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Chapter 45 Roth's Theorem in Ten Minutes

Project by: Jashanraj Singh Gosain, Geo Lee, and Trevor Noble.

\(\textbf{Summary:}\)The aim of our project was to introduce Roth's theorem on arithmetic progressions to our classmates. Since some of the concepts used in the proof of Roth's theorem are beyond the scope of our course, we intend to prove Roth's theorem in such a way that is digestible for everyone in the class to learn something.

Here is a simplified statement of of Roth's theorem:

If a subset of natural numbers is divided into a finite number of non–overlapping parts and if a particular part has positive upper density, then we can find a 3–term arithmetic progression in that part.

A pdf file with our class presentation is available here: Roth's Theorem by Jashanrajm, Geo, and Trevor.

Here is a video with our slides and music composed and performed by Leifshane Estrada, Vanessa Gottfriedson, and Matthew Tong: