Description

Book Synopsis

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermatâs Last Theorem, Fifth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsâthe quest for a proof of Fermatâs Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers, initially from a relatively concrete point of view. Students will see how Wilesâs proof of Fermatâs Last Theorem opened many new areas for future work.

New to the Fifth Edition

  • Pell's Equation x^2-dy^2=1: all solutions can be obtained from a single `fundamental' solution, which can be found using continued fractions.
  • Galois theory of number field extensions, relating the field structure to that of the group of automorphisms.
  • More material on cyclotomic fields, and some results on cubic fields

Algebraic Number Theory and Fermats Last Theorem

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A Paperback by Ian Stewart

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    View other formats and editions of Algebraic Number Theory and Fermats Last Theorem by Ian Stewart

    Publisher: CRC Press
    Publication Date: 12/24/2024
    ISBN13: 9781032610931, 978-1032610931
    ISBN10: 103261093X
    Also in:
    Discrete mathematics

    Description

    Book Synopsis

    Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermatâs Last Theorem, Fifth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsâthe quest for a proof of Fermatâs Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers, initially from a relatively concrete point of view. Students will see how Wilesâs proof of Fermatâs Last Theorem opened many new areas for future work.

    New to the Fifth Edition

    • Pell's Equation x^2-dy^2=1: all solutions can be obtained from a single `fundamental' solution, which can be found using continued fractions.
    • Galois theory of number field extensions, relating the field structure to that of the group of automorphisms.
    • More material on cyclotomic fields, and some results on cubic fields

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