Cauchy-Riemann equations

2–3 Integration

- Riemann-Stieltjes integrals and line

integrals

- Liouville’s Theorem, Theorems of

Morera and Goursat

- Cauchy’s integral formula

4–6 Conformal mapping

- Schwarz Lemma

- Fractional Linear Transformations

7–8 Approximation theory

- Runge’s theorem

6 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

9–10 General properties of elliptic functions 6 - - Assigned instructor(s)

for the semester.

11–12 Analytic continuation

- Schwarz Reflection

- Riemann surfaces

11. Teaching Method(s)

Lecture, homework and presentations.

6 - - Assigned instructor(s)

for the semester.

SCMA 326 (1/2) 133 Complex Analysis


12. Teaching Media


13. Measurement and Evaluation of Student Achievement

- Take home assignments 10 %

- Class assignments 15 %

- Midterm examination 30 %

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. Conway, Functions of one complex variable, (Springer-Verlag).

2. Ahlfors, Complex Analysis, (McGraw-Hill Book Co).

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 326 (2/2) 134 Complex Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 336 Course Title Elementary Differential Geometry

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 113 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Curves and surfaces in R 3 ; local curve theory; Serret-Frenet formulas; global curve theory; Fenchel’s

Theorem; local surface theory.

9. Course Objective(s)

To provide the students with elementary concepts and theory of differential geometry and its applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction and historical notes

- Analytic geometry: a quick review

3 - - Assigned instructor(s)

for the semester.

2 - Background knowledge 3 - - Assigned instructor(s)

for the semester.

3 - Curves and surfaces in R 3 3 - - Assigned instructor(s)

for the semester.

4 - Curves and surfaces in R 3 3 - - Assigned instructor(s)

for the semester.

5 - Local curve theory 3 - - Assigned instructor(s)

for the semester.

6 - Local curve theory 3 - - Assigned instructor(s)

for the semester.

7 - Local curve theory 3 - - Assigned instructor(s)

for the semester.

8 - Serret-Frenet formulas 3 - - Assigned instructor(s)

for the semester.

9 - Global curve theory 3 - - Assigned instructor(s)

for the semester.

10 - Global curve theory 3 - - Assigned instructor(s)

for the semester.

11 - Fenchel’s Theorem 3 - - Assigned instructor(s)

for the semester.

12 - Fenchel’s Theorem 3 - - Assigned instructor(s)

for the semester.

SCMA 336 (1/2) 135 Elementary Differential Geometry


13 - Local surface theory 3 - - Assigned instructor(s)

for the semester.

14 - Local surface theory 3 - - Assigned instructor(s)

for the semester.

15 - Local surface theory 3 - - Assigned instructor(s)

for the semester.

16 - Introduction to differential geometry

of abstract spaces

for the semester.

3 - - Assigned instructor(s)

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

1. Manfredo P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., 1976.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 336 (2/2) 136 Elementary Differential Geometry


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 342 Course Title Numerical Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 241 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Introduction to the theory and practice of computation; numerical solutions to nonlinear equations;

interpolation and approximation; numerical differentiation and integration; numerical solutions to differential

equations; matrix calculation; solutions to systems of linear equations.

9. Course Objective(s)

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction to the theory and practice

of computation

for the

3 - - Assigned instructor(s)

semester.

2–3 Numerical solutions to nonlinear

equations

6 - - Assigned instructor(s)

for the semester.

4–5 Interpolation and approximation 6 - - Assigned instructor(s)

for the semester.

6–7 Numerical differentiation and

integration

8–10 Numerical solution of differential

equations

6 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

11–13 Matrix calculation 9 - - Assigned instructor(s)

for the semester.

14–16 Solutions to systems of linear

9 - - Assigned instructor(s)

equations

for the semester.

11. Teaching Method(s)

Instructor gives lecture 48 hours.

12. Teaching Media

1. Personal computer 1 set / 1 student

2. LCD projector 1 set

3. Powerpoint presentation

13. Measurement and Evaluation of Student Achievement

On successful completion of this unit, student should be able to

1. design computer algorithms for solving the mathematical problems,

2. analyze the error of computations.

14. Course Evaluation

1. Two assignments 20%

SCMA 342 (1/2) 137 Numerical Analysis


2. Two short test during week 6 and week 14 20%

3. End of semester two-hour(?) examination 60%

To pass the unit, the student must obtain an overall mark of at least 50 percent.

15. Reference(s)

16. Instructor(s)

1. Lect. Benchawan Wiwatanapataphee

2. Lect. Kalaya

3. Lect. Patchara

4. Lect. Meechoke choodaung

5. Lect. Somkid Amorsamankul

6. Lect. Julian

17. Course Coordinator

Head of Department and undergraduate committee.

SCMA 342 (2/2) 138 Numerical Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 350 Course Title Number Theory I

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Properties of integers; divisibility; congruences; Diophantine equations; Euler-Fermat Theorem; perfect

numbers; arithmatic functions; the two and four square problems; quadratic residues.

9. Course Objective(s)

The student will gain familiarity with number theory topics, ability to prove some major results of number

theory, algebraic manipulative skills, and computational sophitical.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Properties of integers 3 - - Assigned instructor(s)

for the semester.

2–4 - Divisibility: division algorithm,

greatest common divisors, Euclidean

algorithm, the diophantine

equation, fundamental theorem of

arithmetic.

5–7 - Congruence: arithmetic properties,

linear congruence ax ≡ b(mod m),

residue classes, system of linear

congruences, the Chinese Remainder

Theorem

8–9 - The Euler-Fermat Theorem: complete

system of residues, reduced

system of residues, the Euler-

Fermat Theorem, primitive roots

10 - Perfect Numbers: Sigma and Tau

functions, even perfect numbers

11–12 - Arithmetic functions: calculus of

arithmetic functions, the Möbious

inversion formula

13 - The Two and Four Square

Problems

9 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 350 (1/2) 139 Number Theory I


14–15 - Quadratic residues: Euler’s criterion,

the lemma of Gauss, the

quadratic reciprocity law

6 - - Assigned instructor(s)

for the semester.

16 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

1. Lecture

2. Discussion

3. Presentation

12. Teaching Media

1. Text and handouts

2. Transparencies

13. Measurement and Evaluation of Student Achievement

Grades will be assigned according to the following point scale:

90–100 A

85–89 B +

80–84 B

75–79 C +

70–74 C

60–69 D +

50–59 D

0–49 F

14. Course Evaluation

- Graded homework, participation in class and group work 10%

- Exam I 20%

- Exam II 20%

- Quizzes 10%

- Final exam 40%

15. Reference(s)

1. Apostal, Introduction Analytic Number Theory, Springer-Verlag, New York, 1999.

2. Burton, Elementary Number Theory, McGraw-Hill, New York, 1998.

3. Uspensky, J. V., Elementary Number Theory, McGraw-Hill, New York, 1939.

4. Hard and Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 350 (2/2) 140 Number Theory I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 351 Course Title Linear Algebra

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 163 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Vector spaces; linear transformations; eigenvalues and eigenvectors; canonical forms; inner product spaces.

9. Course Objective(s)

By the end of this course, students should:

1. understand the fundamental concepts of vector spaces,

2. understand the concept of linear transformation and be able to derive their basic properties,

3. understand the notions of eigenvalues and eigenvectors, and know their relation with diagonalization and

canonical form.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–3 General vector spaces

9 - - Assigned instructor(s)

- linear independence

for the semester.

- bases, etc.

4–6 Inner product spaces

- Inner products

- Orthogonality

7–9 Eigenvalues and Eigenvectors

- Diagonization

9 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

10–12 Linear transformation 9 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

1. Howard Anton, Elementary Linear Algebra, 7th Edition, John Wiley and Sons, 1994.

2. G Strang, Linear Algebra and its Applications, Harcourt Brace, 1988.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 351 (1/1) 141 Linear Algebra


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 352 Course Title Abstract Algebra I

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Basic properties of groups and rings; binary operations; number theory; groups; subgroups; permutations;

abelian groups; cyclic groups; isomorphisms; Cayley’s Theorem; direct products; cosets; normal subgroups;

factor groups; homomorphism; rings; integral domains.

9. Course Objective(s)

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Logic, Sets and classes; 3 - - Assigned instructor(s)

for the semester.

2 Mappings, Relations and partitions;

cartesian Products

3 The Integers; Axiom of choice, Order

and Zorn’s lemma;

4 Cardinal and Ordinals; Categories

and Functors.

5 Groups, subgroups and group

homomorphisms;

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 Cayley’s Theorem; Normal subgroups; 3 - - Assigned instructor(s)

for the semester.

7 Kernel and Cokernel of group homomorphisms;

Exact sequences;

8 Free abelian groups, torsion groups

and divisible groups.

9 Rings, right and left ideals, two-sided

ideals; Ring homomorphisms.

10 Integral domains. Modules and

homomorphisms;

11 Free, Projective, and Injective

modules;

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

12 The Functor Hom and duality; 3 - - Assigned instructor(s)

for the semester.

SCMA 352 (1/2) 142 Abstract Algebra I


13 Tensor Products and Flat modules; 3 - - Assigned instructor(s)

for the semester.

14 Module over a Principal Ideal

3 - - Assigned instructor(s)

Domain;

for the semester.

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 352 (2/2) 143 Abstract Algebra I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 356 Course Title Group Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Elements of group theory; concepts of homomorphy and groups with operators; structure and construction of

composite groups; cyclic groups; p-groups; Sylow p-groups.

9. Course Objective(s)

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Semigroups, Monoids and Groups; 3 - - Assigned instructor(s)

for the semester.

2 Homomorphisms and subgroups; 3 - - Assigned instructor(s)

for the semester.

3 Cyclic groups, Cosets and counting 3 - - Assigned instructor(s)

for the semester.

4 Normality, Quotient groups and

homomorphisms;

5 Symmetric, alternating, and Dihedral

Groups;

6 Categories and Functors; Products,

coproducts and Free objects;

7 Direct products and direct sums of

groups;

8 Free groups, Free products, Generators

and Relations;

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 Free abelian groups; 3 - - Assigned instructor(s)

for the semester.

10 Finitely generated abelian groups; 3 - - Assigned instructor(s)

for the semester.

11 The Krull-Schmidt Theorem 3 - - Assigned instructor(s)

for the semester.

12 The action of a group on a set; 3 - - Assigned instructor(s)

for the semester.

13 The Sylow Theorem; 3 - - Assigned instructor(s)

for the semester.

SCMA 356 (1/2) 144 Group Theory


14 Classification of finite groups; 3 - - Assigned instructor(s)

for the semester.

15 Nilpotent and solvable groups; 3 - - Assigned instructor(s)

for the semester.

16 Normal and subnormal series of

groups.

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 356 (2/2) 145 Group Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 362 Course Title Mathematics in Physical Sciences

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Applications of mathematical knowledge in solving problems in the physical sciences such as mathematical

modeling of such problems; solutions by computational and analytical methods.

9. Course Objective(s)

The primary aim of this course is to apply mathematical knowledge in solving problems in the physical

sciences. In this syllabus example we study modeling of such problems.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 - Modeling Change

- Modeling Change with Difference

Equations

- Approximating Change with Difference

Equations

- Solutions to Dynamical Systems

- Systems of Difference Equations

7.5 - - Assigned instructor(s)

for the semester.

3–5 - The Modeling Process, Proportionality,

and Geometric Similarity

- Mathematical Models

- Modeling Using Proportionality

- Modeling Using Geometric

Similarity

6–8 - Modeling Fitting

- Fitting Models to Data Graphically

- Analytic Methods of Model Fitting

- Applying the Least-Square

Criterion

8–10 - Experimental Modeling

- High-Order Polynomial Models

- Smoothing: Low-Order Polynomial

Models

- Cubic Spline Models

7.5 - - Assigned instructor(s)

for the semester.

7.5 - - Assigned instructor(s)

for the semester.

