Algebraic Number Theory and Fermat's Last Theorem

Ian Stewart, David Tall

314 pages, parution le 30/01/2002 (3^eme édition)

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Résumé

One of the most exciting and widely publicized recent mathematical discoveries was the proof, by Andrew Wiles, of Fermat's Last Theorem, a 300-year-old conjecture that had eluded both professional mathematicians and serious amateurs until very recently. The problem is part of the theory of algebraic numbers, and its solution draws on an incredible range of modern mathematics.

This new, completely revised edition of a classic text introduces all elements necessary for understanding Wiles' proof, as well as new developments and unsolved problems. Written by two distinguished mathematicians, this book weaves together the historical development of the subject and a presentation of mathematical techniques. The result is a solid introduction to one of the most active research areas of mathematics for serious math buffs and a textbook accessible to undergraduates.

Contents

Preface

Index of Notation

The Origins of Algebraic Number Theory

I/ Algebraic Methods

1/ Algebraic Background
2/ Algebraic Numbers
3/ Quadratic and Cyclotomic Fields
4/ Factorization into Irreducibles
5/ Ideals

II/ Geometric Methods

6/ Lattices
7/ Minkowski's Theorem
8/ Geometric Representation of Algebraic Numbers
9/ Class group and Class-Number

III/ Number-Theoretic Applications

10/ Computational Methods
11/ Kummer's Special Case of Frmat's Last Theorem
12/ The Path to the Final Breakthrough
13/ Elliptic Curves
14/ Elliptic Functions

IV/ Appendices

A/ Quadriatic Residues
B/ Dirichlet's Units Theorem

Bibliography

Index

L'auteur - Ian Stewart

Ian Stewart, professeur émérite de mathématiques à l'université de Warwick (Grande-Bretagne), prix Faraday 2001 de la Royal Society, a publié plus de quatre-vingts livres, dont de nombreux best-sellers. Sont disponibles dans la collection Champs : Dieu joue-t-il aux dés ?, La Chasse aux trésors mathématiques, 17 équations qui ont changé le monde.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	AK Peters
Auteur(s)	Ian Stewart, David Tall
Parution	30/01/2002
Édition	3^eme édition
Nb. de pages	314
Format	15,5 x 23,5
Couverture	Broché
Poids	561g
Intérieur	Noir et Blanc
EAN13	9781568811192
ISBN13	978-1-56881-119-2