Algebraic Number Theory and Fermat's Last Theorem
暫譯: 代數數論與費馬最後定理
Stewart, Ian, Tall, David
- 出版商: CRC
- 出版日期: 2020-09-30
- 售價: $2,190
- 貴賓價: 9.5 折 $2,081
- 語言: 英文
- 頁數: 322
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0367658712
- ISBN-13: 9780367658717
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商品描述
Updated to reflect current research, Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics--the quest for a proof of Fermat's Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles's proof of Fermat's Last Theorem opened many new areas for future work.
New to the Fourth Edition
- Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper's proof that Z(√14) is Euclidean
- Presents an important new result: Mihăilescu's proof of the Catalan conjecture of 1844
- Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat's Last Theorem
- Improves and updates the index, figures, bibliography, further reading list, and historical remarks
Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.
商品描述(中文翻譯)
本書已更新以反映當前的研究，代數數論與費馬最後定理（第四版） 介紹了代數數的基本概念，並探討了數學史上最引人入勝的故事之一——尋求費馬最後定理的證明。作者利用這個著名的定理來激發對代數數理論的一般研究，從相對具體的角度出發。學生將看到，威爾斯（Wiles）對費馬最後定理的證明為未來的研究開啟了許多新領域。
第四版的新內容
- 提供有關實二次數域的唯一質因數分解的最新資訊，特別是哈珀（Harper）證明 Z(√14) 是歐幾里得的結果
- 呈現一個重要的新結果：米哈伊萊斯庫（Mihăilescu）對1844年卡塔蘭猜想的證明
- 將一章修訂並擴展為兩章，涵蓋有關模函數的經典思想，並突顯弗雷（Frey）、威爾斯（Wiles）及其他人提出的新思想，這些思想導致了長期以來尋求的費馬最後定理的證明
- 改善並更新索引、圖形、參考書目、進一步閱讀清單及歷史備註
由著名數學家伊恩·斯圖爾特（Ian Stewart）和大衛·塔爾（David Tall）撰寫，本書繼續教導學生如何將自然數的性質擴展到更一般的數字結構，包括代數數域及其代數整數環。它還解釋了代數數理論中的基本概念如何用於解決數論中的問題。
作者簡介
Ian Stewart is an emeritus professor of mathematics at the University of Warwick and a fellow of the Royal Society. Dr. Stewart has been a recipient of many honors, including the Royal Society's Faraday Medal, the IMA Gold Medal, the AAAS Public Understanding of Science and Technology Award, and the LMS/IMA Zeeman Medal. He has published more than 180 scientific papers and numerous books, including several bestsellers co-authored with Terry Pratchett and Jack Cohen that combine fantasy with nonfiction.
David Tall is an emeritus professor of mathematical thinking at the University of Warwick. Dr. Tall has published numerous mathematics textbooks and more than 200 papers on mathematics and mathematics education. His research interests include cognitive theory, algebra, visualization, mathematical thinking, and mathematics education.
作者簡介(中文翻譯)
伊恩·斯圖爾特是華威大學的數學名譽教授，也是英國皇家學會的院士。斯圖爾特博士曾獲得多項榮譽，包括英國皇家學會的法拉第獎章、IMA金獎、AAAS科學與技術公共理解獎，以及LMS/IMA齊曼獎。他已發表超過180篇科學論文和多本書籍，其中包括與特里·普拉契特和傑克·科恩共同撰寫的幾本暢銷書，這些書籍將奇幻與非小說結合在一起。
大衛·陶爾是華威大學的數學思維名譽教授。陶爾博士已出版多本數學教科書和超過200篇有關數學及數學教育的論文。他的研究興趣包括認知理論、代數、可視化、數學思維和數學教育。
