Syllabus of Math 386, Combinatorics
Fall, 2002
Textbook
Introductory Combinatorics, 3rd 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, 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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