- 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 some of the following topics:
Van der Waerden's theorem and van der Waerden numbers. Erdős's refinement of Turán's theorem. Erdős-Stone theorem and Erdős-Stone-Simonovits formula. Jensen's inequality and Cauchy-Bunyakovski-Schwarz inequality. Extremal graph theory. Ramsey's theorem and Ramsey numbers. Graphs with a large chromatic number and no short cycles. The Erdős-Rényi random graphs and their evolution. Hamilton cycles. Erdős's proof of Bertrand's postulate. Sperner's theorem and the Erdős-Ko-Rado theorem. Extremal set theory.
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| The subject and the instructor, ca.1976 |
