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
| 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 |
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| 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(Solution), Quiz (Solution ) |
| Feb 4 M | 3.1. Predicates and Quantified Statements I; The Universal Quantifier, The Existential Quantifier, Universal Conditional Statements, Equivalent forms of Universal and Existential Statement: 3.2. Predicates and Quantified Statements II; Negation of Quantified Statements, Negations of Universal conditional statements | |
| Feb 6 W | Finishing 3.2. Predicates and Quantified Statements II | |
| Feb 8 F | Quiz | Group Quiz, Quiz |
| Feb 11 M | 3.4. Arguments with Quantified Statements: Universal Modus Ponens, Universal Modus Tollens | |
| Feb 13 W | 3.4. Arguments with Quantified Statements:Using Diagrams to Test Validity, Group quiz | Group Quiz |
| Feb 15 F | Review for the Exam | Study Guide |
| Feb 18 M | Exam 1 | Exam 1 ( Range: Chapter 1, 2, and 3 )(Martino's Solution ) |
| Feb 20 W | 4.1. Direct proof and counterexample I: Introduction Definitions; proving existential statements; disproving universal statements by counter example; proving universal statements; directions for writing proofs of universal statements; | |
| Feb 22 F | 4.1. Direct proof and counterexample I: Introduction, getting proofs started; showing that an existential statement is false; conjecture, proof and disproof | Mini-Make-Up Exam 1 |
| Feb 25 M | 4.2. Direct proof and counterexample II: Rational numbers, 4.3. Direct proof and counterexample III: Divisibility Proving properties of divisibility; counterexamples and divisibility | |
| Feb 27 W | 4.3. Direct proof and counterexample III: Divisibility; the unique factorization of integers theorem | Group Quiz ( Solution ) |
| 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 ( Solution ) |
| 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 ( Solution ) |
| 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 ( Solution ) |
| 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 ( Solution ) |
| 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. |
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| Apr 26 F | Inauguration Day( Class cancelled ) | |
| Apr 29 M | Final Exam ( Comprehensive Exam ): 8-10 A.M. | Final Exam |