The Turán number and probabilistic combinatorics

Abstract

In this short expository article, we describe a mathematical tool called the probabilistic method, and illustrate its elegance and beauty through proving a few well-known results. Particularly, we give an unconventional probabilistic proof of a classical theorem concerning the Turán number $T(n,k,l)$. Surprisingly, this proof cannot be found in existing literature.

5 pages; to appear in Amer. Math. Monthly 2012