Binghamton University

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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.

Go to course home page | announcements | homework assignments.