7.5 - - Assigned instructor(s)

for the semester.

SCMA 362 (1/2) 146 Mathematics in Physical Sciences


11–13 - Simulation Modeling

- Simulating Deterministic Behavior:

Area Under a Curve

- Generating Random Numbers

- Simulating probabilistic Behavior

9 - - Assigned instructor(s)

for the semester.

14–16 - Dimensional analysis and similitude 9 - - Assigned instructor(s)

- Dimensions as Products

for the semester.

- The Process of dimensional

Analysis

11. Teaching Method(s)

Lecture and biweekly assignment.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

Homework 20%

Midterm Examinations 40%

Final Examinations 40%

14. Course Evaluation

Grade is evaluated from homework, midterm and final examinations in the form of A, B + , B, C + , C, D + , D

and F using normal curve.

15. Reference(s)

F. R. Giordano, M.D. Weir, W. P. Fox, A First Course in Mathematical Modeling, THOMSON, 2003

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 362 (2/2) 147 Mathematics in Physical Sciences


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 363 Course Title Partial Differential Equations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 163 or consent of instructor

5. Type of Course Core course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

First order linear equations; classification of second order equations; canonical forms; boundary value

problems; separation of variables; Abel’s Theorem; Sturm-Liouville theory; eigenfunction expansions; separation

by subproblems; solutions in geometry of Cartesian, cylindrical and spherical symmetry; evolution problems;

existence, uniqueness and continuity of solutions; Laplace and Fourier transforms; initial value problems;

semi-infinite domains; nonhomogeneous equations; Helmholtz and telegraph equations.

9. Course Objective(s)

Core course in the mathematics program.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction to partial differential 3 - - Assigned instructor(s)

equations

for the semester.

2 - First order linear equations 3 - - Assigned instructor(s)

for the semester.

3 - Classification of second order equations

- Canonical coordinate transformations

4 - Well-posed problems

- D’Alembert’s solution of the wave

equation

5 - Boundary conditions

- Separation of variables, Fourier series

- Abel’s theorem

6 - Sturm-Liouville theory

- Completeness

7 - Separation by subproblem

- Solutions in cylindrical coordinates

- Fourier-Bessel series

8 - Solutions in spherical coordinates

- Fourier-Legendre series

- Double Fourier series

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 363 (1/2) 148 Partial Differential Equations


9 - Evolution problems

- Partial eigenfunction expansions

- Existence of solution

10 - Uniqueness of solution

- Maximum-minimum principles

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

11 - Laplace transforms 3 - - Assigned instructor(s)

for the semester.

12 - Evolution problems with nonhomogeneous

boundary conditions

13 - Initial value problems

- Fourier transforms

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

14 - Semi-infinite domains 3 - - Assigned instructor(s)

for the semester.

15 - Nonhomogeneous partial differential

equations

3 - - Assigned instructor(s)

for the semester.

16 - Helmholtz equation

3 - - Assigned instructor(s)

- Telegraph equation

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the properties and solutions of partial differential equations

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Fourier Series and Boundary Value Problems, J. W. Brown and R. V. Churchill, McGraw Hill.

2. Applied Partial Differential equations for Scientists and Engineers, S. J. Farlow, Wiley.

3. Applied Partial Differential Equations, P. DuChateau and D. Zachmann, Harper & Row.

16. Instructor(s)

To be arranged.

17. Course Coordinator

Attend all classes. Complete all assignments without copying.

SCMA 363 (2/2) 149 Partial Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 364 Course Title Integral Equations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 363 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

General properties of integral equations; Fredholm and Volterra equations; equations of the first and second

kinds; kernels; series solutions; orthogonalization; biorthogonal functions; Neumann series; solutions by integral

transforms; Hilbert-Schmidt theory; nonhomogeneous equations; Green’s functions.

9. Course Objective(s)

To provide an introduction to the analytical issues posed by integral equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction to integral equations 3 - - Assigned instructor(s)

for the semester.

2 - Fredholm integral equations 3 - - Assigned instructor(s)

for the semester.

3 - Volterra integral equations 3 - - Assigned instructor(s)

for the semester.

4 - Integral equations of the first and

second kinds

3 - - Assigned instructor(s)

for the semester.

5 - Existence of solutions 3 - - Assigned instructor(s)

for the semester.

6 - Review of Sturm-Liouville theory 3 - - Assigned instructor(s)

for the semester.

7 - Kernels of integral equations 3 - - Assigned instructor(s)

for the semester.

8 - Series solutions 3 - - Assigned instructor(s)

for the semester.

9 - Orthogonalisation 3 - - Assigned instructor(s)

for the semester.

10 - Solutions via biorthogonal

functions

3 - - Assigned instructor(s)

for the semester.

11 - Neumann series 3 - - Assigned instructor(s)

for the semester.

12 - Review of integral transforms 3 - - Assigned instructor(s)

for the semester.

SCMA 364 (1/2) 150 Integral Equations


13 - Solution of integral equations by

integral transforms

3 - - Assigned instructor(s)

for the semester.

14 - Hilbert-Schmidt theory 3 - - Assigned instructor(s)

for the semester.

15 - Nonhomogeneous integral equations 3 - - Assigned instructor(s)

for the semester.

16 - Solutions via Green’s functions 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the properties and solutions of integral equations

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Integral Equations, F. Smithes, Cambridge.

2. Methods of Theoretical Physics, P. M. Morse and H. Feshbach, McGraw Hill.

3. Mathematical Methods for Physicists, G. Arfken and H. Weber, Harcourt/Academic

4. Introduction to Integral Equations with Applications, A. J. Jerri, Wiley.

5. A Course on Integral Equations, A. C. Pipkin, Springer-Verlag.

6. Integral Equations, H. Hochstadt, Wiley.

7. Integral Equations, B. L. Moiseiwitsch, Pitman.

16. Instructor(s)

To be arranged.

17. Course Coordinator

To be arranged.

SCMA 364 (2/2) 151 Integral Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 365 Course Title Special Functions

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Infinite series; improper integrals and infinite products; Gamma functions and related functions; Legendre

polynomials; other orthogonal polynomials; Bessel functions; boundary value problems.

9. Course Objective(s)

The primary aim of this course is to study special functions that commonly arise in practice both in Physics

and Engineering in the form of solutions of certain differential equations.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 - Infinite Series, Improper Integrals,

and Infinite Products

- Infinite Series of Constants

- Infinite Series of Functions

- Asymptotic Series

- Fourier Trigonometric Series

- Improper Integrals

- Infinite Products

6 - - Assigned instructor(s)

for the semester.

3–5 - The Gamma Function and Related

Functions

- Gamma Function

- Beta Function

- Incomplete Gamma Function

- Digamma and Polygamma Functions

- The Error Function

9 - - Assigned instructor(s)

for the semester.

SCMA 365 (1/2) 152 Special Functions


6–8 - Legendre polynomials and Related

Functions

- The Generating Function

- Other Representations of the Legendre

Polynomials

- Legendre Series

- Convergence of the Series

- Legendre Functions of the Second

Kind

- Associated Legendre Functions

9–11 - Other Orthogonal Polynomials

- Hermite Polynomials

- Laguerre Polynomials

11–14 - Bessel Functions

- Bessel Functions of the First Kind

- Integral Representations and Integrals

of Bessel Functions

- Bessel Series

- Bessel Functions of the Second and

Third Kinds

- Differential equations Related to

Bessel’s Equation

15–16 - Boundary-Value Problems

- Spherical Domains: Legendre Functions

- Circular and Cylindrical Domains:

Bessel Functions

9 - - Assigned instructor(s)

for the semester.

7.5 - - Assigned instructor(s)

for the semester.

10.5 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture and biweekly assignment.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

Homework 20%

Midterm Examinations 40%

Final Examinations 40%

14. Course Evaluation

Grade is evaluated from homework, midterm and final examinations in the form of A, B + , B, C + , C, D + , D

and F using normal curve.

15. Reference(s)

C. Andrews, Special Functions for Engineers and Applied Mathematics, L. Macmillan Publishing Company,

1985

16. Instructor(s)

Assigned instructor(s) for the semester.

SCMA 365 (2/2) 153 Special Functions


17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 365 (3/2) 154 Special Functions


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 366 Course Title Life Actuarial Mathematics I

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Stochastic approach to life insurance models using the life table and mathematics of finance; calculation of

net premiums and reserves for life insurance; types of annuity products.

9. Course Objective(s)

For students to have knowledge on concepts of life actuarial mathematics.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Stochastic approach to life insurance

models using the life table and

mathematics of finance

3 - Stochastic approach to life insurance

models using the life table and

mathematics of finance

4 - Stochastic approach to life insurance

models using the life table and

mathematics of finance

5 - Stochastic approach to life insurance

models using the life table and

mathematics of finance

6 - Stochastic approach to life insurance

models using the life table and

mathematics of finance

7 - Calculation of net premiums and

reserves for life insurance

8 - Calculation of net premiums and

reserves for life insurance

9 - Calculation of net premiums and

reserves for life insurance

10 - Calculation of net premiums and

reserves for life insurance

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 366 (1/2) 155 Life Actuarial Mathematics I


11 - Types of annuity products 3 - - Assigned instructor(s)

for the semester.

12 - Types of annuity products 3 - - Assigned instructor(s)

for the semester.

13 - Types of annuity products 3 - - Assigned instructor(s)

for the semester.

14 - Types of annuity products 3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 366 (2/2) 156 Life Actuarial Mathematics I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 367 Course Title Game Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Matrix games; extensive forms; game trees; mixed strategies; dominating strategies; bimatrix games; normal

forms; Nash equilibrium; repeated games.

9. Course Objective(s)

The student should know the basic concepts and theorems of game theory and be able to apply them.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Two-Person Zero-Sum Games:

- Matrix games

6 - - Assigned instructor(s)

for the semester.

3 - Game trees 3 - - Assigned instructor(s)

for the semester.

4–5 - Utility theory 6 - - Assigned instructor(s)

for the semester.

6–7 Two-Person Non-Zero-Sum Games:

- Nash Equilibrium

6 - - Assigned instructor(s)

for the semester.

8 - Prisoners’ Dilemma 3 - - Assigned instructor(s)

for the semester.

9–10 - Evolutionary Game Theory 6 - - Assigned instructor(s)

for the semester.

11–12 N-Person Games:

- Stable sets

6 - - Assigned instructor(s)

for the semester.

13–14 - The Core 6 - - Assigned instructor(s)

for the semester.

15–16 - Repeated Games 6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm Exam 50%

2. Final Exam 50%

SCMA 367 (1/2) 157 Game Theory


14. Course Evaluation

Final course grades are assigned based on a 100-point total as follows:

90–100 A

86–89 B +

80–85 B

76–79 C +

70–75 C

66–69 D +

60–65 D

0–59 F

15. Reference(s)

1. Game Theory And Strategy, Philip Straffin, 1993, The Mathematical Association of America.

2. A Course In Game Theory, Osbourne and Rubinstein, 1994, Massachusetts Institute of Technology.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 367 (2/2) 158 Game Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 368 Course Title Mathematical Transforms

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Laplace transforms; Fourier transforms; cosine and sine transforms; finite transforms; Z-transforms; other

transforms.

9. Course Objective(s)

To provide an introduction to the subject of mathematical transforms, including their analytical properties

and applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction to the Laplace

transform

3 - - Assigned instructor(s)

for the semester.

2 - Existence of the Laplace transform 3 - - Assigned instructor(s)

for the semester.

3 - Convolution 3 - - Assigned instructor(s)

for the semester.

4 - Review of residue theory 3 - - Assigned instructor(s)

for the semester.

5 - Complex inversion formula

- Bromwich contour

6 - Applications of the Laplace

transform

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

7 - Fourier integral theorem 3 - - Assigned instructor(s)

for the semester.

8 - Fourier transform 3 - - Assigned instructor(s)

for the semester.

