Algebraic Number Theory and Fermat's Last Theorem: Third Edition / Edition 3

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Overview

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it is also eminently suited as a text for self-study.

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Editorial Reviews

From the Publisher
"The book remains, as before, an extremely attractive introduction to algebraic number theory, from the ideal-theoretic perspective." -Andrew Bremner, Mathematiacl Reviews, February 2003
From The Critics
This text for undergraduates presents an introduction to the fundamental ideas of algebraic numbers using the proof of Fermat's Last Theorem—a 300-year-old conjecture that had until recently eluded mathematicians—as the main example. The volume discusses all of the elements necessary for understanding the proof, including Euclidean imaginary fields and Minkowski's theorem on convex sets relative to a lattice. Stewart and Tall (both mathematics, U. of Warwick, UK) conclude with a survey of new developments and unsolved problems relating to the Theorem. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781568811192
  • Publisher: Taylor & Francis
  • Publication date: 12/1/2001
  • Edition description: Subsequent
  • Edition number: 3
  • Pages: 336

Table of Contents

Preface
Index of Notation
The Origins of Algebraic Number Theory 1
I Algebraic Methods 7
1 Algebraic Background 9
2 Algebraic Numbers 35
3 Quadratic and Cyclotomic Fields 61
4 Factorization into Irreducibles 73
5 Ideals 101
II Geometric Methods 127
6 Lattices 129
7 Minkowski's Theorem 139
8 Geometric Representation of Algebraic Numbers 145
9 Class-Group and Class-Number 151
III Number-Theoretic Applications 167
10 Computational Methods 169
11 Kummer's Special Case of Fermat's Last Theorem 183
12 The Path to the Final Breakthrough 201
13 Elliptic Curves 213
14 Elliptic Functions 235
IV Appendices 271
A Quadratic Residues 273
B Dirichlet's Units Theorem 293
Bibliography 303
Index 309
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