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1. Abstract algebra [2004]

Book
xii, 932 p. : ill. ; 25 cm.
  • Preface.Preliminaries.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.Index.
  • (source: Nielsen Book Data)9780471433347 20160528
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.
(source: Nielsen Book Data)9780471433347 20160528
Science Library (Li and Ma)
MATH-120-01, MATH-122-01
Book
xv, 551 p. : ill. ; 24 cm.
The primary goal of these lectures is to introduce a beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed sparingly, and then mainly as useful and unifying language to describe phenomena already encountered in concrete cases. The book begins with a brief tour through representation theory of finite groups, with emphasis determined by what is useful for Lie groups. The focus then turns to Lie groups and Lie algebras and finally to the heart of the course: working out the finite dimensional representations of the classical groups. The goal of the last portion of the book is to make a bridge between the example-oriented approach of the earlier parts and the general theory.
(source: Nielsen Book Data)9780387974958 20160528
Science Library (Li and Ma)
MATH-122-01