Department of Mathematical Sciences
Binghamton University

Syllabus of Math 386, Combinatorics

Fall 2010

Textbook

List of material covered

This list is not the same every year. The topics are not necessarily in order.

• Chapter 1: What is Combinatorics?

  Introduction to combinatorics.
  Sections 1, 2, 4, 6 on various types of combinatorial problems.

• Chapter 2: Permutations and Combinations

  All sections: basic counting, with and without repetition. Application to probability.

• Chapter 5: The Binomial Coefficients

  Sections 1-2, 4: Binomial identities, combinatorial proofs, binomial theorem.
  Section 5: Multinomial theorem.

• 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.

• Chapter 7: Recurrence Relations and Generating Functions

  Sections 1, 3: Generating functions.
  Sections 4-5: Recurrence relations.
  Section 6: Application to a geometry problem.

• Chapter 8: Special Counting Sequences

  Section 1: Catalan numbers.
  Section 2: Difference sequences. Stirling numbers.

• Chapter 3: The Pigeonhole Principle

  Sections 1-2: The pigeonhole principle.