Project IV (MATH4072) 2008-2009


Fermat's Last Theorem

J Funke and H Gangl

Description

In this project, we will study the various approaches to "Fermat's Last Theorem" throughout history, beginning with Fermat in the 17th century via Euler, Germain, and Kummer to Wiles's successful solution at the end of the 20th century.

Prerequisites

This project is for students who are strongly interested in algebra and number theory.

Corequisite: Number Theory (MATH4211)

Resources

The individual chapters of the book "Notes on Fermat's Last Theorem" by A.J. van der Poorten make a nice introductory read and can be found online here.

Here is a very recent text focussing on the role of Sophie Germain in the attempts to prove FLT which could form the thread for a project

R. Laubenbacher, D. Pengelley: "Voici ce que j'ai trouvé:" Sophie Germain's grand plan to prove FLT

Historical approaches to Fermat's last theorem can be found in the following reference which covers a lot of elementary approaches and makes an exciting read:

P. Ribenboim: 13 Lectures on Fermat's Last Theorem

Somewhat more sophisticated in that it motivates and uses algebraic number theory to solve certain cases of FLT is

H.M. Edwards: Fermat's last theorem: a genetic introduction to algebraic number theory

There are more modern books on the subject, a particularly beautiful one being

Y. Hellegouarch: Invitation to the Mathematics of Fermat-Wiles

and two rather sophisticated conference volumes

Gary Cornell, Joseph H. Silverman, Glenn Stevens (eds.): Modular Forms and Fermat's Last Theorem

John Coates, S.T. Yau (eds.): Elliptic curves, modular forms and Fermat's last theorem: proceedings of a conference held in the Institute of Mathematics of the Chinese University of Hong Kong.


A good (albeit dense) set of lecture notes on modular forms is here

Don Zagier: Modular Forms of One Variable

email: Jens Funke Herbert Gangl


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