Introduction to Combinatorics

MATH 474 (Spring 2004) course announcement

Instructor: Dr. André Kündgen
Email: akundgen@csusm.edu
Office: Science Hall 2, 339
Office phone: (760) 750-8070

CRN: 21403
Lectures: Tuesday, Thursday 14:30-15:45 (SCI2 Room 306).
Webpage: http://courses.csusm.edu/math474ak

Textbook

R.A. Brualdi, Introductory Combinatorics (3rd edition), Prentice Hall (1999), ISBN 0-13-181488-5 (hardcover).

Prerequisites

A certain amount of mathematical maturity is necessary for this course. MATH 350, MATH 370 or a similar discrete mathematics course that stresses the ability to understand and write proofs is required.

Course content

"In how many ways can you ..." is the key question in Combinatorics, aka "The art of counting". The goal of this course is to tackle many problems of this type.

The core material consists of the pigeonhole principle, combinations (binomial coefficients) and permutations (factorials), recurrence relations (and how to solve them), generating functions, and the principle of Inclusion/Exclusion. We will also encounter some assorted topics: partially ordered sets, derangements, Fibonacci numbers, Catalan numbers, Stirling numbers, and maybe even Pólya counting or a bit on design theory.