Fermat’s Last Theorem
A Genetic Introduction to Algebraic Number Theory
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ISBN-13:
9780387950020
Veröffentl:
2000
Einband:
Paperback
Erscheinungsdatum:
14.01.2000
Seiten:
432
Autor:
Harold M. Edwards
Gewicht:
651 g
Format:
235x155x24 mm
Serie:
50, Graduate Texts in Mathematics
Sprache:
Englisch
Beschreibung:
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.
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.
1 Fermat.- 2 Euler.- 3 From Euler to Kummer.- 4 Kummer's theory of ideal factors.- 5 Fermat's Last Theorem for regular primes.- 6 Determination of the class number.- 7 Divisor theory for quadratic integers.- 8 Gauss's theory of binary quadratic forms.- 9 Dirichlet's class number formula.- Appendix: The natural numbers.- Answers to exercises.
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