N. Alon, J. Spencer, The Probabilistic Method, Wiley, 1992.
Additional course notes may be distributed.
This scheme may be adjusted slightly as circumstances warrant.
The main theme of the course will be concerned with applications of probabilistic methods in discrete mathematics. The basics theory was developed by Erdos and Renyi in the 1950's. Today, this is one of the inevitable tools in modern combinatorics, and has enabled profound applications in graph theory, combinatorics, discrete geometry, number theory, and theoretical computer science. On the other hand, all these applications motivated further development of probability theory, where important new areas have been discovered.
We shall uncover the beauty of this subject by following the textbook written by Noga Alon and Joel Spencer.
The following topics will be covered:
Each of the above lecture topics will take about 1-2 weeks.
Students will be asked to present some of the topics in an informal Instructional-Seminar-like setting.
Homework (due a week after being appointed): NOT AVAILABLE BEFORE THE DATE SHOWN