Summer semester 2023

Discrete Mathematics of Paul Erdős


  • 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


Top of this page   ☆   Sources   ☆   Bulletin board   ☆   Homeworks   ☆   Record of the material covered in class   ☆   Erdős links

Sources:


Top of this page   ☆   Sources   ☆   Bulletin board   ☆   Homeworks   ☆   Record of the material covered in class   ☆   Erdős links

Bulletin board


Top of this page   ☆   Sources   ☆   Bulletin board   ☆   Homeworks   ☆   Record of the material covered in class   ☆   Erdős links


Homeworks


Top of this page   ☆   Sources   ☆   Bulletin board   ☆   Homeworks   ☆   Record of the material covered in class   ☆   Erdős links

Record of the material covered in class

Date             Material covered
15.2 pp. 151--155. Károly Jordán
22.2 Lemma 10.4
1.3                                                                                                                                                                         
8.3                                                                                                                                                                         
15.3                                                                                                                                                                         
23.3                                                                                                                                                                         
29.3                                                                                                                                                                         
5.4                                                                                                                                                                         
12.4                                                                                                                                                                         
19.4                                                                                                                                                                         
26.4                                                                                                                                                                         
3.5                                                                                                                                                                         
10.5                                                                                                                                                                         


Top of this page     Sources     Bulletin board     Homeworks     Record of the material covered in class     Erdős links


Top of this page     Sources     Bulletin board     Homeworks     Record of the material covered in class     Erdős links

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