Algebraic Number Theory and Fermat's Last Theorem

by Ian Stewart, David Tall

Updated to reflect current research, Algebraic Number Theory and Fermat s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics the quest for a proof of Fermat s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles s proof of Fermat s Last Theorem opened many new areas for future work.

New to the Fourth Edition


Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper s proof that Z( 14) is Euclidean Presents an important new result: Mih ilescu s proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat s Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks
Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory. "

Genres: Mathematics, Algebra, Textbooks, Reference

342 pages, Hardcover

First published January 1, 1979

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Jon-Erik]

I have been working on understanding the proof of Fermat's Last Theorem for several years. I'm pretty strong in analysis and algebra, but I really know nothing about modularity. Hoping this one teaches me enough to get me there.

P.S. I need some work on modular forms to really understand the proof, but this gave me enough context to understand the broader strokes. I'm good with the elliptic curves, numbers, and algebra and this book explains it well too.

[George Law · Rating 4 out of 5]

A very good account of algebraic-number theory, a branch of mathematics whose genesis was motivated by the search for a proof of Fermat’s last theorem, as well as a brief discussion of the ideas used by Andrew Wiles for his Wolfskehl Prize winning proof. I thought the theory of ideals could be developed a bit further, but I understand that the central theme of the book is on FLT.

[Chris · Rating 5 out of 5]

A captivating beach read for the algebraically literate non-specialist.

[Amar Pai · Rating 4 out of 5]

Good overview of algebraic number theory as it applies to FLT, however not exactly pitched at beginners. You'll want to have a grounding in abstract algebra & linear algebra at the minimum. Still, even if you don't, you can get a good sense of the "big picture" and a high-level understanding of the advances in mathematics that were directly or indirectly related to attempts to solve FLT. Overall a fascinating read if you're a math geek who wants something a little deeper than Simon Singh's pop treatment of Wiles' proof.

[Peng Gao · Rating 4 out of 5]

The book with shorter title seems more useful but cannot find it in this database