9 - Applications of the Fourier

transform

3 - - Assigned instructor(s)

for the semester.

10 - Cosine and sine transforms 3 - - Assigned instructor(s)

for the semester.

11 - Finite Fourier transforms 3 - - Assigned instructor(s)

for the semester.

12 - Fast Fourier transforms 3 - - Assigned instructor(s)

for the semester.

SCMA 368 (1/2) 159 Mathematical Transforms


13 - Z transforms 3 - - Assigned instructor(s)

for the semester.

14 - Linear, time invariant systems 3 - - Assigned instructor(s)

for the semester.

15 - Hankel transforms 3 - - Assigned instructor(s)

for the semester.

16 - Mellin transforms 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media

Whiteboards

13. Measurement and Evaluation of Student Achievement

- Development of analytical thinking processes

- Practical knowledge concerning the properties and solutions of mathematical transforms

14. Course Evaluation

Either

- Final examination 70%

Assignments 30%

Or

- Final examination 50%

Mid-term exam 30%

Assignments 20%

15. Reference(s)

1. Laplace Transforms, Schaum Outline Series, McGraw Hill.

2. Integral Transforms and Their Applications, L. Debnath, CRC Press.

3. Advanced Mathematics for Engineers and Scientists, Schaum Outline Series, McGraw Hill.

4. Fourier Series and Boundary Value Problems, J. W. Brown and R. V. Churchill, McGraw Hill.

5. Operational Mathematics, R. V. Churchill, McGraw Hill.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 368 (2/2) 160 Mathematical Transforms


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 369 Course Title Mathematical Methods

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Mathematical methods useful in any field which is of current interest.

9. Course Objective(s)

For students to have knowledge on concepts of mathematical methods.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2–15 - Mathematical methods useful in

any field which is of current interest

to students and the instructor

42 - - Assigned instructor(s)

for the semester.

16 - Mellin transforms 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 369 (1/1) 161 Mathematical Methods


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 370 Course Title Introduction to Discrete Mathematics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Sets, relations and functions; sequences; mathematical induction and recursion; elementary number theory;

graph theory; algorithms and applications to computing problems; boolean algebra; applications to computer

logic and logical designs.

9. Course Objective(s)

Study a number of topics which are often called discrete mathematics, such as set theory, combinatorics, and

graph theory. The concepts and techniques are useful in computer science, engineering and further study in

mathematics.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 - Sets, relations and functions, 6 - - Assigned instructor(s)

sequences

for the semester.

3–5 - Mathematical induction and recursion,

elementary number theory

9 - - Assigned instructor(s)

for the semester.

6–8 - relations, boolean algebra 9 - - Assigned instructor(s)

for the semester.

9–11 - graph theory 9 - - Assigned instructor(s)

for the semester.

12–13 - algorithms and applications to

computing problems

14–15 - applications to computer logic and

logical designs

6 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

16 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

1. Lecture

2. Discussion

3. Presentation

12. Teaching Media

1. Text and handouts

2. Transparencies

SCMA 370 (1/2) 162 Introduction to Discrete Mathematics


13. Measurement and Evaluation of Student Achievement

Grades will be assigned according to the following point scale:

90–100 A

85–89 B +

80–84 B

75–79 C +

70–74 C

60–69 D +

50–59 D

0–49 F

14. Course Evaluation

- Graded homework, participation in class and group work 10%

- Exam I 20%

- Exam II 20%

- Quizzes 10%

- Final exam 40%

15. Reference(s)

1. Grimaldi, R., Discrete and Combinatorial Mathematics, 4th ed., Addison-Wesley, New York, U.S.A.

2. Hein, J., Discrete Mathematics, Jones and Bantlett Publishers, Massachusetts, U.S.A.

3. Kolman/Busky/Ross, Discrete Mathematical Structures, Prentice Hall, N.J., U.S.A.

4. Rosen, K., Discrete Mathematics and Its Applications, McGraw-Hill, U.S.A.

5. Truss, J., Discrete Mathematics for Computer Scientists, Addison-Wesley, U.S.A.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 370 (2/2) 163 Introduction to Discrete Mathematics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 372 Course Title Coding Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Introduction to coding theory; basic algebra; linear code; use of matrices in linear code; maximum likelihood;

extended code; cyclic code.

9. Course Objective(s)

To understand and can apply the several types of coding.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 1.Introduction to coding theory

- Entropy and Mutual information

9 - - Assigned instructor(s)

for the semester.

4 - Rate-distortion function 3 - - Assigned instructor(s)

for the semester.

5 - Source coding theorem 3 - - Assigned instructor(s)

for the semester.

6 - Capacity-Cost function 3 - - Assigned instructor(s)

for the semester.

7 - Channel coding Theorem 3 - - Assigned instructor(s)

for the semester.

8 - Maximum likelihood 3 - - Assigned instructor(s)

for the semester.

9 2.Linear code

- Generator Parity-Check Matrices

2 - - Assigned instructor(s)

for the semester.

9–10 - Syndrome decoding 2 - - Assigned instructor(s)

for the semester.

10 - Hamming codes 2 - - Assigned instructor(s)

for the semester.

11 - Extended code 3 - - Assigned instructor(s)

for the semester.

11–12 - MacWilliams identities 3 - - Assigned instructor(s)

for the semester.

12–13 - Goppa codes 3 - - Assigned instructor(s)

for the semester.

SCMA 372 (1/2) 164 Coding Theory


13–14 3.Cyclic code

- BCH codes

3 - - Assigned instructor(s)

for the semester.

15 - Reed-Solomon codes

- Golay codes

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture in class and home assignment are given.

12. Teaching Media

-

13. Measurement and Evaluation of Student Achievement

1. Two class tests 50%

2. Final exam 50%

14. Course Evaluation

Grading scale is

85–100 A

80–85 B +

74–79 B

68–73 C +

62–67 C

56–61 D +

50–55 D

0–49 F

15. Reference(s)

1. The Theory of Information and coding,R.J.McEliece, Addison-Wesley Publishing Co.

2. Basic Concepts in Information Theory and Coding, S.W.Golomb, Plenum Press, New York and London.

16. Instructor(s)

Dr. Boriboon Novaprateep

17. Course Coordinator

Dr. Boriboon Novaprateep

SCMA 372 (2/2) 165 Coding Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 373 Course Title Introduction to Mathematical Logic

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Induction; formal systems; language of propositional logic; tautological consequence; adequate set of

connectives; Soundness Theorem; first-order logic.

9. Course Objective(s)

The student should know the definitions and theorems of mathematical logic and be able to use them.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Propositional Logic:

- Formal Systems

6 - - Assigned instructor(s)

for the semester.

3 - Languange of Propositional Logic 3 - - Assigned instructor(s)

for the semester.

4–5 - Induction 6 - - Assigned instructor(s)

for the semester.

6 - Connectives 3 - - Assigned instructor(s)

for the semester.

7–8 - Soundness and Compactness 6 - - Assigned instructor(s)

for the semester.

9–10 First-Order Logic:

- First-Order Language

4 - - Assigned instructor(s)

for the semester.

10–12 - Models and Truth 6 - - Assigned instructor(s)

for the semester.

12–14 - Deductive Calculus 8 - - Assigned instructor(s)

for the semester.

15–16 - Soundness and Completeness 6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm Exam 50%

2. Final Exam 50%

SCMA 373 (1/2) 166 Introduction to Mathematical Logic


14. Course Evaluation

Final course grades are assigned based on a 100-point total as follows:

90–100 A

86–89 B +

80–85 B

76–79 C +

70–75 C

66–69 D +

60–65 D

0–59 F

15. Reference(s)

A Mathematical Introduction to Logic, Herbert Enderton, 2001, Academic Press.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 373 (2/2) 167 Introduction to Mathematical Logic


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 374 Course Title Introduction to Graph Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Fundamental concepts; connectedness of a graph; paths; trees; circuits; cutsets; matrix representations;

planar and dual graphs; domination; independence; chromatic numbers; transport network; Max-Flow Min-Cut

Theorem; complete matching; maximal matching.

9. Course Objective(s)

Students understand the fundamental concepts of graph theory and improve their ability to read and create

mathematical proofs.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Basic concepts and definitions 6 - - Assigned instructor(s)

for the semester.

3–4 Tree and Distance 6 - - Assigned instructor(s)

for the semester.

5–6 Connectivity Paths and Digraphs 6 - - Assigned instructor(s)

for the semester.

7 Adjacency matrix

- Counting walks, and triangles

in a graph, using power of the

adjacency matrix.

3 - - Assigned instructor(s)

for the semester.

8 Midterm 3 - - Assigned instructor(s)

for the semester.

9–10 Graph Coloring 6 - - Assigned instructor(s)

for the semester.

11–12 Planar Graphs 6 - - Assigned instructor(s)

for the semester.

13–14 Ramsey Theory 6 - - Assigned instructor(s)

for the semester.

15–16 Additional Topics depending on student

interest

11. Teaching Method(s)

Lecture

12. Teaching Media


6 - - Assigned instructor(s)

for the semester.

SCMA 374 (1/2) 168 Introduction to Graph Theory


13. Measurement and Evaluation of Student Achievement

There will be two regular exams: midterm test and final exam. Several homework are assigned and collected

for grading.

14. Course Evaluation

Grade will be based on: 20 % for the homework, 40 % for midterm, 40 % for the final. Course grades will be

determined roughly as :

85–100 A

81–84 B +

75–80 B

70–74 C +

60–69 C

55–59 D +

51–54 D

0–50 F

15. Reference(s)

1. Graphs and Digraphs, 3rd edition, G.Chartrand and L.Lesniak.

2. Graph an Introductory Approach, Robin J.Wilson and John J.Watkins.

16. Instructor(s)

Staff

17. Course Coordinator

Staff

SCMA 374 (2/2) 169 Introduction to Graph Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 376 Course Title Introduction to Combinatorial

3. Number of Credits 3(3-0) (Lecture-Lab)

Mathematics

4. Prerequisite SCMA 283 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Permutations and combinations; Stirling’s formula; generating functions; partition of integers; recurrence

relations; inclusion-exclusion principle; derangements; Polya’s theory of counting; equivalence classes;

generalization of Polya’s Theorem.

9. Course Objective(s)

To achieve in learning in combinatorial mathematics and important concern theorems.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 - Introduction

- Permutation and Combination

6 - - Instructor of Mathematics

Department

3–4 - Stirling Formula 6 - - Assigned instructor(s)

for the semester.

5–6 - Generating Function 6 - - Assigned instructor(s)

for the semester.

7 - Partition and Integers 3 - - Assigned instructor(s)

for the semester.

8 - Recurrence Relations 3 - - Assigned instructor(s)

for the semester.

9–10 - Inclusion-exclusion principle 6 - - Assigned instructor(s)

for the semester.

11 - Derengements 3 - - Assigned instructor(s)

for the semester.

12–13 - Polya’s Theory of counts 6 - - Assigned instructor(s)

for the semester.

14 - Equivalent classes 3 - - Assigned instructor(s)

for the semester.

15–16 - Generalization of Polya’s Theorem 6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture and Practice.

12. Teaching Media

Transparency; Computer; Overhead Projector; or consent of instructor.

SCMA 376 (1/2) 170 Introduction to Combinatorial Mathematics


13. Measurement and Evaluation of Student Achievement

Examination and Senior Project; or consent of instructor.

14. Course Evaluation

- Class Attendance & Senior Project 20%

- Midterm Examination 30%

- Final Examination 50%

15. Reference(s)


16. Instructor(s)

Instructor of Mathematics Departments

17. Course Coordinator

Instructor of Mathematics Departments

SCMA 376 (2/2) 171 Introduction to Combinatorial Mathematics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 380 Course Title Probability Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 213 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Probability spaces; random variables; probability distributions; special distributions; law of large numbers;

limiting distributions.

