#
Syllabus of Math 386, Combinatorics

Fall, 2003

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###
Textbook

Introductory Combinatorics, 3rd edition, by Richard A. Brualdi.

### List of material covered

(This list is **subject to change** and is not the same every year.)

####
Chapter 1: What is Combinatorics?

Introduction to combinatorics.

Sections 1, 2, 3, 5, on various types of combinatorial problems.
####
Chapter 2: The Pigeonhole Principle

Sections 1-2: The pigeonhole principle.

Section 3: Ramsey's theorem.
####
Chapter 3: Permutations and Combinations

All sections: basic counting, with and without repetition.
#### Chapter 5: The Binomial Coefficients

Binomial identities, combinatorial proofs, binomial and multinomial theorems.

Unimodality and Sperner's theorem.

Section 6: Newton's binomial theorem.

(Section 7: omitted.)
#### Chapter 6: The Inclusion-Exclusion Principle and Applications

The Principle of Inclusion and Exclusion and a variety of ways to
apply it, notably combinations with repetition, derangements,
permutations with forbidden positions, circular permutations with
forbidden relations.
#### Chapter 7: Recurrence Relations and Generating Functions

Recurrence relations: Section 7.1 and the beginning of 7.2.

Generating functions: Sections 7.4-6.
#### Chapter 8: Special Counting Sequences

Section 8.1: Catalan numbers.

Section 8.4: A Geometric Problem.

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