Instructor: Dr. Seongchun (Michelle) Kwon
email: kwonseon at hotmail dot com
Office: Miller Science Center 103C
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 AM11:50 AM, Miller Hall 112
Text:
Discrete Mathematics with Applications, 4th edition by Susanna S. Epp
ISBN10: 0495391328, ISBN13: 9780495391326
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 setroster and setbuilder 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 IfThen 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( MidTerm day )  
Mar 4 M  4.4. Direct proof and counterexample IV: Division into cases and the quotientremainder 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; Nary 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  MiniMakeUp 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  SelfReview for the Final exam Tip: The final exam will cover all materials you learnt this semester. The problems will be very similar to the midterm 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 ): 810 A.M.  Final Exam 