Math 450: Combinatorics
(Credit Hours:Lecture Hours:Lab Hours)
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
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
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.
Possibly Ramsey theory