Number Theory I: Fermat's Dream

by Kazuya Kato, Nobushige Kurokawa, Takeshi Saito

This is the English translation of the original Japanese book.

In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers.

Genres: Mathematics

154 pages, Paperback

First published January 1, 2000

Reviews

[Woflmao · Rating 5 out of 5]

A well-written and original introduction to algebraic number theory. In the first chapter, some classical problems from number theory are discussed, and motivated by these problems, the book proceeds quickly to today's relevant research problems. This is a very beautiful way to introduce the abstract concepts studied in number theory today. Some previous knowledge on elementary number theory is helpful, but can be done without if one is willing to take certain results for granted.

[Isaac]

Unfortunately DNF as the loan is due back to the library after a busy month. But I hope it makes its way back into my life at some point, because what I did read was excellent. Concisely written, but a few reads of a tricky sentence should typically be enough to extract the hidden meaning, for anyone who has had at least one college proof-based math course. I found the historical approach using Fermat’s notes surprisingly deftly interwoven with the material rather than distracting as it typically is. There were a few instances that I felt I was glimpsing deep mathematics, which is a testament to both the rich subject material (elliptic curves, etc.) and the authors’ guidance. If I had finished it, I’m sure this would be a 5-star book.

[Xingyu]

Awesome and terse chapter on p-adic numbers. Beautifully written and approachable. It covers the materials in its own way.

[Yasiru · Rating 5 out of 5]

Alas, I have had to pause mid-way.