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

By: Contributor(s): Material type: TextTextPublication details: Boca Raton: CRC Press, ©2016.Edition: 4th edDescription: xix, 322 p. : illustrations ; 24 cmISBN:
  • 9781498738392 (hbk. : acidfree paper)
Subject(s): DDC classification:
  • 512.74 23 St849
Contents:
1. Algebraic background -- 2. Algebraic numbers -- 3. Quadratic and cyclotomic fields -- 4. Factorization into irreducibles -- 5. Ideals -- 6. Lattices -- 7. Minkowski's theorem -- 8. Geometric representation of algebraic numbers -- 9. Class-group and class-number -- 10. Computational methods -- 11. Kummer's special case of Fermat's last theorem -- 12. The path to the final breakthrough -- 13. Elliptic curves -- 14. Elliptic functions -- 15. 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.74 St849 (Browse shelf(Opens below)) Available 137305
Total holds: 0

Includes bibliographical references and index.

1. Algebraic background --
2. Algebraic numbers --
3. Quadratic and cyclotomic fields --
4. Factorization into irreducibles --
5. Ideals --
6. Lattices --
7. Minkowski's theorem --
8. Geometric representation of algebraic numbers --
9. Class-group and class-number --
10. Computational methods --
11. Kummer's special case of Fermat's last theorem --
12. The path to the final breakthrough --
13. Elliptic curves --
14. Elliptic functions --
15. 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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