# Discrete Mathematics (MATH 321 A)

## Spring 2013

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com
Office:   Miller Science Center 103-C
Office hours:   10:00- 11:00 AM on MWF and 3:00- 4:00 PM on TTR or by appointment
Class hours:   MWF 11:00 AM-11:50 AM, Miller Hall 112

Text:    Discrete Mathematics with Applications, 4th edition by Susanna S. Epp ISBN-10: 0-495-39132-8, ISBN-13: 978-0-495-39132-6
Publisher: Cengage Learning

Materials covered:     Logic, methods of proof, sets, relations, functions, equivalences, combinatorics, induction, recursion, elementary number theory, linear programming, and an introduction to mathematical modeling

Final Exam:   April 29 (Monday)      8:00 - 10:00

• Syllabus;     Tentative Schedule
• Suggested Problems
• Lecture Note ( Printer friendly version will be more cost effective when you print out. )

## Progress, Problems and Solutions

 Date Progress Problems,Solutions Jan 9 W Introduction Jan 11 F Chapter 1. Speaking mathematically 1.1. Variables: Using variables in mathematical discourse; Introduction to universal, existential and conditional statements 1.2. The Language of sets: The set-roster and set-builder notations; subsets; Cartesian products Jan 14 M 1.3. The language of relations and functions: Definition of a relation from one set to another; Arrow diagram of a relation Jan 16 W Quiz Group Quiz, Quiz Jan 18 F 1.3. The language of relations and functions: Definition of functions, Chapter 2. The logic of compound statements 2.1. Logical form and logical equivalence:Statements; compound statements Jan 23 W 2.1. Logical form and logical equivalence: truth values; evaluating the truth of more general compound statements; logical equivalence Jan 25 F Quiz: Class cancelled due to inclement weather: Please work out the quiz problems and turn those in at the begining of Monday's class. Group Quiz, Quiz Jan 28 M 2.1. Logical equivalence; tautologies and contradictions, 2.2. Conditional statements Logical equivalences involving →; representation of If-Then A Or; The negation of a conditional statement; The contrapositive of a conditional statement Jan 30 W 2.2. The converse and inverse of a conditional statement; only if and the biconditional; necessary and sufficient conditions; remarks, 3.1.Predicates and Quantified Statements I Feb 1 F Quiz Group Quiz , Quiz Mar 1 F No Class( Mid-Term day ) Mar 4 M 4.4. Direct proof and counterexample IV: Division into cases and the quotient-remainder theorem, 4.6. Indirect argument; Contradiction and contraposition: Proof by contradiction Mar 6 W Class Cancelled because of inclement weather Mar 8 F 4.7. Indirect argument: Two classical theorems The irrationality of square root of 2; Are there infinitely many prime numbers?; When to use indirect proof Mar 11, 13 and 15 Spring Break Mar 18 M 4.8. Application: Algorithm; The Euclidean Algorithm Mar 20 W Quiz Group Quiz, Quiz Mar 22 F 8.1. Relations on sets Additional examples of relations; The inverse of a relation; directed graph of a relation; N-ary relations and relational databases, 8.2. Reflexivity, Symmetry, and transitivity Mar 25 M 8.2. Reflexivity, Symmetry, and transitivity Mar 27 W Quiz Group Quiz, Quiz Mar 29 F Good Friday (No Class) Apr 1 M Review for the exam Study Guide Apr 3 W Exam 2 ( Chapter 4, sec 8.1 and sec 8.2 ) Exam 2 April 5 F 8.3.Equivalence relations April 8 M 8.3.Equivalence relations, 8.4. Modulo arithmatic with applications to cryptography Mini-Make-Up Exam April 10 W 8.4. Modulo arithmatic with applications to cryptography, Properties of Congruence Modulo n April 12 F Quiz Quiz , Group Quiz April 15 M Properties of Congruence Modulo n in 8.4. April 17 W Properties of Congruence Modulo n in 8.4. (up to p70 in Powerpoint) Apr 19 F Quiz Group Quiz Apr 22 M Existence of inverse modulo n, Euclid's Lemma, Fermat's Little Theorem Group Quiz Apr 24 W Self-Review for the Final exam Tip: The final exam will cover all materials you learnt this semester. The problems will be very similar to the mid-term exam problems or the quiz problems and the examples we learnt during the class( especially, for the materials covered after the 2nd exam). However, you need to study the past problems in depth extensively. Apr 26 F Inauguration Day( Class cancelled ) Apr 29 M Final Exam ( Comprehensive Exam ): 8-10 A.M. Final Exam