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Algebraic Number Theory and Fermat's Last Theorem

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Algebraic Number Theory and Fermat's Last Theorem Synopsis

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.

About This Edition

ISBN: 9781498738392
Publication date: 13th October 2015
Author: Ian (University of Warwick, UK) Stewart, David (University of Warwick, UK) Tall
Publisher: Chapman & Hall/CRC an imprint of Taylor & Francis Inc
Format: Hardback
Pagination: 342 pages
Genres: Discrete mathematics
Number theory
Combinatorics and graph theory