Graduate Research and Discovery Symposium (GRADS)

Title

Congruent Numbers, Elliptic Curves, and a Million Dollar Problem

Advisor

Professor Jim Brown

Document Type

Poster

Department

Mathematical Sciences

Publication Date

Spring 2013

Abstract

Number theory is an area of mathematics which is concerned with properties of the integers, and because of this many of the problems in number theory can be stated in a simple way. However, just because a problem has a simple statement does not mean that its solution will be as simple. It is precisely this contrast between simply stated problems and extremely difficult solutions which makes number theory so intriguing. In this poster, we draw a connection between the congruent number problem, the oldest major problem in number theory, and the Birch and Swinnerton-Dyar conjecture, which is one of the Clay Mathematics Institute's millennium problems. In light of this conjecture of Birch and Swinnerton-Dyar, we will present some of our current results which contribute to the understanding of the objects involved.

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