Syllabus of Math 386, Combinatorics
Fall, 2004
Under development

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Textbook

Introductory Combinatorics, 4th 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.

Chapter 3: Permutations and Combinations

All sections: basic counting, with and without repetition.

Chapter 4: Generating Permutations and Combinations

Section 5: Partial orders and equivalence relations.

Chapter 5: The Binomial Coefficients

Sections 1-3, 5: Binomial identities, combinatorial proofs, binomial and multinomial theorems.
Section 4: Unimodality and Sperner's theorem.
Section 6: Newton's binomial theorem.
Section 7: More on partially ordered sets.

Chapter 6: The Inclusion-Exclusion Principle and Applications

Sections 1-4: 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

Section 1 and the beginning of Section 2: Recurrence relations.
Sections 4-5: Generating functions.