Description
This is a course in number theory. An elliptic curve is an equation of the form y2 = x3 + ax2 + bx + c, where a, b, c are given rational numbers. The aim of the course is to be able to find the solutions (x, y) to this equation with x and y rational numbers. The methods used are from geometry and algebra. The study of elliptic curves is an important part of current research in number theory and cryptography. It was central to the proof of Fermat's last theorem. There are still many unsolved problems in this area, in particular the Birch-Swinnerton-Dyer conjecture, for which there is a $1 million prize offered by the Clay Institute.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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