Algebraic number theory and Fermat's last theorem /
General Material Designation
[Book]
First Statement of Responsibility
Ian Stewart, David Tall.
EDITION STATEMENT
Edition Statement
Fourth edition.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Boca Raton :
Name of Publisher, Distributor, etc.
Chapman & Hall/CRC,
Date of Publication, Distribution, etc.
2015.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource :
Other Physical Details
illustrations (black and white)
GENERAL NOTES
Text of Note
Previous edition: Natrick: AK Peters, 2001.
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
In Cyclotomic Fields Geometric Methods ; Lattices; Lattices; The Quotient Torus Minkowski's Theorem ; Minkowski's Theorem; The Two-Squares Theorem; The Four-Squares Theorem Geometric Representation of Algebraic Numbers; The Space 1st Class-Group and Class-Number; The Class-Group; An Existence Theorem; Finiteness of the Class-Group; How to Make an Ideal Principal; Unique Factorization of Elements in an Extension Ring Number-Theoretic Applications ; Computational Methods; Factorization of a Rational Prime; Minkowski Constants; Some Class-Number Calculations; Table of Class-Numbers Kummer's Special Case of Fermat's Last Theorem ; Some History; Elementary Considerations; Kummer's Lemma; Kummer's Theorem; Regular Primes The Path to the Final Breakthrough.
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SUMMARY OR ABSTRACT
Text of Note
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.