DescriptionIn 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.PrerequisitesThis project is for students who are strongly interested in algebra and number theory.Corequisite: Number Theory (MATH4211) ResourcesThe 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.
Don Zagier: Modular Forms of One Variable
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email: Jens Funke Herbert Gangl