Jeffry Kahn
Probabilistic methods
Probabilistic methods are central in contemporary combinatorics and have been key to many of the most exciting discrete results of recent decades. This course will combine development of relevant methods, discussion of applications in combinatorics and beyond, and study of discrete random models (e.g.\random graphs and hypergraphs, random walk) for their own sake.
Alon-Spencer, The Probabilistic Method (optional and we won't follow it, but a good source for much of what we'll cover).
I will try to make the course self-contained except for basic combinatorics and very basic probability. Check with me if in doubt.