Discrete Mathematical Structures - Computer Science

Discrete Mathematical Structures
CSCI 2427 Spring 2015
Class Time: 05:00 p.m. — 06:15 p.m. TTh
Class Room: Bate Building, Room No. 1028
Instructor: Dr. K. Gopalakrishnan
Office Location: Suite C-114, Science and Technology Building
Office Phone: (252)-328-9688
Office Hours: 02:30 p.m. — 04:30 p.m. MW
06:15 p.m. — 06:45 p.m. TTh
and by appointment.
Email address: gopal@ecu.edu
Home Page URL: http://www.cs.ecu.edu/∼gopal
About the course
Discrete Mathematics isarguablythe most important course in theundergraduate
computer science curriculum. Itlaysthefoundationforseveral coursesthatyoumight
probablytake infuture. Thecourse objective is twofold. Thefirst objective isto learn
several basic topics in discrete mathematics and applications of them. The second
and more important objective is to develop mathematical thinking. More specifically,
you will learn to appreciate the need for proofs and mathematical rigor, write proofs
formally and develop problem solving skills & algorithmic thinking.
Text Book
• Discrete Mathematics and Its Applications by Kenneth H. Rosen, McGraw-Hill
Inc., Seventh Edition, 2012.
This isanexcellenttext bookwritten in a lucid style andat thesame timewithout
loss of mathematical rigor. I will be sticking to the book closely in this course.
Earlier editions of the same book might also suffice. We would be covering Chapter
1 thoroughly and then a selection of topics from the chapters 2, 5, 6, 9 and 10. More
specific details about the topics to be covered would be given later.
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Prerequisites
• MATH 1065 College Algebra or an equivalent course.
Grading Policy
Your grade in this course will be based on your performance in Assignments and
examinations. The weights for different components are given below.
Exam I ...... 20%
Exam II ...... 20%
Final Exam ...... 25%
Assignments ...... 35%
Assignments must be taken seriously and must be submitted in time. There will
not be any programming assignments in this course. Part of the assignments will be
doneusingthewebbased“McGraw-Hill’sConnect”System(thatwillbeauto-graded)
and the remaining part will be traditional paper based assignments.
The details of the examinations are as follows. There will be two regular examinations
during the semester and a final comprehensive examination at the end of
the semester. The exact dates for the regular examinations will be announced later.
The final examination will be held as per the university examination schedule. You
will not be allowed to use your books or notes in examinations. However, you may
use non-programmable calculators and a crib sheet. Make up examinations would be
given only under truly exceptional circumstances and only if arrangements for such
is made prior to the regularly scheduled examination.
The tentative guidelines for grades are:
≥ 85 A
≥ 80 and < 85 A−
≥ 77 and < 80 B+
≥ 72 and < 77 B
≥ 69 and < 72 B−
≥ 66 and < 69 C+
≥ 61 and < 66 C
≥ 58 and < 61 C−
≥ 56 and < 58 D+
≥ 52 and < 56 D
≥ 50 and < 52 D−
< 50 F
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McGraw-Hill’s Connect
McGraw-Hill’s Connect is a web-based assignment and assessment solution required
for this course. Connect is designed to assist you with your coursework based
on your needs. As outlined in the grading policy, assignments will make up a significant
portion of your overall course grade.
Connect access codes may be packaged with a new textbook in the bookstore.
Connect can also be purchased online at our section’s unique Connect web address:
http://connect.mheducation.com/class/k-gopalakrishnan-sp15. If you purchase
Connect online, you will have the option of purchasing Connect or Connect
Plus, which includes an interactive eBook version of the required textbook for this
course. You can also register in Connect and have access without a code for a limited
time period (typically three weeks).
To register in Connect, please visit the following web site and click “Register
Now”: http://connect.mheducation.com/class/k-gopalakrishnan-sp15
If you have any issues while registering or using Connect, please contact McGraw-
Hill’s Customer Experience team through http://www.mhhe.com/support or at 800-
331-5094. To avoid problems related to technical issues, you are advised not to wait
until the last moment to complete assignments. Please review your “Connect Student
Quick Tips” document for further support.
Learning Outcomes
As the course consists of many different discrete topics, the student would have
acquired many different skills by successfully completing the course. Here is a list
(non-exhaustive) of some of the skills.
• Translate English Sentences into Propositional Logic and vice versa.
• Translate English Sentences into Predicate Logic and vice versa.
• Determine whether two given logical expressions are equivalent or not.
• Determine whether a given logical argument is valid or not.
• Determine whether a given mathematical proof is correct or not.
• Construct simple mathematical proofs using standard techniques.
• Prove universally quantified statements using Mathematical Induction.
• Model word problems using set theory and solve them.
• Identify whether a given mapping is a function and if so, is it 1-1 and onto.
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• Compose functions and determine inverse functions when feasible.
• Countthenumberofarrangementssatisfyingcertainspecificationsusingvarious
principles of elementary combinatorics.
• Determine properties of a given relation
• Model real life problems using graph theory and solve them.
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