Abstract Algebra 3/e (H)
售價
$
2,000
- 一般書籍
- ISBN：9780471433347
- 作者：David S. Dummit
- 版次：3
- 年份：2004
- 出版商：John Wiley
- 頁數/規格：932頁/精裝單色
書籍介紹
目錄
Description
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
Table of Contents
PART I: GROUP THEORY
Chapter 1. Introduction to Groups
Chapter 2. Subgroups
Chapter 3. Quotient Group and Homomorphisms
Chapter 4. Group Actions
Chapter 5. Direct and Semidirect Products and Abelian Groups
Chapter 6. Further Topics in Group Theory
PART II: RING THEORY
Chapter 7. Introduction to Rings
Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
Chapter 9. Polynomial Rings
PART III: MODULES AND VECTOR SPACES
Chapter 10. Introduction to Module Theory
Chapter 11. Vector Spaces
Chapter 12. Modules over Principal Ideal Domains
PART IV: FIELD THEORY AND GALOIS THEORY
Chapter 13. Field Theory
Chapter 14. Galois Theory
PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA
Chapter 15. Commutative Rings and Algebraic Geometry
Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
Chapter 17. Introduction to Homological Algebra and Group Cohomology
PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS
Chapter 18. Representation Theory and Character Theory
Chapter 19. Examples and Applications of Character Theory
PART I: GROUP THEORY
Chapter 1. Introduction to Groups
Chapter 2. Subgroups
Chapter 3. Quotient Group and Homomorphisms
Chapter 4. Group Actions
Chapter 5. Direct and Semidirect Products and Abelian Groups
Chapter 6. Further Topics in Group Theory
PART II: RING THEORY
Chapter 7. Introduction to Rings
Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
Chapter 9. Polynomial Rings
PART III: MODULES AND VECTOR SPACES
Chapter 10. Introduction to Module Theory
Chapter 11. Vector Spaces
Chapter 12. Modules over Principal Ideal Domains
PART IV: FIELD THEORY AND GALOIS THEORY
Chapter 13. Field Theory
Chapter 14. Galois Theory
PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA
Chapter 15. Commutative Rings and Algebraic Geometry
Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
Chapter 17. Introduction to Homological Algebra and Group Cohomology
PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS
Chapter 18. Representation Theory and Character Theory
Chapter 19. Examples and Applications of Character Theory
