MAT101 - Suffolk County Community College

1SUFFOLK COUNTY COMMUNITY COLLEGECOLLEGE-WIDE COURSE SYLLABUSMAT101 (formerly MA21)I. COURSE TITLE:Survey of Mathematical ReasoningII.III.IV.CATALOG DESCRIPTION:Liberal arts mathematics course which provides insight into the nature ofmathematical reasoning by examining basic structures such as logic, sets, realnumbers, numeration systems and inductive reasoning. Prerequisite: MAT007 orequivalent. Note: Credit given for MAT101 or MAT107, but not both.A-E-G / 3 cr. hrs.COURSE GOALS:A. Expose students to the foundations of mathematical methodsB. Introduce inductive and deductive reasoning.COURSE OBJECTIVES:Upon successful completion of this course, students will be able to:A. distinguish between deductive and inductive reasoning and be able toapply each in problem solving;B. make connections between mathematical discoveries and the history ofhuman thought;C. perform the basic operations of set theory including: intersection, unionand complement;D. analyze basic data-type questions (survey results) using subsets and Venndiagrams;E. translate verbal statements into symbolic forms of implication,conjunction, disjunction and biconditional;F. test for the validity of arguments using various methods, indirect as wellas direct;G. define logical connectives using truth tables and be able to discovertautologies and prove theorems using truth tables;H. convert to any base using expanded numeral concept as well as thedivision algorithm.Depending on the instructor's choice of optional topics, students should also beable to:I. distinguish between rational and irrational numbers using the infinitedecimal concept;J. solve problems on a calculator or computer involving loans, interest,mortgages, annuities and life insurance;K. analyze switching circuits using logical equivalences;L. write programs in basic which utilize a loop, using proper structuredprogramming techniques;Revised: Fall 2008

2M. diagram the logical design of a computer or calculator.V. Topics Outline with TimelineTopicsA. Logic (Mathematical Thinking)1. deductive thought2. inductive thought3. conjecture, proof4. history of logic5. definitions: disjunction, conjunction, conditional,bi-conditional, negation6. truth tables7. arguments, theorems, proof (direct and indirect)8. validityB. Sets1. history2. definition3. operations with sets4. Venn diagrams, survey problems5. arguments, theorems, proof, conjecture (optional)6. finite sets7. equivalent sets8. 1-1 correspondence9. cardinal numbers (optional)10. infinite sets (optional)11. Cantor's theorems (optional)Additional Topics: at least 3D. Real numbers1. natural numbers2. integers3. rational numbers4. irrational numbers5. properties of the systems (closure, etc.)6. calculatorsa. historyb. algorithmsc. order of operationsE. Switching Circuits1. definitions2. problems3. theoremsApproximateTime(IncludingExaminations)3-5 weeks2-3 weeks2-3 weeks1 weekRevised: Fall 2008

3F. Boolean algebra1. definitions2. theorems3. proofsG. Numeration system1. historical2. positionalH. Number Bases1. unique representation2. other bases3. connecting to other bases4. application - to computerI. Inductive Reasoning1. find the nth term of a sequence2. prove sum of arithmetic and geometric seriesJ. Computers1. history2. processing3. flow chart4. programming1-2 weeks2-3 weeks2-3 weeks2-3 weeks2-3 weeksVI.VII.Evaluation of Student Performance:To be determined by the instructorPrograms that require this course:Communication and Media Arts: Journalism/AA (recommended)VIII. Courses that require this course as a prerequisite:NoneIX.Supporting Information:Mathematics tutoring services, as well as video and computer aids, are providedfor all students through the Math Learning Center (Ammerman Campus,Riverhead 235), the Center for Academic Excellence (Grant Campus, Health,Sports and Education Center 129), and the Academic Skills Center (EasternCampus, Orient 213).Revised: Fall 2008