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.
Go to course home page | announcements | homework
assignments.