An Invitation to Abstract Algebra
暫譯: 抽象代數入門

Rosenberg, Steven J.

  • 出版商: CRC
  • 出版日期: 2021-12-22
  • 售價: $3,600
  • 貴賓價: 9.5$3,420
  • 語言: 英文
  • 頁數: 372
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367748614
  • ISBN-13: 9780367748616
  • 立即出貨 (庫存 < 3)

商品描述

Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics.

To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout.

The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois' achievement in understanding how we can--and cannot--represent the roots of polynomials.

The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory.

The presentation includes the following features:

  • Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters.
  • The text can be used for a one, two, or three-term course.
  • Each new topic is motivated with a question.
  • A collection of projects appears in Chapter 23.

Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks--period. This book is offered as a manual to a new way of thinking. The author's aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.

商品描述(中文翻譯)

學習抽象代數可以是一場令人驚嘆的發現之旅。這個主題不必被簡化,也不應該被呈現得好像所有學生都會成為數學教師。這是一個美麗、深刻且有用的領域,是許多數學內外領域共同語言的一部分。

要開始這段發現之旅,具備一些數學推理的經驗是有益的。本書對其主題採取相當嚴謹的方式,並期望讀者能夠理解並創建證明以及例子。

本書遵循一個單一的弧線,從簡單的算術和高中代數開始,逐漸引入抽象結構和概念,最終以尼爾斯·亨利克·阿貝爾(Niels Henrik Abel)和埃瓦里斯特·伽羅瓦(Evariste Galois)在理解我們如何——以及無法——表示多項式根的成就作為高潮。

對數學有經驗的讀者可能會注意到對交換代數的偏好以及對數論的喜愛。

本書的呈現包括以下特點:
- 練習題旨在支持和擴展章節中的材料,並為後續章節做準備。
- 本文可用於一學期、兩學期或三學期的課程。
- 每個新主題都以一個問題作為動機。
- 第23章中包含了一系列項目。

抽象代數確實是一個深奧的主題;它不僅可以改變一個人對數學的思考方式,還可以改變一個人的思考方式——總之。本書作為一種新思維方式的手冊提供。作者的目標是激發對理解材料的渴望,鼓勵更多的發現,並培養對該主題本身的欣賞。

作者簡介

Steve Rosenberg is a professor in the Mathematics and Computer Science Department at the University of Wisconsin-Superior. He received his Ph.D. from the Ohio State University. As an educator, Dr. Rosenberg has both developed and taught a wide array of courses in mathematics and computer science. As a researcher, he has published results in the areas of algebraic number theory, cryptographic protocols, and combinatorial designs, among others. As a software developer, his clients included Coca-Cola Enterprises and the pension agency of Cook County Illinois. He has extensive experience in computer science and software engineering.

作者簡介(中文翻譯)

史蒂夫·羅森伯格(Steve Rosenberg)是威斯康辛大學超級校區(University of Wisconsin-Superior)數學與計算機科學系的教授。他在俄亥俄州立大學(Ohio State University)獲得博士學位。作為一名教育工作者,羅森伯格博士開發並教授了多門數學和計算機科學的課程。作為一名研究者,他在代數數論、密碼協議和組合設計等領域發表了研究成果。作為一名軟體開發人員,他的客戶包括可口可樂企業(Coca-Cola Enterprises)和伊利諾伊州庫克縣的退休金機構(pension agency of Cook County Illinois)。他在計算機科學和軟體工程方面擁有豐富的經驗。