Math 450: Combinatorics

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Catalog Information

Title

Combinatorics.

(Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

Offered

Su

Prerequisite

Math 371.

Description

Permutations, combinations, recurrence relations, applications. Students will learn the basics of combinatorics and its relation to the other areas of mathematics, including algebra and analysis.

Desired Learning Outcomes

Prerequisites

Math 371.

Minimal learning outcomes

Permutations and combinations basics, including the Pigeonhole Principle, binomial coefficients and the Binomial Theorem, Stirling's Approximation, Inclusion/exclusion, Generating functions and recurrence relations (rational functions), Groups, permutations and counting problems -- Polya's Theorem

Textbooks

Possible textbooks for this course include (but are not limited to):

  • Chapters 5-9 of Alan Tucker's Applied Combinatorics, John Wiley & Sons, Inc., 2002.
  • Chapters 1-4 of Russell Merris' Combinatorics, 2nd edition, John Wiley & Sons, Inc., 2003.
  • Richard A. Brualdi, Introductory Combinatorics (5th Edition), Prentice Hall, 2010.

Additional topics

Possibly Ramsey theory

Courses for which this course is prerequisite