9. Course Objective(s)

At the completion of this course students should be able to

1. have a knowledge and understand probability theory

2. explain probability theory

3. solve problems of probability theory

4. apply probability theory to solve some real problems

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 Probability spaces 6 - - Assigned instructor(s)

for the semester.

3–4 Random variables 6 - - Assigned instructor(s)

for the semester.

5–7 Probability distributions 9 - - Assigned instructor(s)

for the semester.

8–11 Special distributions 12 - - Assigned instructor(s)

for the semester.

14–15 Limiting distributions 9 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out.

13. Measurement and Evaluation of Student Achievement

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

15. Reference(s)

1. Cramer H. (1955). The Elements of Probability Theory and Some of Its Applications, John Wiley and

Sons, Inc., New York.

SCMA 380 (1/2) 172 Probability Theory


2. Feller, W. (1957). An Introduction to Probability Theory and Its Applications, 2nd edition, John Wiley

and Sons, Inc., New York.

3. Parzen, E. (1960). Modern Probability and Its Applications, John Wiley and Sons, Inc., New York.

4. Ross, S. (1976). A First Course in Probability, Macmillian Publishing Co., Inc., New York.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 380 (2/2) 173 Probability Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 382 Course Title Experimental Design

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Basic principles of experimental design; colmpletely randomized design; randomized block design; Latin

square design; factorial experiments; confounding; split-plot experiment.

9. Course Objective(s)

At the completion of this course students should be able to

1. have a knowledge and understand experimental design

2. design experiment and explain the experiment

3. analyze data and write a mathematical model and interprete the result from each experiment

4. use experimental design and apply to real problem.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Basic principles of experimental

design

6 - - Assigned instructor(s)

for the semester.

3–4 Completely randomized design 6 - - Assigned instructor(s)

for the semester.

5–6 Randomized block design 6 - - Assigned instructor(s)

for the semester.

7–8 Latin square design 6 - - Assigned instructor(s)

for the semester.

9–11 Factorial experiments 12 - - Assigned instructor(s)

for the semester.

12–13 Confounding 6 - - Assigned instructor(s)

for the semester.

14–15 Split-plot experiment 6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out.

13. Measurement and Evaluation of Student Achievement

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

SCMA 382 (1/2) 174 Experimental Design


14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

15. Reference(s)

1. ¨ÃÑ- ¨Ñ¹·ÅÑ¡¢³Ò (2523) ÊÔµÔÇÔ¸ÕÇÔà¤ÃÒÐËŒáÅÐÇҧἹ§Ò¹ÇԨѠÊíҹѡ¾ÔÁ¾Œä·ÂÇѲ¹Ò¾Ò¹Ôª ¡Ãا෾ÁËÒ¹¤Ã

2. ÊØþŠÍØ»´ÔÊÊ¡ØÅ (2536) ÊÔµÔ¡ÒÃÇҧἹ¡Ò÷´Åͧ àňÁ 1 ÊËÁÔµÃÍÍ¿à«· ¡Ãا෾ÁËÒ¹¤Ã

3. Box, G.E.P.; Hunter, W.G. and Hunter, J.S. (1978). Statistics for experiments: An Introduction to design,

data analysis, and model building. John Wiley and Sons, Inc., New York.

4. Cochran, W.G. and Cox, G.M. (1957). Experimental designs. 2nd edition, John Wiley and Sons, Inc.,

New York.

5. Cox, D.R.(1958). Planning of Experiments. John Wiley and Sons, Inc., New York.

6. John, P.W.M. (1971). Statistical design and analysis of experiments. Macmillan Company, New York.

7. Kempthorne, O. (1983). Design and analysis of experiments. Robert E. Krieger Publishing Company,

Florida.

8. Montgomery, D.C. (1991). Design and analysis of experiments. 3rd edition, John Wiley and Sons, Inc.,

New York.

9. Snedecor, G.W. and Cochran, W.G. (1967). Statistical Methods. 6th edition, the Iowa State University

Press, Iowa.

10. Steel, R.G.D. and Torrie, J.H. (1960). Principles and procedures of statistics. McGraw-Hill Book Co.,

Inc., New York.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 382 (2/2) 175 Experimental Design


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 383 Course Title Statistical Methods

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Data description; probability and probability distributions; statistical inferences; categorical data; inferences

about population variance; linear regression and correlation; inferences related to linear regression and

correlation; introduction to the analysis of variance; multiple regression and the general linear model; analysis

of variance for some standard experimental designs; multiple comparisons; the analysis of covariance; data

management.

9. Course Objective(s)

To introduce essential concepts of some statistical methods and to develop students’ skills in using statistical

program SPSS.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Chapter 1 Describing Data with

Graphs

- 1.1 Types of Variables

- 1.2 Graphs for Categorical Data

- 1.3 Graphs for Quantitative Data

- 1.4 Relative Frequency Histograms

Introducing SPSS

3 - - Assigned instructor(s)

for the semester.

2 Chapter 2 Describing Data with Numerical

Measures

- 2.1 Measures of Center

- 2.2 Measures of Variability

- 2.3 Measures of Relative Standing

- 2.4 The Five-Number Summary

and the Box Plot

3 - - Assigned instructor(s)

for the semester.

SCMA 383 (1/3) 176 Statistical Methods


3 Chapter 3 Describing Bivariate Data

- 3.1 Bivariate Data

- 3.2 Graphs for Quantitative Variables

- 3.3 Scatterplots for Two Quantitative

Variables

- 3.4 Numerical Measures for Quantitative

Bivariate Data

Chapter 4 Probability Distributions

- 4.1 Probability Distributions for

Discrete Random Variables

4 - 4.2 Probability Distributions for

Continuous Random Variables

- 4.3 The Normal Distribution

5 Chapter 5 Statistical Inferences

- 5.1 Interval Estimation of Some

Parameters

- 5.2 Tests of Hypotheses about

Some Parameters

6 Chapter 6 The Analysis of Variance

- 6.1 The Design of an Experiment

- 6.2 The Completely Randomized

Design: A One-Way Classification

- 6.3 The Analysis of Variance for a

Completely Randomized Design

7 - 6.4 Ranking Population Means

- 6.5 The Randomized Block Design:

A Two-Way Classification

- 6.6 The Analysis of Variance for a

Randomized Block Design

8 - 6.7 The a × b Factorial Experiment:

A Two-Way Classification

- 6.8 The Analysis of Variance for an

a × b Factorial Experiment

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 Midterm Examination 3 - - Assigned instructor(s)

for the semester.

10 Chapter 7 Linear Regression and Correlation

- 7.1 A Simple Linear Model

- 7.2 The Method of Least Squares

- 7.3 An Analysis of Variance for

Linear Regression

3 - - Assigned instructor(s)

for the semester.

SCMA 383 (2/3) 177 Statistical Methods


11 - 7.4 Inferences about Regression

Parameters

- 7.5 Measuring the Strength of the

Relationship

- 7.6 Checking the Regression

Assumptions

12 - 7.7 Estimation and Prediction Using

the fitted Line

- 7.8 Correlation Analysis

13 Chapter 8 Multiple Regression Analysis

- 8.1 The Multiple Regression Model

- 8.2 A Multiple Regression Analysis

- 8.3 A Polynomial Regression Model

14 - 8.4 Using Quantitative And Qualitative

Predictor Variables in a Regression

Model

- 8.5 Testing Sets of Regression

Coefficients

15 Chapter 9 Analysis of Categorical

Data

- 9.1 The Goodness-of-Fit Test

- 9.2 Test for Independence

16 - 9.3 Test for Homogeneity

- 9.4 Testing for Several Proportions

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instructor gives lecture weekly. Students can ask questions while the class is conducted. Students have to

submit homework assigned regularly by the instructor.

12. Teaching Media

A required textbook, chalk and board or any desired media such as an overhead projector or a visual

presentation.

13. Measurement and Evaluation of Student Achievement

- Homework 20%

- Midterm Examination 40%

- Final Examination 40%

14. Course Evaluation

90–100 A

84–89 B +

78–83 B

72–77 C +

66–71 C

60–65 D +

54–59 D

SCMA 383 (3/3) 178 Statistical Methods


0–53 F

15. Reference(s)

1. Probability and Statistics. Eleventh Edition. Mendenhall, Beaver and Beaver.

2. Probability and Statistics for Engineers and Scientists. Fifth Edition. Walpole and Myers.

16. Instructor(s)

A staff from mathematics department.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 383 (4/3) 179 Statistical Methods


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 384 Course Title Nonparametric Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Selected nonparametric methods; one and two sample location tests; estimation methods; measures of

association; relationship with classical parametric procedures.

9. Course Objective(s)

Nonparametric methods are recognized as a significant branch of modern statistics. Classical methods for

measurement data are based on the assumption of normality for populations sampled; however, student will be

introduced nonparametric methods which were designed to avoid this assumption.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 1. An Introduction to Nonparametric

Statistical Methods

2. The Dichotomous Data Problem

- A Binomial Test

- An Estimator for the Probability of

Success

- A Confidence interval for the Probability

of Success

3 - - Assigned instructor(s)

for the semester.

2 3. The One-Sample Location Problem

- A Distribution-Free Signed Rank

Test

- An Estimator Associated with

Wilcoxon’s Signed Rank Statistic

- A Distribution-Free Confidence Interval

Based on Wilcoxon’s Signed

Rank Test

3 - A Distribution-Free Sign Test

- An Estimator Associated with the

Sign Statistic

- A Distribution-Free Confidence Interval

Based on the Sign Test

4 - An Asymptotically Distribution-

Free Test of Symmetry

- Efficiencies

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 384 (1/3) 180 Nonparametric Statistics


5 4. The Two-Sample Location Problem

- A Distribution-Free Rank Sum Test

- An Estimator Associated with

Wilcoxon’s Rank Sum Statistic

- A Distribution-Free Confidence Interval

Based on Wilcoxon’s Rank

Sum Test

- Efficiencies

6 5. The Two-Sample Dispersion Problem

- A Distribution-Free Rank Test

- A Distribution-Free Ranklike Test

- An Estimator Associated with

Moses’ Ranklike Statistic

7 - A Distribution-Free Confidence Interval

Based on Moses’ Ranklike

Test

- An Asymptotically Distribution-

Free Test Based on the Jackknife

- Efficiencies

8 6. The One-Way Layout

- A Distribution-Free Test

- A Distribution-Free Test for Ordered

Alternatives

9 - A Distribution-Free Multiple Comparisons

- A contrast Estimator

- Efficiencies

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

10 - Midterm Examination 3 - - Assigned instructor(s)

for the semester.

11 7. The Two-Way Layout

- Analyses Associated with Friedman

Rank Sums

12 - Analyses Associated with Wilcoxon

Signed Ranks

13 8. The Independence Problem

- A Distribution-Free Test for Independence

- An Estimator Associated with the

Kendal Statistic

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 384 (2/3) 181 Nonparametric Statistics


14 - An Asymptotically Distribution-

Free Confidence Interval Based on

the Kendal Statistic

- Efficiencies

3 - - Assigned instructor(s)

for the semester.

15 9. Regression Problems Involving

Slopes

3 - - Assigned instructor(s)

for the semester.

- One Regression Line

- Two Regression Lines

11. Teaching Method(s)

Instructor gives lecture weekly. Students can ask questions while the class is conducted. Students have to

submit homework assigned regularly by the instructor.

12. Teaching Media

A required textbook, chalk and board or any desired media such as an overhead projector or a visual

presentation.

13. Measurement and Evaluation of Student Achievement

- Homework 20%

- Midterm Examination 40%

- Final Examination 40%

14. Course Evaluation

90–100 A

84–89 B +

78–83 B

72–77 C +

66–71 C

60–65 D +

54–59 D

0–53 F

15. Reference(s)

1. Jean D. G. Nonparametric Methods for Quantitative Analysis. Holt, Rinehart and Winston.

2. Jean D. G. Nonparametric Methods for Quantitative Analysis. Holt, Rinehart and Winston.

3. Wolfe D. and Hollander M. Nonparametric Statistical Methods. John Wiley & Sons.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 384 (3/3) 182 Nonparametric Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 386 Course Title Queuing Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 283 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Queuing models; probability distributions of interarrival times; probality distributions of service times; single

server model with Poisson input and exponential service; multiple server model with Poisson input and

exponential service; birth and death process; other queuing models.

