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 instructor. Limited to 24 students. Fall semester. Professor Folsom.
If Overenrolled: Preference will be given to Amherst College sophomores and juniors