{"product_id":"abstract-algebra-isbn-9780471433347","title":"Abstract Algebra","description":"\u003cp\u003eThis revision of Dummit and Foote's widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics.  \u003c\/p\u003e  \u003cp\u003e 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 student's understanding. With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.\u003c\/p\u003e  \u003cp\u003e The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year.  Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.\u003c\/p\u003e  Preface.  \u003cp\u003ePreliminaries.\u003c\/p\u003e \u003cp\u003ePART I: GROUP THEORY.\u003c\/p\u003e \u003cp\u003eChapter 1. Introduction to Groups.\u003c\/p\u003e \u003cp\u003eChapter 2. Subgroups.\u003c\/p\u003e \u003cp\u003eChapter 3. Quotient Group and Homomorphisms.\u003c\/p\u003e \u003cp\u003eChapter 4. Group Actions.\u003c\/p\u003e \u003cp\u003eChapter 5. Direct and Semidirect Products and Abelian Groups.\u003c\/p\u003e \u003cp\u003eChapter 6. Further Topics in Group Theory.\u003c\/p\u003e \u003cp\u003ePART II: RING THEORY.\u003c\/p\u003e \u003cp\u003eChapter 7. Introduction to Rings.\u003c\/p\u003e \u003cp\u003eChapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.\u003c\/p\u003e \u003cp\u003eChapter 9. Polynomial Rings.\u003c\/p\u003e \u003cp\u003ePART III: MODULES AND VECTOR SPACES.\u003c\/p\u003e \u003cp\u003eChapter 10. Introduction to Module Theory.\u003c\/p\u003e \u003cp\u003eChapter 11. Vector Spaces.\u003c\/p\u003e \u003cp\u003eChapter 12. Modules over Principal Ideal Domains.\u003c\/p\u003e \u003cp\u003ePART IV: FIELD THEORY AND GALOIS THEORY.\u003c\/p\u003e \u003cp\u003eChapter 13. Field Theory.\u003c\/p\u003e \u003cp\u003eChapter 14. Galois Theory.\u003c\/p\u003e \u003cp\u003ePART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA.\u003c\/p\u003e \u003cp\u003eChapter 15. Commutative Rings and Algebraic Geometry.\u003c\/p\u003e \u003cp\u003eChapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.\u003c\/p\u003e \u003cp\u003eChapter 17. Introduction to Homological Algebra and Group Cohomology.\u003c\/p\u003e \u003cp\u003ePART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS.\u003c\/p\u003e \u003cp\u003eChapter 18. Representation Theory and Character Theory.\u003c\/p\u003e \u003cp\u003eChapter 19. Examples and Applications of Character Theory.\u003c\/p\u003e \u003cp\u003eAppendix I: Cartesian Products and Zorn's Lemma.\u003c\/p\u003e \u003cp\u003eAppendix II: Category Theory.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e  \u003cp\u003eDavid S. Dummit and Richard M. Foote are the authors of Abstract Algebra, 3rd Edition, published by Wiley.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988651720933,"sku":"NP9780471433347","price":114.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471433347.jpg?v=1761781122","url":"https:\/\/k12savings.com\/products\/abstract-algebra-isbn-9780471433347","provider":"K12savings","version":"1.0","type":"link"}