Methods in modern Combinatorics

Noga Alon
 

Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas , and its study has experienced an impressive growth in recent years. I will discuss two of the main general techniques that played a crucial role in the development of modern comdinatorics ; algebraic tools and probabilistic methods. Both techniques will be illustrated by examples , were the emphasis is on the basic ideas , the connection to other areas and some future challenges.