16:642:582 Combinatorics I

Fall 2019

Jeffry Kahn

Course Description:

This is the first part of the two-semester course surveying basic topics in combinatorics.
Topics for the full year should (at least) include most of:

Enumeration (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics)

Matching theory, polyhedral and fractional issues

Partially ordered sets and lattices, Mobius functions

Theory of finite sets, hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities

Probabilistic methods

Algebraic and Fourier methods

Entropy methods

Textbook:

A Course in Combinatorics by van Lint and Wilson

Prerequisites:

There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having had good courses in linear algebra (such as 640:350) and real analysis (such as 640:411) at the undergraduate level. It will help to have seen at least a little prior combinatorics, and (very) rudimentary probability will also occasionally be useful. See me if in doubt.