Syllabus of Math 386, Combinatorics

Textbook

Introductory Combinatorics, 3rd edition, by Richard A. Brualdi.
 
 

List of material to be covered

This list is not absolutely fixed.  The material mentioned in Chapters 1, 2, 3, 5, 6, and 10 generally forms the heart of the course but it is supplemented and may be partially replaced by other material.

Chapter 1:  What is Combinatorics?

Introduction to combinatorics.
Sections 1-3, 5, possibly 7, 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

Part or all may be covered.
 

Chapter 5: The Binomial Coefficients

Binomial identities, combinatorial proofs, binomial and multinomial theorems.
Possibly omitted: Section 6: Newton's binomial theorem.
 

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, permutations with forbidden positions, circular permutations with forbidden relations.
Derangements.
 

Chapter 10: Combinatorial Designs

Orthogonal sets of Latin squares (Section 4).
Modular arithmetic (with some finite field arithmetic) and applications to orthogonal Latin squares (Sections 1, 4).
 

Partially Ordered Sets and Equivalence Relations

(Optional.)  This is in Sections 4.5 and 5.7.
 

Recurrence Relations and Generating Functions

(Optional.)
Recurrence relations: Sections 7.1-3.
Generating functions: Sections 7.4-7 and 8.1.
 

Other optional topics

(not necessarily listed here) may be covered at the discretion of the instructor.
Go to course home page | announcements | homework assignments.