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超级新品 A Book of Abstract Algebra 英文原版 抽象代数 Charles C Pinter【中商原版

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  • 作者: Pinter著
  • 出版社: 培生(Pearson)
  • 出版时间:2010-01-14
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  • 作者: Pinter著
  • 出版社:培生(Pearson)
  • 出版时间:2010-01-14
  • 版次:2
  • 印次:2
  • 页数:400
  • 开本:25开
  • ISBN:9780486474175
  • 版权提供:培生(Pearson)

A Book of Abstract Algebra 英文原版 抽象代数 Charles C Pinter


基本信息

Author Charles C. Pinter

Format Paperback | 400 pages

Dimensions 136 x 216 x 23mm | 408g

Publication date 14 Jan 2010

Publisher Dover Publications Inc.

Publication City/Country New York, United States

Language English

Edition Statement 2nd ed.

Illustrations note Illustrations, unspecified

ISBN10 0486474178

ISBN13 9780486474175

页面参数仅供参考,具体以实物为准


内容简介


这篇引人入胜但严谨的文章涵盖了基础抽象代数典型课程中涵盖的所有主题。它的易读方法提供了一种直观的方法,包括非正式讨论和主题安排的练习。适用于抽象代数的本科课程,适用于初中和高级数学专业以及未来的数学教师。第二版提供附加练习,以提高学生对应用程序的熟悉程度。

介绍性章节从抽象代数的历史根源开始。后续章节避免使用定义定理证明推论示例的传统格式;相反,他们采取与学生讨论的形式,着重于解释和提供动力。每章都基于一个中心主题,通常是一个特定的应用或用途。作者根据需要提供基本的背景知识,并按通常的顺序讨论标准主题。他在丰富的练习中介绍了许多高级和外围学科,并辅以充足的指导和评论,并为不同水平的学生提供了广泛的经验。

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.

An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.


作者简介


Charles C. Piner is Professor Emeritus of Mathematics at Bucknell University.


书籍目录


Chapter 1 Why Abstract Algebra

Chapter 2 Operations

Chapter 3 The Definition of Groups

Chapter 4 Elementary Properties of Groups

Chapter 5 Subgroups

Chapter 6 Functions

Chapter 7 Groups of Permutations

Chapter 8 Permutations of a Finite Set

Chapter 9 Isomorphism

Chapter 10 Order of Group Elements

Chapter 11 Cyclic Groups

Chapter 12 Partitions and Equivalence Relations

Chapter 13 Counting Cosets

Chapter 14 Homomorphism

Chapter 15 Quotient Groups

Chapter 16 The Fundamental Homomorphism Theorem

Chapter 17 Rings: Definitions and Elementary Properties

Chapter 18 Ideals and Homomorphism

Chapter 19 Quotient Rings

Chapter 20 Integral Domains

Chapter 21 The Integers

Chapter 22 Factoring into Primes

Chapter 23 Elements of Number Theiory (Optional)

Chapter 24 Rings of Polynomials

Chapter 25 Factoring Polynomials

Chapter 26 Substitution in Polynomials

Chapter 27 Extensions of Fields

Chapter 28 Vector Spaces

Chapter 29 Degrees of Field Extensions

Chapter 30 Ruler and Compass

Chapter 31 Galois Theory: Preamble

Chapter 32 Galois Theory: The Heart of the Matter

Chapter 33 Solving Equations by Radicals

Appendix A Review of Set Theory

Appendix B Review of the Integers

Appendix C Review of Mathematical Integers

锘�Answers to Selected Exercises

Index

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