Probabilistic Methods in Discrete Mathematics

The probabilitistic method proves the existence of a combinatorial structure by showing a random element in an appropriate probability space has the desired properties with positive probability. The course will introduce the basic techniques and give applications in graph theory, combinatorics, discrete optimization, theoretical CS. In particular, some of the following will be considered: linearity of expectation; alterations; the second moment method; bounding of large deviations; the local lemma; correlation inequalities; martingales and tight concentration; discrepancy; derandomization.