- 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 disciplin 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. The Erdős-Szekeres, the Sylvester-Gallai, and the De Bruijn-Erdős theorems. 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. Turán numbers. Property B and hypergraph colouring. 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. Chromatic number of graphs and the probabilistic method. The Erdős-Rényi random graphs and their evolution. Hamilton cycles.
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| The subject and the instructor, ca.1976 |
