Description: This is the first part of a 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
van Lint-Wilson is nice but optional. There is really no text; various relevant books will be on reserve.
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.