Spring 2021 - Jeffry Kahn
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full year should (at least) incude most of the topics below. 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 (nice but optional); various relevant books will be on reserve.
There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having taken serious undergraduate courses in linear algebra and/or real analysis. (Basic linear algebra will be helpful, real analysis less so; it will be good to have seen at least a little combinatorics.) Taking 583 without having been in 582 is possible: check with me if in doubt.
Schedule of Sections:
- Spring 2021 Prof. Kahn
- Spring 2020 Prof. Narayanan
- Spring 2018 Prof. Beck