Graduate Student Seminar: Transcendental Numbers

Friday, March 4, 2016 - 4:00pm
111 MSB
Nick Cox-Steib (Univ of Missouri)

Abstract: Diophantine approximation is the study of rational approximations to arbitrary numbers. Deep results in this area, such as Roth’s theorem, provide powerful criteria for determining the irrationality and transcendence of a given number. The purpose of this talk is to sketch a very broad overview of these results and the techniques involved, with the goal of motivating the proof, due to Charles Hermite, that the number e is transcendental.  Prerequisites are minimal: familiarity with reduction modulo a prime will be helpful.

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