Algebraic Number Theory
暫譯: 代數數論

Mollin, Richard A.

Algebraic Number Theory
  • 出版商: CRC
  • 出版日期: 2024-10-14
  • 售價: $2,700
  • 貴賓價: 9.5 折 $2,565
  • 語言: 英文
  • 頁數: 442
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 1032919825
  • ISBN-13: 9781032919829
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

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商品描述

Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and class groups in the third chapter. Applications are now collected in chapter four and at the end of chapter five, where primality testing is highlighted as an application of the Kronecker-Weber theorem. In chapter five, the sections on ideal decomposition in number fields have been more evenly distributed. The final chapter continues to cover reciprocity laws.

New to the Second Edition

  • Reorganization of all chapters
  • More complete and involved treatment of Galois theory
  • A study of binary quadratic forms and a comparison of the ideal and form class groups
  • More comprehensive section on Pollard's cubic factoring algorithm
  • More detailed explanations of proofs, with less reliance on exercises, to provide a sound understanding of challenging material

The book includes mini-biographies of notable mathematicians, convenient cross-referencing, a comprehensive index, and numerous exercises. The appendices present an overview of all the concepts used in the main text, an overview of sequences and series, the Greek alphabet with English transliteration, and a table of Latin phrases and their English equivalents.

Suitable for a one-semester course, this accessible, self-contained text offers broad, in-depth coverage of numerous applications. Readers are lead at a measured pace through the topics to enable a clear understanding of the pinnacles of algebraic number theory.

商品描述(中文翻譯)

將材料更新以反映現代應用，代數數論（第二版）已經完全重寫和重新組織，以融入新的風格、方法論和呈現方式。本版的重點在於第一章的整數範疇、理想和唯一分解；第二章的域擴展；以及第三章的類群。應用現在集中在第四章和第五章的結尾，其中強調了素性測試作為克羅內克-韋伯定理的應用。在第五章中，數域中理想分解的部分已經更均勻地分佈。最後一章繼續涵蓋互反律。

第二版的新內容



  • 所有章節的重新組織

  • 對伽羅瓦理論的更完整和深入的處理

  • 對二次二元形式的研究以及理想和形式類群的比較

  • 對波拉德立方因式分解算法的更全面的部分

  • 對證明的更詳細解釋，減少對練習題的依賴，以提供對挑戰性材料的扎實理解

本書包括著名數學家的迷你傳記、方便的交叉引用、全面的索引和大量練習題。附錄提供了主文本中使用的所有概念的概述、序列和級數的概述、希臘字母及其英語音譯，以及拉丁短語及其英語對應的表格。

本書適合一學期的課程，這本易於理解的自成體系的文本提供了對眾多應用的廣泛而深入的覆蓋。讀者將以適當的速度逐步了解主題，以便清晰理解代數數論的巔峰。

作者簡介

Richard A. Mollin is a professor in the Department of Mathematics and Statistics at the University of Calgary. In the past twenty-five years, Dr. Mollin has founded the Canadian Number Theory Association and has been awarded six Killam Resident Fellowships. He has written more than 200 publications, including Advanced Number Theory with Applications (CRC Press, August 2009), Fundamental Number Theory with Applications, Second Edition (CRC Press, February 2008), An Introduction to Cryptography, Second Edition (CRC Press, September 2006), Codes: The Guide to Secrecy from Ancient to Modern Times (CRC Press, May 2005), and RSA and Public-Key Cryptography (CRC Press, November 2002).

作者簡介(中文翻譯)

Richard A. Mollin 是卡爾加里大學數學與統計系的教授。在過去的二十五年中，Mollin 博士創立了加拿大數論協會，並獲得了六項 Killam 常駐研究獎學金。他撰寫了超過 200 篇出版物，包括 應用進階數論（CRC Press，2009 年 8 月）、應用基礎數論（第二版）（CRC Press，2008 年 2 月）、密碼學導論（第二版）（CRC Press，2006 年 9 月）、密碼：從古代到現代的保密指南（CRC Press，2005 年 5 月）以及 RSA 與公鑰密碼學（CRC Press，2002 年 11 月）。

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