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 Erdős-Rényi random graphs and their evolution. Proof of Bertrand's postulate. Turán's theorem and Turán numbers. Hamilton cycles. Extremal graph theory. Delta-systems and Deza's proof of an Erdős-Lovász 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

• Instructor: Vašek Chvátal
  • Email:     c h v a t a l (at) c s e (dot) c o n c o r d i a (dot) c a
    

• Textbook: The Discrete Mathematical Charms of Paul Erdős (also at Megabooks and at Amazon)

• Classes: Wednesdays 9:00--10:35 in S8
  

• Prerequisities: Ease with the notation of elementary set theory and with matrix descriptions of systems of linear equations. Elementary calculus (such as: all powers grow faster than all logarithms, l'Hopital's rule, the Taylor expansion of the exponential).

• Grading scheme: 50% homeworks, 50% final exam
  

Sources:

• Collected Papers of Paul Erdős up to 1989

Erdős quotations Property is a nuisance. There will be plenty of time to rest in the grave. A theorem a day means promotion and pay; a theorem a year and you're out on your ear. Another roof, another proof. Favourites of Erdős, often attributed to him, but originating elsewhere A mathematician is a machine for turning coffee into theorems. (Alfréd Rényi) Chebyshev said it and I say it again: There is always a prime between n and 2n. (Nathan Fine) Websites dedicated to Erdős Erdős site from Zentralblatt für Mathematik Erdős page from the Mathematical Institute in Budapest References and links to information about Erdős from the Erdős Number Project. Articles on Erdős Two Places at Once (A Remembrance of Paul Erdős) by János Pach Paul Erdős (1913 -- 1996) by László Babai and Joel Spencer The Mathematics of Paul Erdős by László Babai, Carl Pomerance, and Péter Vértesi Reminiscences of Paul Erdős (1913-1996) by Melvin Henriksen Remembering Paul Erdős by Aleksandar Ivić Biography from MacTutor Obituaries from The New York Times and The Washington Post Two films on Erdős by George Csicsery N is a Number: A Portrait of Paul Erdős (1993) Erdős 100 Plus (a DVD compilation of ten videos totaling 180 minutes) A book on Erdős Bruce Schechter, My Brain is Open : The Mathematical Journeys of Paul Erdős , Simon & Schuster, 1998.

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