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Algebraic number theory and Fermat's last theorem/ Ian Stewart and David Tall

By: Contributor(s): Publication details: Boca Raton: CRC Press, 2022Edition: 4thDescription: xix, 322 pages; 23 cmISBN:
  • 9781032296272
Subject(s): DDC classification:
  • 23rd 512.74 St849
Contents:
Algebraic Methods -- Algebraic background -- Algebraic numbers -- Quardratic and cyclotomic fields -- Factorization into irreducibles -- Ideals -- Geometric methods -- Lattices -- Minkowski's theorem -- Geometric representation of algebraic numbers -- Class-group and class number -- Number-theoretic applications -- Computational methods -- Kummer's special case of Fermat's last theorem -- The Path to the final breakthrough -- Elliptic curves -- Elliptic functions -- Wiles's strategy and recent developments -- Appendices -- A Quadratic residues -- B Dirichlet's units theorem
Summary: This book 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.
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Includes bibliography and index

Algebraic Methods --
Algebraic background -- Algebraic numbers -- Quardratic and cyclotomic fields -- Factorization into irreducibles -- Ideals --
Geometric methods --
Lattices -- Minkowski's theorem -- Geometric representation of algebraic numbers -- Class-group and class number --
Number-theoretic applications --
Computational methods -- Kummer's special case of Fermat's last theorem -- The Path to the final breakthrough -- Elliptic curves -- Elliptic functions -- Wiles's strategy and recent developments --
Appendices --
A Quadratic residues -- B Dirichlet's units theorem

This book 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.

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