Extremal Combinatorics

In Extremal Combinatorics we study problems of the form ``How large (or small) can a parameter associated to a finite structure be under certain restrictions"? In this course we will study several problems of this kind and learn some exciting theorems from Ramsey theory, extremal set theory, etc. There will be an equal emphasis on the methods used to solve these problems. In particular, we will learn the probabilistic method, polynomial method and topological method.