 Course description:
Paul Erdős
(1913  1996) was an outstanding, prolific, influential, legendary mathematician. We will study a
selection of his results in number theory, geometry, Ramsey theory,
extremal combinatorial problems, and graph theory that laid the foundations of discrete mathematics before it matured into the rich and vibrant discipline of today. From time to time we will stray from his own work to the work of his confréres and disciples, but we shall never escape the gravitational pull of
the great man.
At a leisurely pace, we shall cover a subset of the following topics:
The ErdősRényi random graphs and their evolution.
Proof of Bertrand's postulate.
Turán's theorem and Turán numbers.
Hamilton cycles.
Extremal graph theory.
Deltasystems and Deza's proof of an ErdősLovász conjecture.
Van der Waerden's theorem and van der Waerden numbers.
The Friendship Theorem, strongly regular graphs, and Moore graphs of diameter two.



The subject and the instructor, ca.1976

