By Ian Stewart,David Tall

Updated to mirror present learn, Algebraic quantity idea and Fermat’s final Theorem, Fourth Edition introduces basic rules of algebraic numbers and explores the most exciting tales within the historical past of mathematics—the quest for an explanation of Fermat’s final Theorem. The authors use this celebrated theorem to encourage a basic learn of the idea of algebraic numbers from a comparatively concrete standpoint. scholars will see how Wiles’s facts of Fermat’s final Theorem opened many new components for destiny work.


New to the Fourth Edition



  • Provides up to date info on special leading factorization for actual quadratic quantity fields, specifically Harper’s facts that Z(√14) is Euclidean

  • Presents a huge new outcome: Mihăilescu’s facts of the Catalan conjecture of 1844

  • Revises and expands one bankruptcy into , overlaying classical principles approximately modular services and highlighting the recent principles of Frey, Wiles, and others that resulted in the long-sought evidence of Fermat’s final Theorem

  • Improves and updates the index, figures, bibliography, extra examining checklist, and ancient remarks


Written through preeminent mathematicians Ian Stewart and David Tall, this article maintains to coach scholars tips to expand homes of common numbers to extra common quantity constructions, together with algebraic quantity fields and their jewelry of algebraic integers. It additionally explains how simple notions from the speculation of algebraic numbers can be utilized to resolve difficulties in quantity idea.

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