# Math 450: Combinatorics

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## Contents

## Catalog Information

### Title

Combinatorics.

### (Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

### Offered

Su

### Prerequisite

### Description

Permutations, combinations, recurrence relations, applications. Students will learn the basics of combinatorics and its relation to the other areas of mathematics, including algebra and analysis.

## Desired Learning Outcomes

### Prerequisites

Math 371.

### Minimal learning outcomes

Permutations and combinations basics, including the Pigeonhole Principle, binomial coefficients and the Binomial Theorem, Stirling's Approximation, Inclusion/exclusion, Generating functions and recurrence relations (rational functions), Groups, permutations and counting problems -- Polya's Theorem

### Textbooks

Possible textbooks for this course include (but are not limited to):

- Chapters 5-9 of Alan Tucker's
*Applied Combinatorics*, John Wiley & Sons, Inc., 2002. - Chapters 1-4 of Russell Merris'
*Combinatorics*, 2nd edition, John Wiley & Sons, Inc., 2003. - Richard A. Brualdi,
*Introductory Combinatorics (5th Edition)*, Prentice Hall, 2010.

### Additional topics

Possibly Ramsey theory