This course is aimed at Ph.D. students from different fields who expect to use discrete probability in their research. Graduate level measure theoretic probability will be useful, but not a requirement. I expect the course will be accessible to advanced undergraduates who have had sufficient exposure to probability.
We shall illustrate some important techniques in studying discrete random structures through a number of examples. The techniques we shall focus on will include (if time permits)
the probabilistic method;
first and second moment methods, martingale techniques for concentration inequalities;
coupling techniques, monotone coupling and censoring techniques;
correlation inequalities, FKG and BK inequalities;