9. Course Objective(s)

To achieve learning in various Queuing Models and how to apply them to situation in real life.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–2 - Introduction

6 - - Staff of the department

- Basic Structure of Queuing models

of mathematics who

- Example of Real Queuing Systems

teaches this course in

-

that semester.

3–4 - System Approach:

- Formulation, Modeling, Evaluating,

Decision, System Analysis in

Queuing

5 - Probability distributions of interarrival

times

6 - Probability distributions of service

times

7 - Single server models with Poisson

input and Exponential service

8 - Multiple server model with Poisson

input and Exponential service

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 - Birth and Death process 3 - - Assigned instructor(s)

for the semester.

10–13 - Other queuing models 12 - - Assigned instructor(s)

for the semester.

14–16 - Application of Queuing Theory and

System Approach; Practice by doing

Senior Project (Self Study)

11. Teaching Method(s)

Lecture and Practice.

12 - - Assigned instructor(s)

for the semester.

SCMA 386 (1/2) 183 Queuing Theory


12. Teaching Media

Transparency; Computer; Overhead Projector; or consent of instructor.

13. Measurement and Evaluation of Student Achievement

Examination and Senior Project; or consent of instructor.

14. Course Evaluation

- Class Attendance & Senior Project 20%

- Midterm Examination 30%

- Final Examination 50%

15. Reference(s)

Queuing Methods for Service and Manufacturing, Radolph W. Hall, 1991, Prentice Hall, Inch.

16. Instructor(s)

Instructor of Mathematics Departments

17. Course Coordinator

Instructor of Mathematics Departments

SCMA 386 (2/2) 184 Queuing Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 387 Course Title Inventory Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Inventory models; use of linear programming; convex and concave costs; algorithms; planning horizon

analysis; probabilistic inventory models; static models; order quantity models; stochastic dynamic continuous

review models.

9. Course Objective(s)

To achieve in Learning in Inventory Models, and use of Linear Programming; Convex and Concave cost;

Algorithm; Planning horizon analysis; Probabilistic inventory models; Static models; Order quantity models;

Stochastic dynamic continuous review models.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 - Inventory Models 6 - - Instructor of Mathematics

Department

3–4 - Use of Linear Programming 6 - - Assigned instructor(s)

for the semester.

5–7 - Convex and Concave cost 9 - - Assigned instructor(s)

for the semester.

8–10 - Algorithm; Planning horizon

analysis

11–14 - Probabilistic inventory models;

Static models; Order quantity

models

9 - - Assigned instructor(s)

for the semester.

12 - - Assigned instructor(s)

for the semester.

15–16 - Stochastic dynamic continuous review

models.

for the semester.

9 - - Assigned instructor(s)

11. Teaching Method(s)

Lecture and Practice.

12. Teaching Media

Transparency; Computer; Overhead Projector; or consent of instructor.

13. Measurement and Evaluation of Student Achievement

Examination and Senior Project; or consent of instructor.

14. Course Evaluation

- Class Attendance & Senior Project 20%

- Midterm Examination 30%

- Final Examination 50%

SCMA 387 (1/2) 185 Inventory Theory


15. Reference(s)

Inventory Theory

16. Instructor(s)

Instructor of Mathematics Departments

17. Course Coordinator

Instructor of Mathematics Departments

SCMA 387 (2/2) 186 Inventory Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 391 Course Title Special Topics I

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 3 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 45 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 391 (1/1) 187 Special Topics I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 392 Course Title Special Topics II

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 3 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 45 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 392 (1/1) 188 Special Topics II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 396 Course Title Seminar I

3. Number of Credits 1(1-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Core course

6. Session/Academic Year

First semester/2007

7. Course Conditions 1

8. Course Description

Topics to be announced by students during the term; attendance required.

9. Course Objective(s)

To provide students with an opportunity to do a self-study guided by instructors and to practise a

mathematical presentation.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Students and instructors set up agreements

on the course.

for the semester.

3 - - Assigned instructor(s)

2–16 Students do their searching and selfstudy,

announce their schedules

for the semester.

45 - - Assigned instructor(s)

and abstracts, give presentations,

and attend every class member’s

presentation.

11. Teaching Method(s)

Seminar.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

To be set up at the first class.

14. Course Evaluation

To be set up at the first class.

15. Reference(s)

Provided by students.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 396 (1/1) 189 Seminar I


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 397 Course Title Seminar II

3. Number of Credits 1(1-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course/core course for Distinction Program

6. Session/Academic Year

Second semester/2007

7. Course Conditions 2

8. Course Description

Topics to be announced by students during the term; attendance required.

9. Course Objective(s)

To provide students with an opportunity to do a self-study guided by instructors and to practise a

mathematical presentation.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Students and instructors set up agreements

on the course.

for the semester.

3 - - Assigned instructor(s)

2–16 Students do their searching and selfstudy,

announce their schedules

for the semester.

45 - - Assigned instructor(s)

and abstracts, give presentations,

and attend every class member’s

presentation.

11. Teaching Method(s)

Seminar.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

To be set up at the first class.

14. Course Evaluation

To be set up at the first class.

15. Reference(s)

Provided by students.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 397 (1/1) 190 Seminar II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 401 Course Title Special Topics I (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 391:

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 4 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 60 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 401 (1/2) 191 Special Topics I (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 402 Course Title Special Topics II (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 392:

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 4 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 60 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 402 (1/2) 192 Special Topics II (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 403 Course Title Special Topics III (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 491:

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 4 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 60 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 403 (1/2) 193 Special Topics III (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 404 Course Title Special Topics IV (Distinction)

3. Number of Credits 4(4-0) (Lecture-Lab)

4. Prerequisite Consent of instructor

5. Type of Course Specialized course/Distinction specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Rigorous approaches and proofs, challenging problems and self-study on the topics covered in SCMA 492:

Topics of current interest.

9. Course Objective(s)

To provide students with knowledge on topics of special interest to instructor.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 Introduction 4 - - Assigned instructor(s)

for the semester.

2–16 Topics of special interest to instructor 60 - - Assigned instructor(s)

- Rigorous discussion on challenging

for the semester.

problems and selected topics for

independent study

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

Depends on the topics.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 404 (1/2) 194 Special Topics IV (Distinction)


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 410 Course Title History of Mathematics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Introduction to the development of major mathematical concepts; evolution of abstract concept of spaces;

evolution of abstract algebra; evolution of function concepts; changes in the concept of rigor in mathematics

from 600 B.C.

9. Course Objective(s)

Student should know the historical development and applications of the following: arithmetic in various

number systems; the geometry associated with various number systems; practical mathematics of various

cultures; algebra, trigonometry and methods of solving equations, number theory and discrete mathematics,

statistics and probability, calculus, proofs including mathematical induction.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Egyptian Mathematics 1 - - Assigned instructor(s)

for the semester.

1 - Babylonian Mathematics 2 - - Assigned instructor(s)

for the semester.

2 - Greek Arithmetic 1 - - Assigned instructor(s)

for the semester.

2 - Geometry before Euclid 2 - - Assigned instructor(s)

for the semester.

3 - Books of Euclid 2 - - Assigned instructor(s)

for the semester.

3–4 - Archimedes and Apollonius 2 - - Assigned instructor(s)

for the semester.

4 - Roman Empire 1 - - Assigned instructor(s)

for the semester.

4–5 - China and India 3 - - Assigned instructor(s)

for the semester.

5 - Islamic algebra 2 - - Assigned instructor(s)

for the semester.

6 - Dark Ages 1 - - Assigned instructor(s)

for the semester.

SCMA 410 (1/3) 195 History of Mathematics


6 - Renaissance 1 - - Assigned instructor(s)

for the semester.

6–7 - Descartes, Fermat, etc. 2 - - Assigned instructor(s)

for the semester.

7 - Newton, Leibniz, etc. 1 - - Assigned instructor(s)

for the semester.

7–8 - Probability 2 - - Assigned instructor(s)

for the semester.

8 - Analysis 2 - - Assigned instructor(s)

for the semester.

9 - Algebra 2 - - Assigned instructor(s)

for the semester.

9–10 - Number Theory 2 - - Assigned instructor(s)

for the semester.

10 - Times of Revolution 2 - - Assigned instructor(s)

for the semester.

11 - The Age of Gauss 3 - - Assigned instructor(s)

for the semester.

12 - Analysis before midcentury 1 - - Assigned instructor(s)

for the semester.

12 - Geometry 2 - - Assigned instructor(s)

for the semester.

13 - Analysis after midcentury 1 - - Assigned instructor(s)

for the semester.

13–14 - Algebras 5 - - Assigned instructor(s)

for the semester.

15–16 - Twentieth Century 6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm Exam 50%

2. Final Exam 50%

14. Course Evaluation

Final course grades are assigned based on a 100-point total as follows:

90–100 A

86–89 B +

80–85 B

76–79 C +

70–75 C

SCMA 410 (2/3) 196 History of Mathematics


66–69 D +

60–65 D

0–59 F

15. Reference(s)

1. A History of Mathematics, Jeff Suzuki, 2002, Prentice-Hall.

2. Mathematicians and Their Times, Laurence Young, 1981, North-Holland.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 410 (3/3) 197 History of Mathematics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 430 Course Title General Topology

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

Second semester/2007

7. Course Conditions 1

8. Course Description

Topological spaces; continuous functions; product topology; convergence; separation and countability;

compactness; connectedness; metrizability.

9. Course Objective(s)

By the end of this course, students should:

1. understand the fundamental definitions and theorems of point set topology,

2. understand the topological notion of connectedness and compactness, and be able to derive their basic

properties,

3. understand the concepts of countability and separation, and know their significance in metrization theory.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 Topological spaces

- Subspace topology

6 - - Assigned instructor(s)

for the semester.

- Product topology on X × Y

3 Open and closed sets, Continuity 3 - - Assigned instructor(s)

for the semester.

4 The general product topology and

Metric Topology

3 - - Assigned instructor(s)

for the semester.

5–7 Connectedness 9 - - Assigned instructor(s)

for the semester.

8–10 Compactness 9 - - Assigned instructor(s)

for the semester.

11–12 The countability and separation axioms

- The Urysohn metrization theorem

6 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

1. M. A. Armstrong Basic Topology Springer.

2. J. Munkres, Topology Prentice Hall.

SCMA 430 (1/2) 198 General Topology


16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 430 (2/2) 199 General Topology


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 433 Course Title Elementary Algebraic Topology

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 430 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Topological spaces; continuous mappings; finite products; connectivity; compactness; manifolds; classifications

of surfaces; homotopic maps; fundamental groups; covering spaces; Lifting Theorem.

9. Course Objective(s)

The aim is to provide an introduction to topology and homotopy to students so that they know the meaning

of Topological spaces, compactness, manifolds and some important theorems for future studies and applications.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction

- Metric Topology

3 - - Prof. Yongwimon

Lenbury

2 - Properties of Metric Spaces 3 - - Assigned instructor(s)

for the semester.

3 - Topological Spaces 3 - - Assigned instructor(s)

for the semester.

4 - Construction of Spaces 3 - - Assigned instructor(s)

for the semester.

5 - Connectedness 3 - - Assigned instructor(s)

for the semester.

6 - Compactness 3 - - Assigned instructor(s)

for the semester.

7 - Separation and Convering Properties 3 - - Assigned instructor(s)

for the semester.

8 - Fundamental Group 3 - - Assigned instructor(s)

for the semester.

9 - Fundamental Group (continued) 3 - - Assigned instructor(s)

for the semester.

10 - Homotopy 3 - - Assigned instructor(s)

for the semester.

