Mathematics 281 - Combinatorics

This course emphasizes enumerative combinatorics, a classical subject in mathematics related to the theory of counting. Problems in this area often pertain to finding the number of possible arrangements of a set of objects under some particular constraints. This course incorporates a wide set of problems involving enumerative combinatorics, as well as theory and applications. Topics include the sum and product rules; combinations and permutations; binomial and multinomial coefficients; the principle of inclusion and exclusion; generating functions; recurrence relations; Catalan, Stirling, Bell and Eulerian numbers; partitions; tableaux; and stable marriage. Additional topics may vary.

Requisite: MATH 121, and MATH 220 or other prior experience with basic mathematical proof techniques (e.g., induction) by consent of the instructor. Limited to 24 students. Fall semester. Professor Folsom.