Modular Forms and Fermat’s Last Theorem

The successful proof of Fermat's Last Theorem by Andrew Wiles was probably the most widely publicized mathematical result of the 20th century. And once again, among their numerous other applications, elliptic curves are employed in the proof. The book is a compilation of articles written by first-class mathematicians, the reading of which will give one a thorough understanding of the proof, along with an overview of some very interesting topics in number theory and algebraic geometry. The reader who undertakes an understanding of the proof already no doubt has a substantial amount of 'mathematical maturity', and no review, no matter how complete, would influence greatly such a reader. Suffice it to say then that this book is excellent, and even a reader interested solely in elliptic curves and modular forms could benefit greatly from the reading of this book.

This item is very instructively, not only for "real" mathematicians. Of course, sometimes it's very difficult to "read". It gives me pleasure to own the proof of FLT.

As you'd expect from a Springer work of this nature, there's not a lot of basics before you're up there swimming with the best of them. This is a meaty and fascinating tome that expects you to know what's what before you start. This is not a text book - it's more for the (pretty advanced) mathematician to find out exactly what's behind Wiles' famous proof, complete with the work that buttressed it all that had been done in the previous four centuries. Extensive references give you everything you need to read up on the background to anything you need to study in further depth. In short, this is all you need to understand this vital and highly important intellectual achievement.

フェルマー向けの本はいろいろありますが、これは完全に専門家向け フェルマーが解決した年に行われた会議の報告集です。 ワイルズ氏の論文でつかわれている理論の解説が主です。 理解するのに整数論専門の大学院レベルは必要でしょう。米国有数 の学者たちが関連する内容の講義をしてそれを記録したもの。 シルバーマン氏の楕円曲線概説、テイト氏の有限平坦群スキーム論,..... ワイルズ氏の論文を読む大変さが一部分わかる気がする。