Jeffry Kahn
Probability in Discrete Mathematics
Probabilistic ideas have been the key to and/or subjective of many of the most spectacular developments in discrete mathematics/combinatorics. With discussion of a few of these an eventual goal, this course will cover: methods and machinery as needed (a function of intended uses and participants' backgrounds); combinatorial applications of probability, preferably where no probability seems called for; and analysis of discrete random systems (random graphs being the prototypical example).
Alon-Spencer, The Probabilistic Method (optional and we won't follow it, but a good source for some things 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.