11 - Homotopy (continued) 3 - - Assigned instructor(s)

for the semester.

12 - Group Theory 3 - - Assigned instructor(s)

for the semester.

SCMA 433 (1/2) 200 Elementary Algebraic Topology


13 - Group Theory (continued) 3 - - Assigned instructor(s)

for the semester.

14 - Surfaces and Manifolds 3 - - Assigned instructor(s)

for the semester.

15 - Convering Spaces and Lifting 3 - - Assigned instructor(s)

theorem

for the semester.

11. Teaching Method(s)

1. Instruction by in class lectures with students occasionally required to present proofs in front of class.

2. Exercises and Assignments are given for students to get hands on practice.

12. Teaching Media

1. Transparencies

2. Occasionally Distributed Sheets

13. Measurement and Evaluation of Student Achievement

1. Exercise and Assignments 30%

2. Class Participation 30%

3. Paper Examination (Take Home over Night) 40%

14. Course Evaluation

Students performance is graded on a normal curve, according to the class mean and standard deviation,

assigning letter grades of A-D and F.

15. Reference(s)

An Introduction to Topology and Homotopy, Allan J. Sieradski, Thomson International Publishing, 1996.

16. Instructor(s)

Prof. Dr. Yongwimon Lenbury

17. Course Coordinator

Prof. Dr. Yongwimon Lenbury

SCMA 433 (2/2) 201 Elementary Algebraic Topology


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 435 Course Title Transformation Geometry

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Geometry for the study of properties invariant under congruences; similarities; affine transformations and

projection.

9. Course Objective(s)

To provide the students with concepts and theory of transformation geometry.

10. Course Outline

Week

Topic

Lecture/Seminar Hours Lab Hours

Instructor

3 - - Assigned instructor(s)

1 - Introduction and historical notes

surfaces in R 3

- Review of geometry of curves and

for the semester.

2 - Geometry for the study of properties

invariant under congruences

3 - Geometry for the study of properties

invariant under congruences

4 - Geometry for the study of properties

invariant under congruences

5 - Geometry for the study of properties

invariant under congruences

6 - Geometry for the study of properties

invariant under congruences

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

7 - Similarities 3 - - Assigned instructor(s)

for the semester.

8 - Similarities 3 - - Assigned instructor(s)

for the semester.

9 - Similarities 3 - - Assigned instructor(s)

for the semester.

10 - Similarities 3 - - Assigned instructor(s)

for the semester.

11 - Similarities 3 - - Assigned instructor(s)

for the semester.

12 - Affine transformations and

projection

3 - - Assigned instructor(s)

for the semester.

SCMA 435 (1/2) 202 Transformation Geometry


13 - Affine transformations and

projection

14 - Affine transformations and

projection

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

15 - Affine transformations and

3 - - Assigned instructor(s)

projection

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

-

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 435 (2/2) 203 Transformation Geometry


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 436 Course Title Differential Geometry and Tensor

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 234 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

Analysis

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Curvilinear coordinate systems; topological spaces; smooth manifolds; tangent vectors; curves; surfaces;

transformation groups; tensor fields; geodesics; curvature tensor; homology theory.

9. Course Objective(s)

To provide the students with concepts and theory of differential geometry and tensor analysis.

10. Course Outline

Week

Topic

Lecture/Seminar Hours Lab Hours

Instructor

3 - - Assigned instructor(s)

1 - Introduction and historical notes

surfaces in R 3

- Review of geometry of curves and

for the semester.

2 - Curvilinear coordinate systems 3 - - Assigned instructor(s)

for the semester.

3 - Topological spaces 3 - - Assigned instructor(s)

for the semester.

4 - Smooth manifolds 3 - - Assigned instructor(s)

for the semester.

5 - Tangent vectors and tangent

bundles

3 - - Assigned instructor(s)

for the semester.

6 - Curves 3 - - Assigned instructor(s)

for the semester.

7 - Surfaces 3 - - Assigned instructor(s)

for the semester.

8 - Transformation groups 3 - - Assigned instructor(s)

for the semester.

9 - Vector fields and integral curves 3 - - Assigned instructor(s)

for the semester.

10 - Tensor fields 3 - - Assigned instructor(s)

for the semester.

11 - Connections 3 - - Assigned instructor(s)

for the semester.

SCMA 436 (1/2) 204 Differential Geometry and Tensor Analysis


12 - Riemannian metrics 3 - - Assigned instructor(s)

for the semester.

13 - Geodesics 3 - - Assigned instructor(s)

for the semester.

14 - Curvature tensor 3 - - Assigned instructor(s)

for the semester.

15 - Homology theory 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

1. Richard L. Bishop and Samuel I. Goldberg, Tensor Analysis on Manifolds, Dover Publications, Inc., 1980.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 436 (2/2) 205 Differential Geometry and Tensor Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 448 Course Title Computer Applications in Statistics

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Use of computers in statistics; significance testing; correlation; analysis of variance; curve fitting; factor

analysis; nonparametric method.

9. Course Objective(s)

At the completion of this course students should be able to,

1. have knowledge and understand computer applications in statistics.

2. have knowledge and understand how to use computer package.

3. analyze data by using statistical packages on computer.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–3 Use of computer in statistics 6 Related lab 6 Assigned instructor(s)

for the semester.

4–6 Estimation and significance testing 6 Related lab 6 Assigned instructor(s)

for the semester.

7–9 Analysis of Variance 6 Related lab 6 Assigned instructor(s)

for the semester.

10–11 Correlation 4 Related lab 4 Assigned instructor(s)

for the semester.

12–14 Curve fitting 6 Related lab 6 Assigned instructor(s)

for the semester.

15–16 Nonparametric method 4 Related lab 4 Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Teaching method consists of lecture, practice and do exercises/assignments.

12. Teaching Media

Teaching media consists of overhead projector, hand out, LCD, statistical packages, and computer.

13. Measurement and Evaluation of Student Achievement

Course achievement will consider from exercises, assignments, midterm exam, and final exam.

14. Course Evaluation

Students will be evaluated by grade system, i.e., A, B + , B, C + , C, D + , D, and F. We consider from

exercises, assignment, midterm exam, and final exam.

SCMA 448 (1/2) 206 Computer Applications in Statistics


15. Reference(s)

1. ÈÔÃԪѠ¾§ÉŒÇԪѠ(2537) ¡ÒÃÇÔà¤ÃÒÐËŒ¢‰ÍÁÙÅ·Ò§ÊÔµÔ´‰Ç¤ÍÁ¾ÔÇàµÍÃŒ âç¾ÔÁ¾Œ¨ØÌÒŧ¡Ã³ŒÁËÒÇÔ·ÂÒÅÑ ¡Ãا෾ÁËÒ

¹¤Ã

2. ÊêÑ ¾ÔÈÒźصà (2528) à·¤¹Ô¤¡ÒÃà¡çºÃǺÃÇÁ¢‰ÍÁÙÅà¾×èÍ¡ÒÃÇԨѠÊíҹѡ¾ÔÁ¾Œ¨ØÌÒŧ¡Ã³ŒÁËÒÇÔ·ÂÒÅÑ ¡Ãا෾ÁËÒ

¹¤Ã

3. Dobson, A.J. (1983). An Introduction to Statistical Modelling, Chapman & Hall, Ltd., USA.

4. Draper, N.R. and Smith, H. (1966). Applied Regression Analysis, John Wiley & Son, Inc., USA.

5. Graybill, F.A. (1961). An Introduction to Linear Statistical Models Volume I. McGraw-Hill Book

Company, Inc., USA.

6. Graybill, F.A. (1967). Theory and Application of Linear Model. Duxbury Press, USA.

7. Neter, J.; Wasserman, William and Kutner, M.H. (1990). Applied Linear Statistical Models. 3nd Edition,

Toppan, Co., Tokyo, Japan.

8. Norusis, M.J. (1992). SPSS/PC+ for the IBM PC/XT/AT. Chicago, SPSS Inc., USA.

9. SPSS for Windows : Base System User’s Guide, Release 6.0 (1993) Spss Inc.

10. SPSS Base 7.5 Application Culde (1977) Spss Inc., USA.

16. Instructor(s)

Instructor from Department of Mathematics, Faculty of Science, Mahidol University.

17. Course Coordinator

Instructor from Department of Mathematics, Faculty of Science, Mahidol University

SCMA 448 (2/2) 207 Computer Applications in Statistics


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 449 Course Title Theory of Computation

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Formal language; finite automata; nondeterminism; pushdown automata; Turing machines; post machines;

Minsky’s Theorem; limits of language acceptence; universal Turing machines; unsolvable problems;

computability; recursive function theory.

9. Course Objective(s)

The objective of this course is to familiarize students with foundations and basic principles of abstract

models of computers.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Mathematical notation and Techniques

- Basic mathematical definitions

- Mathematical induction and recursive

definitions

3 - - Assigned instructor(s)

for the semester.

2–5 Regular languages and finite automata

- Regular expressions and regular

languages

- Finite automata

- Nondeterminism

- Kleen’s theorem

- Minimal finite automata

- Regular languages and nonregular

languages

12 - - Assigned instructor(s)

for the semester.

SCMA 449 (1/2) 208 Theory of Computation


6–10 Context-free languages and Pushdown

automata

- Context-free languages

- Derivation trees and ambiguity

- Simplified forms and normal forms

- Pushdown automata

- The equivalence of CFGs and

PDAs

- Parsing

- CFLs and Non-CFLs

15 - - Assigned instructor(s)

for the semester.

11–16 Turing machines, their languages, and

computation

18 - - Assigned instructor(s)

for the semester.

- Variation of Turing machines

- Recursively enumerable languages

- More general grammars

- Unsolvable decision problems

- Computability: Primitive recursive

functions

- Computability: µ-Recursive

functions

11. Teaching Method(s)

Lecture, homework and presentation.

12. Teaching Media

Computer

13. Measurement and Evaluation of Student Achievement

- Take home assignment 10

- Class assignment 15 %

- Midterm examination 30

- Final examination 45 %

14. Course Evaluation

Grade is evaluated from take home assignments, class assignments, midterm examination and final

examination. The grade will be A, B + , B, C + , C, D + , D and F by using normal curve.

15. Reference(s)

1. John C. Martin., Introduction to languages and the theory of computation.omputation.

2. John E. Hopcroft and Jeffrey D. Ullman., Introduction to automata theory languages and computation.

3. Michael Sipser., Introduction to the theory of computation.

4. Peter Linz., An introduction to formal languages and automata.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 449 (2/2) 209 Theory of Computation


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 450 Course Title Number Theory II

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 350 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Introduction to modern analytic and algebraic techniques used in the study of quadratic forms; distribution

of prime numbers; Diophantine approximations and other topics of classical number theory.

9. Course Objective(s)

Upon completion of this course students will be able to:

1. develop an ability to apply number theory in other subjects;

2. produce and appreciate imaginative and creative work arising from mathematical idea;

3. analyze a problem, select a suitable strategy and apply an appropriate technique to obtain its solution.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1–4 - Introduction to modern analytic 12 - - Assigned instructor(s)

and algebraic techniques used in

for the semester.

the study of quadratic forms

5–6 - Distribution of prime numbers 6 - - Assigned instructor(s)

for the semester.

7–15 - Diophanine approximations and

other topics of classical number

theory

27 - - Assigned instructor(s)

for the semester.

16 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

1. Lecture

2. Discussion

3. Presentation

12. Teaching Media

1. Text and handouts

2. Transparencies

13. Measurement and Evaluation of Student Achievement

Grades will be assigned according to the following point scale:

90–100 A

85–89 B +

80–84 B

75–79 C +

SCMA 450 (1/2) 210 Number Theory II


70–74 C

60–69 D +

50–59 D

0–49 F

14. Course Evaluation

- Graded homework, participation in class and group work 10%

- Exam I 20%

- Exam II 20%

- Quizzes 10%

- Final exam 40%

15. Reference(s)

1. Brown, Stephen I., On Prime Comparison, National Council of Teachers of Mathematics, 1978.

2. Hardy and Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford.

3. Niven, I. and Zuckerman, H. S., an Introduction to the Gauss by Applied Technical Systems in the $300

Range.

