This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems.
The topics covered in the class will include (but are not limited to): linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, Janson and Talagrand inequalities and pseudo-randomness.
- The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008. - Random Graphs, by B. Bollobás, 2nd Edition, Cambridge University Press, 2001. - Random Graphs, by S. Janson, T. Luczak and A. Rucinski, Wiley, 2000. - Graph Coloring and the Probabilistic Method, by M. Molloy and B. Reed, Springer, 2002.
Performance assessment information (valid until the course unit is held again)