Author: MIT OpenCourseWare
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Instructor: Yufei Zhao
View the complete course: https://ocw.mit.edu/18-217F19
YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX
In an unsuccessful attempt to prove Fermat’s last theorem, Schur showed that every finite coloring of the integers contains a monochromatic solution to x + y = z, an early result in Ramsey theory. Prof. Zhao begins the course with a proof of Schur’s theorem via graph theory and how it led to the modern development of additive combinatorics. He then takes the class on a tour of modern highlights of the field: Roth’s theorem, Szemerédi’s theorem, and the Green-Tao theorem.
License: Creative Commons BY-NC-SA
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Video source Youtube