Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics, 50) - Softcover

Edwards, Harold M.

Softcover

ISBN 10: 0387950028 ISBN 13: 9780387950020

Publisher: Springer, 2000

Synopsis

This book is an introduction to algebraic number theory via the famous problem of "Fermat's Last Theorem." The exposition follows the historical development of the problem, beginning with the work of Fermat and ending with Kummer's theory of "ideal" factorization, by means of which the theorem is proved for all prime exponents less than 37. The more elementary topics, such as Euler's proof of the impossibilty of x+y=z, are treated in an elementary way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummer's ideal theory to quadratic integers and relates this theory to Gauss' theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

About this title

From the Publisher

This book is a genetic introduciton to algebraic number theory which follows the development of the subject in the work of Fermat, Kummer and others, motivating new ideas and techniques by explaining the problems which led to their creation. The central problem is the one indicated in the title, but many other basic questions of algebraic number thoery are also treated.

Edition details

• Publisher: Springer
• Publication date: 2000
• Language: English
• ISBN 10: 0387950028
• ISBN 13: 9780387950020
• Binding: Paperback
• Edition number: 1
• Number of pages: 422