MTH 238, Combinatorics

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed

(none)

Prerequisites

MTH 200W or MTH 235 or MTH 171.

This course is a prerequisite or co-requisite for

(none)

Description

This course will study enumerative combinatorics (rather than graph theory).

Topics covered

Tilings, perfect coverings, parity arguments, the pigeonhole principle, permutations and combinations of sets and multisets, binomial and multinomial coefficients, the inclusion-exclusion principle, derangements, recurrence relations, generating functions, formal power series, Catalan and Stirling numbers, partitions, and Polya’s theory for counting the number of colorings of an object with nontrivial symmetries. We will write proofs and learn proof by induction. Small bits of group theory, linear algebra, and differential equations will be introduced as needed. Prior experience with abstraction and proofs will be helpful. People interested in the Virginia Tech Regional Mathematics Contest or the William Lowell Putnam competition should take this course.

MTH 190