- 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 confrères 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:
Proof of Bertrand's postulate. Erdős's proof of Turán's theorem. Hamilton cycles. Ramsey's theorem and Ramsey numbers. Delta-systems and Deza's proof of an Erdős-Lovász conjecture. Sperner's theorem and the Erdős-Ko-Rado theorem. Van der Waerden's theorem and van der Waerden numbers. Extremal graph theory. The Friendship Theorem, strongly regular graphs, and Moore graphs of diameter two. The Erdős-Rényi random graphs and their evolution.
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| The subject and the instructor, ca.1976 |
