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Math 367 syllabus

Combinatorial Enumeration

Course Description:  

An introduction to the mathematical theory of counting. Topics covered are: basic counting principles, permutations, combinations, pigeonhole principle, inclusion-exclusion principle, partitions, recurrence relations, generating functions, and enumeration under group action.

Prerequisites:   (MA 126 and MA 267) or MA 320 MA 320 is strongly recommended.   

Textbook:  David R. Mazur, Combinatorics: A Guided Tour, MAA (2010).  ISBN: 978-0-88385-762-5

Topics:   Topics covered are: basic counting principles, permutations, combinations, pigeonhole principle, inclusion-exclusion principle, partitions, recurrence relations, generating functions, and enumeration under group action.

Learning Objectives

-Be able to solve a wide variety of problems involving ordered and unordered selections.

- Understand the Inclusion-Exclusion Principle and be able to use it to solve combinatorial problems. 

- Understand the importance of generating functions in combinatorics and be able to use generating functions to solve a variety of combinatorial problems.

- Be able to model and solve a range of combinatorial problems using recurrence relations.

- Be able to apply Burnside’s Lemma.

 

Last Updated February 15, 2024