Introduction to Abstract Algebra, 4/e (Hardcover)

W. Keith Nicholson

  • 出版商: Wiley
  • 出版日期: 2012-03-20
  • 定價: $1,900
  • 售價: 9.5$1,805
  • 語言: 英文
  • 頁數: 560
  • 裝訂: Hardcover
  • ISBN: 1118135350
  • ISBN-13: 9781118135358
  • 立即出貨 (庫存 < 3)

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<內容簡介>

The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.

The Fourth Edition features important concepts as well as specialized topics, including:

  The treatment of nilpotent groups, including the Frattini and Fitting subgroups

  Symmetric polynomials

  The proof of the fundamental theorem of algebra using symmetric polynomials

  The proof of Wedderburn's theorem on finite division rings

  The proof of the Wedderburn-Artin theorem

Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.

Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
<章節目錄>

0 Preliminaries
1 Integers and Permutations
2 Groups
3 Rings
4 Polynomials
5 Factorization in Integral Domains
6 Fields
7 Modules over Principal Ideal Domains
8 p-Groups and the Sylow Theorems
9 Series of Subgroups
10 Galois Theory
11 Finiteness Conditions for Rings and Modules

商品描述(中文翻譯)

《引論抽象代數第四版》持續提供一種易於理解的方法來介紹抽象代數的基本結構:群、環和域。該書獨特的呈現方式通過在定義抽象結構之前提供歸納法、數論、模n的整數和排列的具體例子,幫助讀者立即開始使用抽象概念進行計算,這些概念在本文後面更詳細地發展。

第四版包括重要概念和專門主題,包括:
- 對零幂群的處理,包括Frattini子群和Fitting子群
- 對稱多項式
- 使用對稱多項式證明基本定理
- 對有限除環的Wedderburn定理的證明
- Wedderburn-Artin定理的證明

在整本書中,通過實例和實際問題來說明概念及其應用,有助於讀者無論其數學背景如何,都能完全理解。豐富的計算和理論練習題從基礎到複雜,讓讀者測試對材料的理解。此外,詳細的歷史注釋和數學家傳記為關鍵主題的討論提供了背景和闡明。對於希望獲得對書中練習題部分解答的讀者,還提供了解答手冊。

《引論抽象代數第四版》是高年級本科和初級研究生課程的優秀教材。該書還可作為工程、計算機科學和應用數學領域從業人員的寶貴參考和自學工具。