# Discrete Mathematics

Math 245
Spring 2003
Meeting: MWF, 9:00-10:00.
BA 260
San Diego State University

Professor: Mike O'Sullivan
Email: m.osullivan@math.sdsu.edu
Office: Bus. Adm./Math Building #217, ext. 594-6697
Office Hours: MWF: 10:00-11:30.
Other times: by appointment.

## Text

S. Epp, Discrete Mathematics with Applications, 2nd Ed.

## Detailed Information

 SCHEDULE ASSIGNMENTS REVIEW SHEETS:    First Exam,    Second Exam,    Third Exam,    Final Exam.

## Course Description

Discrete mathematics is an exciting and rapidly growing area of mathematics which has important applications in computer science and in many high technology areas. For example, "secure" internet communication, efficient storage of data (e.g. jpeg) and robust communication networks are developed using techniques from discrete mathematics.

This course serves two main populations, students from mathematics and students from computer science. The course also has two distinct goals: one is to teach the basics of set theory, logic, combinatorics and graph theory. The other is to convey concepts essential to mathematics: clarity and precision in definitions and statements of fact, and rigorous methods for establishing that a statement is true. The fundamental mathematics taught in this course is critical to understanding computer languages and to the development of good programming skills.

## Schedule

Here is a rough idea of the amount of time I expect to spend on each topic, and the order in which we will cover them. I am also open to suggestions if the class would like to spend more time on certain topics or cover items not listed here. A day by day schedule (see above) will be maintained to keep you informed of upcoming and past lectures.

 SECTIONS TOPICS TIME §1.1-4 Logic and logical arguments. 4 classes §2.1-3 Predicates and quantifiers. 4 classes §3.1-7 Proofs: direct, by counterexample, by indirect argument. 6 classes Some number theory. §5.1-3 Sets: subsets, union, intersection. 4 classes Venn diagrams. Algebra of set operations. Cartesian product, power set. §10.1-3,5 Relations. Reflexive, symmetric and transitive relations. 6 classes Equivalence relations. Partially ordered sets §7.1,3,4,5 Functions: one-to-one and onto functions. 4 classes Invertible functions. The pigeonhole principle. Composition of functions. §4.1-4 Sequences, mathematical induction 4 classes §8.1-3 Recursively defined sequences: 4 classes Finding explicit formulas, establishing the formulas by induction. §6.1-7 Combinatorics: Counting and the multiplication rule. 6 classes Permutations and combinations.

We will have weekly assignments, three midterms and a final exam. For the weekly assignments (see above), there will be a small number of problems (10 or so) which you should write up carefully. They will be graded and returned to you promptly (to the best of my ability).

I recommend that you do or at least attempt most of the exercises in the book. That is the best way to learn!

Point value for the work will be as follows (plus or minus 50 points)
 Weekly work 200 Test 1 150 Test 2 150 Test 3 150 Final 350 Total 1000

The first exam is tentatively Wed. Feb. 26.

The second exam is Wed. Mar. 26.

The third exam is tentatively Fri. Apr. 25.

The final exam is Wednesday, May 14, 8:00 -10:00 am.