4. Shanks, Daniel, Solved and Unsolved Problems in Number Theory, Washington, D. C., Spartan Books,

1962.

5. Stein, M. L., et. al., a Visual Display of Some Properties of the Distribution of Primes, American

Mathematical Monthly, 71 (May 1964).

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 450 (2/2) 211 Number Theory II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 452 Course Title Abstract Algebra II

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 352 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Polynomials; factorization; symmetric functions; prime fields; field extensions; roots of unity; finite

commutative fields; Galois groups; conjugate groups; cyclotomic fields; solution to equations by radicals; infinite

field extensions; real fields.

9. Course Objective(s)

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Rings, homomorphisms and ideals; 3 - - Assigned instructor(s)

for the semester.

2 Factorization in commutative rings 3 - - Assigned instructor(s)

for the semester.

3 Rings of quotients and Localization; 3 - - Assigned instructor(s)

for the semester.

4 Rings of Polynomials and Formal

Power series;

3 - - Assigned instructor(s)

for the semester.

5 factorization in Polynomial rings 3 - - Assigned instructor(s)

for the semester.

6 2- Field Extension: the fundamental

Theorem;

7 Splitting Fields, Algebraic Closure

and Normality;

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

8 The Galois group of a Polynomial; 3 - - Assigned instructor(s)

for the semester.

9 Finite Fields; Separability; 3 - - Assigned instructor(s)

for the semester.

10 Cyclic extensions, Cyclotomic extensions

and radical Extensions.

3 - - Assigned instructor(s)

for the semester.

SCMA 452 (1/2) 212 Abstract Algebra II


11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 452 (2/2) 213 Abstract Algebra II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 456 Course Title Algebraic Structure

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 452 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Algebraic field extensions; splitting fields; algebraic closure; separable and unseparable extensions;

Fundamental Theorem of Galois theory; tensor products of modules; applications to abelian groups.

9. Course Objective(s)

For students to have intensive knowledge on concepts of algebraic structure.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Algebraic field extensions 3 - - Assigned instructor(s)

for the semester.

3 - Algebraic field extensions 3 - - Assigned instructor(s)

for the semester.

4 - Splitting fields 3 - - Assigned instructor(s)

for the semester.

5 - Splitting fields 3 - - Assigned instructor(s)

for the semester.

6 - Algebraic closure 3 - - Assigned instructor(s)

for the semester.

7 - Algebraic closure 3 - - Assigned instructor(s)

for the semester.

8 - Separable and unseparable

extensions

9 - Separable and unseparable

extensions

10 - Fundamental Theorem of Galois

theory

11 - Fundamental Theorem of Galois

theory

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

12 - Tensor products of modules 3 - - Assigned instructor(s)

for the semester.

SCMA 456 (1/2) 214 Algebraic Structure


13 - Tensor products of modules 3 - - Assigned instructor(s)

for the semester.

14 - Applications to abelian groups 3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Term project 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 456 (2/2) 215 Algebraic Structure


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 460 Course Title Dynamical Systems

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Dynamics for quadratic family; invariant manifolds; structural stability; hyperbolicity; horseshoe; toral

automorphism; strange attractors.

9. Course Objective(s)

By the end of this course, students should:

1. understand the concepts, techniques of nonlinear dynamics: Quadratic family,

2. understand the concepts involved in invariant manifolds, including the theorem of Hartman-Grobman,

3. know the basic properties of some hyperbolic sets,

4. understand the concept and importance of structural stability in toral automorphisms.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 Periodic points, Limit sets and Recurrence

for Maps

3 - - Assigned instructor(s)

for the semester.

2–3 Dynamics for the quadratic maps

- Conjugacy and Structural stability

4–6 Linear systems

- Contracting and Hyperbolic linear

differential equations

- Topologically conjugate

7–9 Analysis near fixed points and periodic

orbits

- Stability

- Heartman-Grobman Theorem

10–11 Hyperbolicity

- Horseshoe

- Hyperbolic toral automorphisms

6 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

12 Strange Attractors 3 - - Assigned instructor(s)

for the semester.

SCMA 460 (1/2) 216 Dynamical Systems


11. Teaching Method(s)

12. Teaching Media

13. Measurement and Evaluation of Student Achievement

14. Course Evaluation

15. Reference(s)

1. R.L. Devaney, An introduction to chaotic dynamical systems, Benjamin.

2. A Katok, B Hasselblat, Introduction to the Modern Theory of Dynamical Systems, in Encyclopaedia of

Mathematics and its Applications, 54, Cambridge University Press, 1995.

3. J Guckenheimer and P Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of

Vector-Fields, Springer-Verlag, 1983.

4. C Robinson, Dynamical Systems Stability. Symbolic Dynamics, and Chaos. Studies in Advanced

Mathematics, CRC Press, 1998.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 460 (2/2) 217 Dynamical Systems


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 462 Course Title Difference Differential Equations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 163 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Types of equations involved; types of problems where difference differential equations arise; step-by-step

extention of solutions; Laplace transform solutions; characteristic functions; roots of characteristic equations;

inverse Laplace transforms; series expansion of solutions; asymptotic behavior of solutions; non-linear equations.

9. Course Objective(s)

The student should know the basic types of equations, methods both to solve them and analyze the behavior

of the solutions.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Types of equations 3 - - Assigned instructor(s)

for the semester.

2–3 - Applications 6 - - Assigned instructor(s)

for the semester.

4–5 - Method of Steps 6 - - Assigned instructor(s)

for the semester.

6–7 - Laplace Transform Solution 6 - - Assigned instructor(s)

for the semester.

8 - Use of inverse Laplace transform 3 - - Assigned instructor(s)

for the semester.

9–10 - Characteristic equation and its

roots

6 - - Assigned instructor(s)

for the semester.

11–12 - Series expansions 6 - - Assigned instructor(s)

for the semester.

13–15 - Asymptotic behavior 9 - - Assigned instructor(s)

for the semester.

16 - Non-linear equations 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

1. Midterm Exam 50%

SCMA 462 (1/2) 218 Difference Differential Equations


2. Final Exam 50%

14. Course Evaluation

Final course grades are assigned based on a 100-point total as follows:

90–100 A

86–89 B +

80–85 B

76–79 C +

70–75 C

66–69 D +

60–65 D

0–59 F

15. Reference(s)

1. Ordinary and Delay Differential Equations, R. D. Driver, 1977, Springer-Verlag

2. Differential-difference Equations, R. Bellman & K. L. Cooke, 1963, Academic Press.

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 462 (2/2) 219 Difference Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 464 Course Title Boundary Value Problems

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Linear partial differential equations; the wave equation; Green’s function and Sturm-Liouville problems;

Fourier series and Fourier transforms; the heat equation; Laplace’s equation and Poisson’s equation; problems

in higher dimensions.

9. Course Objective(s)

The primary aim of this course is to introduce junior and senior students to boundary value problems, with

related to partial differential equations and to teach the fundamental mathematical procedures for developing

solutions.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1–2 - Boundary and Initial Conditions

- Classification of Partial Differential

Equations

- Boundary and Initial Conditions

- Implicit Boundary Conditions

- Examples of Boundary Value

Problems

6 - - Assigned instructor(s)

for the semester.

3–5 - Fourier Series

- Periodic Functions

- Fourier Series

- Determining Fourier Coefficients

- Fourier Series for Even and Odd

Functions

6–8 - Technique of Separation of Variables

- The Method of Separation of Variables

- Nonhomogeneous Differential Equations

and Boundary Conditions

- Sturm-Liouville Theory

9 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

SCMA 464 (1/2) 220 Boundary Value Problems


9–11 - Fourier Integral

- The Fourier Integral

- An Application of a Physical Problem

- Solving a Boundary Value Problem

Using a Fourier Transform

11–14 - Green’s Functions

- The Dirac Delta Function

- Green’s Function for the Laplace

Operator

- Some other Green’s Functions

- Direct Computation of Green’s

Function

- The Eigenfunction Method

7.5 - - Assigned instructor(s)

for the semester.

9 - - Assigned instructor(s)

for the semester.

14–16 - The Laplace Transform

7.5 - - Assigned instructor(s)

- The Laplace Transform

for the semester.

- Applications to the Heat Equations

- Applications to the Wave Equations

11. Teaching Method(s)

Lecture and biweekly assignment.

12. Teaching Media


13. Measurement and Evaluation of Student Achievement

Homework 20%

Midterm Examinations 40%

Final Examinations 40%

14. Course Evaluation

Grade is evaluated from homework, midterm and final examinations in the form of A, B + , B, C + , C, D + , D

and F using normal curve.

15. Reference(s)

1. M. Humi, W. B. Miller, Boundary Value Problems and Partial Differential Equations, PWS-KENT

Publishing Company, 1992

2. M. A. Pinsky, Partial Differential Equations and Boundary Value Problems with Applications, McGRAW-

HILL, 1991

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 464 (2/2) 221 Boundary Value Problems


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 465 Course Title Theory of Ordinary Differential

Equations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Existence and uniqueness theorems; continuation of solutions; plane autonomous systems; solutions to system

of linear first order equations with constant coefficients; linearly independent solutions; stability; nonlinear

systems; comparison theorems.

9. Course Objective(s)

The aim is to provide the students with the fundamental knowledge about ordinary differential equations,

and related theory of existence and uniqueness. The student should be able to find out the various possible

behavior of the solution in terms of its stability, periodically and boundedness, using basic methodologies of

fundamental importance.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Prof. Yongwimon

Lenbury

2 - First order equations: linear

equations

3 - - Assigned instructor(s)

for the semester.

3 - Equations with parameters 3 - - Assigned instructor(s)

for the semester.

4 - Autonomous equations: stability of

equilibrium

3 - - Assigned instructor(s)

for the semester.

5 - Linear equations: an introduction 3 - - Assigned instructor(s)

for the semester.

6 - Second order linear equations with

constant coefficients

3 - - Assigned instructor(s)

for the semester.

7 - Oscillations 3 - - Assigned instructor(s)

for the semester.

8 - Equations of order n 3 - - Assigned instructor(s)

for the semester.

9 - Review of vectors, matrices and

determinants

3 - - Assigned instructor(s)

for the semester.

10 - Linear systems 3 - - Assigned instructor(s)

for the semester.

SCMA 465 (1/2) 222 Theory of Ordinary Differential Equations


11 - Autonomous second order systems 3 - - Assigned instructor(s)

for the semester.

12 - Lyapunov functions 3 - - Assigned instructor(s)

for the semester.

13 - Existence theorem 3 - - Assigned instructor(s)

for the semester.

14 - Uniqueness and comparison

theorems

3 - - Assigned instructor(s)

for the semester.

15 - Differential equations in a complex 3 - - Assigned instructor(s)

domain and asymptotic expansions

for the semester.

11. Teaching Method(s)

Instruction by in class lectures, giving regular exercise problems and assignments for students to get on hand

practice.

12. Teaching Media

1. Transparencies

2. Occasionally Distributed Sheets

13. Measurement and Evaluation of Student Achievement

1. Exercise and Assignments 20%

2. Midterm Examination 30%

3. Final Examination 50%

14. Course Evaluation

Students performance is graded on a normal curve, according to the class mean and standard deviation,

assigning letter grades of A-D and F.

15. Reference(s)

1. Ordinary Differential Equations, Otto Plaat, Holden-DY Inc., 1971

2. Ordinary Differential Equations, Richard K. Miller and Antony N. Michel, Academic Press, 1985.

16. Instructor(s)

Prof. Dr. Yongwimon Lenbury

17. Course Coordinator

Prof. Dr. Yongwimon Lenbury

SCMA 465 (2/2) 223 Theory of Ordinary Differential Equations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 466 Course Title Life Actuarial Mathematics II

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 366 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Survival probability; joint life probabilities; last survivor and compound status functions; premiums; life

insurance for other status; annuities; annuities paid after death.

