Abstract Algebra / Edition 3by David S. Dummit, Richard M. Foote
Pub. Date: 07/11/2003
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… See more details below
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.
• The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.
- Publication date:
- Edition description:
- New Edition
- Sales rank:
- Product dimensions:
- 7.78(w) x 9.47(h) x 1.64(d)
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.
Appendix I: Cartesian Products and Zorn's Lemma.
Appendix II: Category Theory.
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One of the best Algebra books I have used.
This is simply the best book to learn abstract algebra from. It has really outstanding chapters on group, ring and field theory, but this is not all: linear algebra, commutative algebra and some graduate topics like representation theory, algebraic geometry and homological algebra are presented in a way that is very well suited for self study: lots of motivation, good examples and good exercises. This book is the unique reference for algebra in the qualifying exam syllabus of the math phd program at Harvard University: check their homepage. I think there is not much left to say!