Fermat’s Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics, 50) by Harold M. Edwards (PDF)

Description

This introduction to algebraic number theory via the famous problem of “Fermats Last Theorem” follows its historical development, beginning with the work of Fermat and ending with Kummers theory of “ideal” factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated 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 Kummers theory to quadratic integers and relates this to Gauss’theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

User’s Reviews

Editorial Reviews: 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐item just as described; fast shipment, good packaging: A+

⭐There was a great burst of excitement, and several popular books, when Andrew Wiles proved “Fermat’s last theorem”. The popular books are fine, but they don’t address the deepest issue: among all the many long-standing unsolved problems in number theory that are easy to state but resistant to solution, why did “Fermat’s last theorem” attract the efforts of so many top-flight mathematicians: Euler, Sophie Germain, Kummer, and many others? The problem itself has no useful application or extension, and as stated seems like just another piece of obstinate trivia. So why is it mathematically interesting?The answer, of course, is that attacks on the problem revealed deep and important connections between elementary number theory and various other branches of mathematics, such as the theory of rings. Thus, as so often in mathematics, the importance of the problem lies in where it leads the mind, rather than in the problem itself. Harold M. Edwards’ bookis a minor classic of exposition, showing how the instincts of top-flight research mathematicians lead them to fruitful work from a seemingly unimportant starting point. I’m only sorry that Professor Edwards seems never to have completed the second volume he had hoped to write.Thus book deserves to be read by a much larger audience than it has gotten; in particular, I believe every graduate student in math who hopes to do good research, regardless of specialty, would benefit from reading it. Beyond that, any mathematically inclined reader with a modicum of training in math, is likely to find this a fascinating book.

⭐Molto interessante, sia l’argomento in sè che per come è trattato, l’ho trovato un testo chiaro e che da un lato parte da considerazioni molto semplici, dall’altro porta a risultati che richiedono discrete conoscenze matematiche. Trovo quindi che sia, per quanto possibile, completo ed adatto ad una vasta gamma di persone.Culture personnelle . Un itinéraire d’exception , à mettre entre touts les mains et spécialement TOUT(E) étudiant(e) en Mathématiques ; brillant , complet et exceptionnel de clarté100年も200年も300年も350年もかけて疑問を解いた。ここに多くの考えが生まれた。その深さにロマンを感じます。

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