Syllabus of Math 386, Combinatorics
Fall, 2005
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Textbook

Introductory Combinatorics, 4th edition, by Richard A. Brualdi.

List of material covered

(This list is not the same every year.)

Chapter 1: What is Combinatorics?

Introduction to combinatorics.
Sections 1, 2, 3, on various types of combinatorial problems.

Chapter 2: The Pigeonhole Principle

Sections 1-2: The pigeonhole principle.

Chapter 3: Permutations and Combinations

All sections: basic counting, with and without repetition.

Chapter 5: The Binomial Coefficients

Sections 1-3, 5: Binomial identities, combinatorial proofs, binomial and multinomial theorems.
Section 4: Unimodality and Sperner's theorem.

Chapter 6: The Inclusion-Exclusion Principle and Applications

Sections 1-5: 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 10: Combinatorial Designs

Section 1: Modular arithmetic.
Section 4 (first half, to page 403): Latin squares.
Extra: Affine planes, projective planes, examples of finite fields.