Abstract Algebra: A Comprehensive Introduction
售價
$
1,550
- 一般書籍
- ISBN：9781108836654
- 作者：John W. Lawrence, Frank A. Zorzitto
- 版次：1
- 年份：2021
- 出版商：Cambridge University
- 頁數/規格：638頁/精裝單色
- 參考網頁：International Business 9/e
書籍介紹
目錄
作者介紹
Description
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
- Balances accessibility with rigor, allowing motivated students to gain mastery of advanced topics
- Takes a 'definitions first, examples next' approach, striking the right balance between abstract material and its motivation
- Prepares students for advanced studies in mathematics by offering a uniquely wide base of knowledge in key topics
- Coverage includes: finite abelian groups, Sylow theory, semi-direct products, solvable groups, unique factorization, irreducibility of polynomials, Galois theory and solvability by radicals, ruler and compass constructions, module theory over principal ideal domains, and a novel approach to Gröbner bases
Table of Contents
1. A refresher on the integers
2. A first look at groups
3. Groups acting on sets
4. Basics on rings-mostly commutative
5. Primes and unique factorization
6. Algebraic field extensions
7. Applications of galois theory
8. Modules over principal ideal domains
9. Division algorithms
Appendix A: Infinite sets.
1. A refresher on the integers
2. A first look at groups
3. Groups acting on sets
4. Basics on rings-mostly commutative
5. Primes and unique factorization
6. Algebraic field extensions
7. Applications of galois theory
8. Modules over principal ideal domains
9. Division algorithms
Appendix A: Infinite sets.
John W. Lawrence, University of Waterloo, Ontario
Frank A. Zorzitto, University of Waterloo, Ontario
Frank A. Zorzitto, University of Waterloo, Ontario