9. Course Objective(s)

For students to have knowledge on concepts of life actuarial mathematics.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Survival probability 3 - - Assigned instructor(s)

for the semester.

3 - Survival probability 3 - - Assigned instructor(s)

for the semester.

4 - Joint life probabilities 3 - - Assigned instructor(s)

for the semester.

5 - Joint life probabilities 3 - - Assigned instructor(s)

for the semester.

6 - Last survivor and compound status

functions

7 - Last survivor and compound status

functions

8 - Last survivor and compound status

functions

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

9 - Premiums 3 - - Assigned instructor(s)

for the semester.

10 - Premiums 3 - - Assigned instructor(s)

for the semester.

11 - Life insurance for other status 3 - - Assigned instructor(s)

for the semester.

12 - Life insurance for other status 3 - - Assigned instructor(s)

for the semester.

SCMA 466 (1/2) 224 Life Actuarial Mathematics II


13 - Annuities 3 - - Assigned instructor(s)

for the semester.

14 - Annuities paid after death 3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 466 (2/2) 225 Life Actuarial Mathematics II


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 467 Course Title Control Theory

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Theories used in control feedback systems; introduction to simulation; control feedback systems used in

mechanical, chemical and electrical engineering.

9. Course Objective(s)

For students to have knowledge on concepts of control theory.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Theories used in control feedback

systems

3 - Theories used in control feedback

systems

4 - Theories used in control feedback

systems

5 - Theories used in control feedback

systems

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 - Introduction to simulation 3 - - Assigned instructor(s)

for the semester.

7 - Introduction to simulation 3 - - Assigned instructor(s)

for the semester.

8 - Introduction to simulation 3 - - Assigned instructor(s)

for the semester.

9 - Introduction to simulation 3 - - Assigned instructor(s)

for the semester.

10 - Control feedback systems used in

mechanical, chemical and electrical

engineering

11 - Control feedback systems used in

mechanical, chemical and electrical

engineering

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 467 (1/2) 226 Control Theory


12 - Control feedback systems used in

mechanical, chemical and electrical

engineering

13 - Control feedback systems used in

mechanical, chemical and electrical

engineering

14 - Control feedback systems used in

mechanical, chemical and electrical

engineering

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

15 - Review 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Term project 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 467 (2/2) 227 Control Theory


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 468 Course Title Calculus of Variations

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 263 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Problems which define the calculus of variations; classical necessary conditions and their applications;

canonical form of the Euler-Lagrange equations; Hamilton’s principle; field and sufficient conditions;

Pontryagin’s necessary condition; control theory.

9. Course Objective(s)

For students to have intensive knowledge on concepts of calculus of variations.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Problems which define the calculus

of variations

3 - Problems which define the calculus

of variations

4 - Classical necessary conditions and

their applications

5 - Classical necessary conditions and

their applications

6 - Canonical form of the Euler-

Lagrange equations

7 - Canonical form of the Euler-

Lagrange equations

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

8 - Hamilton’s principle 3 - - Assigned instructor(s)

for the semester.

9 - Hamilton’s principle 3 - - Assigned instructor(s)

for the semester.

10 - Field and sufficient conditions 3 - - Assigned instructor(s)

for the semester.

11 - Field and sufficient conditions 3 - - Assigned instructor(s)

for the semester.

12 - Pontryagin’s necessary condition 3 - - Assigned instructor(s)

for the semester.

SCMA 468 (1/2) 228 Calculus of Variations


13 - Pontryagin’s necessary condition 3 - - Assigned instructor(s)

for the semester.

14 - Control theory 3 - - Assigned instructor(s)

for the semester.

15 - Control theory 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 468 (2/2) 229 Calculus of Variations


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 473 Course Title Operations Research

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite None

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Introduction to quantitative analysis; formulation of linear optimization models; algebraic and geometric

models; simplex method; sensitivity testing; duality; optimization in networks; network algorithms.

9. Course Objective(s)

For students to have knowledge on concepts of operations research.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction to quantitative

3 - - Assigned instructor(s)

analysis

for the semester.

2 - Formulation of linear optimization

models

3 - Formulation of linear optimization

models

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

4 - Algebraic and geometric models 3 - - Assigned instructor(s)

for the semester.

5 - Algebraic and geometric models 3 - - Assigned instructor(s)

for the semester.

6 - Simplex method 3 - - Assigned instructor(s)

for the semester.

7 - Simplex method 3 - - Assigned instructor(s)

for the semester.

8 - Sensitivity testing 3 - - Assigned instructor(s)

for the semester.

9 - Sensitivity testing 3 - - Assigned instructor(s)

for the semester.

10 - Duality 3 - - Assigned instructor(s)

for the semester.

11 - Duality 3 - - Assigned instructor(s)

for the semester.

12 - Optimization in networks 3 - - Assigned instructor(s)

for the semester.

SCMA 473 (1/2) 230 Operations Research


13 - Optimization in networks 3 - - Assigned instructor(s)

for the semester.

14 - Network algorithms 3 - - Assigned instructor(s)

for the semester.

15 - Network algorithms 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 473 (2/2) 231 Operations Research


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 474 Course Title Decision Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Decision models; expected monetary values; decision flow diagrams; probability assessment; optimization

techniques; perfect information; opportunity losses; uncertain payoffs; biased measurements; utility theory;

judgemental probability; normal form of analysis; economics of sampling; risk sharing.

9. Course Objective(s)

For students to have knowledge on concepts of decision analysis.

10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Decision models 3 - - Assigned instructor(s)

for the semester.

3 - Expected monetary values 3 - - Assigned instructor(s)

for the semester.

4 - Decision flow diagrams 3 - - Assigned instructor(s)

for the semester.

5 - Probability assessment 3 - - Assigned instructor(s)

for the semester.

6 - Optimization techniques 3 - - Assigned instructor(s)

for the semester.

7 - Perfect information 3 - - Assigned instructor(s)

for the semester.

8 - Opportunity losses 3 - - Assigned instructor(s)

for the semester.

9 - Uncertain payoffs 3 - - Assigned instructor(s)

for the semester.

10 - Biased measurements 3 - - Assigned instructor(s)

for the semester.

11 - Utility theory 3 - - Assigned instructor(s)

for the semester.

12 - Judgemental probability 3 - - Assigned instructor(s)

for the semester.

SCMA 474 (1/2) 232 Decision Analysis


13 - Normal form of analysis 3 - - Assigned instructor(s)

for the semester.

14 - Economics of sampling 3 - - Assigned instructor(s)

for the semester.

15 - Risk sharing 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Instruction by in-class lectures with discussion, giving regular in-class exercises, homework problems and

assignments for students to practise.

12. Teaching Media

1. Transparencies/whiteboards/blackboards/computerized presentations

2. Distributed sheets

13. Measurement and Evaluation of Student Achievement

1. Assignments 15%

2. Quizes 20%

3. Midterm Examination 25%

4. Final Examination 40%

14. Course Evaluation

Students performance is graded using t-score, assigning letter grades of A-D and F.

15. Reference(s)

16. Instructor(s)

Assigned instructor(s) for the semester.

17. Course Coordinator

Assigned instructor(s) for the semester.

SCMA 474 (2/2) 233 Decision Analysis


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 480 Course Title Sampling Techniques

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Survey methods and planning a survey; elements of random sampling; choices of sampling units; estimation

of sample size; stratified-random sampling; tolerance; required sample size.

9. Course Objective(s)

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10. Course Outline

Topic

Week

Lecture/Seminar Hours Lab Hours

Instructor

1 - Review of some basic concepts

- How to select the sample : The

design of the sample survey

-

- Errors in surveys

3 - - Assigned instructor(s)

for the semester.

2–3 - Simple random sampling

- How to draw a sample random

sample

- Estimation of a population mean

and total

- Selecting the sample size for estimating

population mean and totals

- Estimation of a population proportion

-

-

-

4 - Unequal Probability Sampling

- Sampling with replacement

- Sampling without replacement

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

SCMA 480 (1/4) 234 Sampling Techniques


5–7 - Stratified random sampling

- How to draw a stratified random

sample

- Estimation of a population mean

and total

- Selecting the sample size for estimating

population mean and totals

- Allocation of the sample

-

-

- Estimation of a population proportion

- Selecting the sample size and allocating

the sample to estimate proportion

- An optimal rule for choosing strata

-

- Stratification after selection of the

sample

-

9 - - Assigned instructor(s)

for the semester.

8 Mid-Term Examination 3 - - Assigned instructor(s)

for the semester.

9–10 - Systematic sampling

- How to draw a systematic random

sample

- Estimation of a population mean

and total

- Estimation of variance of estimator

- Precision of Estimator

-

- Estimation of a population proportion

-

4 - - Assigned instructor(s)

for the semester.

SCMA 480 (2/4) 235 Sampling Techniques


11 - Cluster sampling

- How to draw a Cluster random

sample

- Estimation of a population mean

and total

- Selecting the sample size for estimating

population mean and totals

- Selecting the sample size for estimating

population proportions

- Cluster sampling with probabilities

proportional to size

12 - Two - stage Sampling

- How to draw a two-stage sample

- Sample size for two stage sampling

-

-

13–14 - Ratio and Regression estimation

- Ration estimation using simple random

sampling

- Regression estimation using stratified

random sampling

- Regression estimation using simple

random sampling

- Ration estimation using stratified

random sampling

15 - Non sampling Error

- Uncomplete sampling frame , Nonresponse

, Measurement Errors

3 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

6 - - Assigned instructor(s)

for the semester.

3 - - Assigned instructor(s)

for the semester.

16 Present Report 3 - - Assigned instructor(s)

for the semester.

11. Teaching Method(s)

Lecture and participation

12. Teaching Media

Lecture note and power-point

13. Measurement and Evaluation of Student Achievement

1. Mid-term Exam 30%

2. Pop Quiz 10%

3. Homework 15%

4. Report 15%

5. Final Exam 30%

14. Course Evaluation

There are 8 grades : A, B + , B, C + , C, D + , D áÅÐ F ( using t - score )

SCMA 480 (3/4) 236 Sampling Techniques


15. Reference(s)

1. Cochran , W.G. , Sampling Techniques , 3nd edition (1977) , John Wiley and Sons.

2. Mendenhall W. , Elementary Survey Sampling , 5rd edition (1997) , Wadsworth.

3. Taro Yamane , Elementary Sampling Theory , 1967 , Prentice-Hall.

16. Instructor(s)

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

17. Course Coordinator

ÍÒ¨ÒÃÂŒ¨Ò¡ÀÒ¤ÇÔªÒ¤³ÔµÈÒʵÌ

SCMA 480 (4/4) 237 Sampling Techniques


Course Syllabus

1. Program of Study Bachelor of Science in Mathematics Faculty of Science

2. Course Code SCMA 481 Course Title Time Series Analysis

3. Number of Credits 3(3-0) (Lecture-Lab)

4. Prerequisite SCMA 183 or consent of instructor

5. Type of Course Specialized course

6. Session/Academic Year

First or second semester depending on students’ and instructor’s interest/2007

7. Course Conditions 0

8. Course Description

Basic principles of representing time series in both the time and frequency domains; Box and Jenkins

technique of fitting data to autoregressive moving average models in the time domain; model construction;

evaluation and forecasting; analysis of time domain and digital filtering; methods of estimating and interpreting

the spectrum.

9. Course Objective(s)

For students to have knowledge on concepts of time series analysis.

10. Course Outline

Topic

Week

Instructor

Lecture/Seminar Hours Lab Hours

1 - Introduction 3 - - Assigned instructor(s)

for the semester.

2 - Basic principles of representing

time series in both the time and

frequency domai