Syllabus of Math 386, Combinatorics
Fall, 2005
Under development
Go to course home page | announcements | homework
assignments.
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.
Go to course home page | announcements | homework
assignments.