- Course description:
Paul Erdős
(1913 -- 1996) was one of the greatest mathematicians of the twentieth
century. He made pre-eminent contributions to number theory,
probability theory, real and complex analysis, discrete geometry,
approximation theory, and set theory;
some
say that he founded the field of discrete mathematics.We will study a
selection of his results in number theory, geometry, Ramsey theory,
extremal combinatorial problems, and graph theory. From time to time
we will stray from his own work to the work of his disciples, but we
shall never escape the gravitational pull of the great man.
- More detailed outline:
Proof of Bertrand's postulate. The Erdős-Szekeres theorem, the
Sylvester-Gallai Theorem, the de Bruijn-Erdős theorem.
Ramsey's theorem and Ramsey numbers. Van der Waerden's theorem and
van der Waerden numbers. Delta-systems and a proof of the
Erdős-Lovász conjecture. Extremal graph
theory. Graph colouring. Sperner's theorem, the
Erdős-Ko-Rado theorem, extremal set theory. The Friendship
Theorem and strongly regular graphs. Hamiltonian cycles.
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The subject and the instructor, ca.1976
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