Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition

Ian Stewart, David Tall

October 13, 2015 by Chapman and Hall/CRC
Textbook - 322 Pages - 21 B/W Illustrations
ISBN 9781498738392 - CAT# K26583

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  • Develops the basic theory from an algebraic standpoint, enabling students to understand the necessary concepts early on in the text
  • Discusses the history of Catalan’s problem and reviews the current version of the proof, which is an extensive technical application of cyclotomic integers Z(?) where ? is a complex root of unity
  • Illustrates the power of geometric methods arising from Minkowski’s theorem on convex sets relative to a lattice
  • Covers recent applications and discoveries, including the full Taniyama–Shimura–Weil conjecture
  • Incorporates practical examples of number-theoretic concepts
  • Includes a range of exercises at the end of each chapter

Figure slides are available upon qualifying course adoption.


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: Mihăilescu’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.