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  5. A First Course in Abstract Algebra

Overview

For courses in Abstract Algebra.

This ISBN is for the Pearson eText access card.


A comprehensive approach to abstract algebra — in a powerful eText format

A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra – and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose.  This revision also includes applied topics such as RSA encryption and coding theory, as well as examples of applying Gröbner bases. 

 

Key to the 8th Edition has been transforming from a print-based learning tool to a digital learning tool. The eText is packed with content and tools, such as mini-lecture videos and interactive figures, that bring course content to life for students in new ways and enhance instruction. A low-cost, loose-leaf version of the text is also available for purchase within the Pearson eText. 


Pearson eText is a simple-to-use, mobile-optimized, personalized reading experience. It lets students read, highlight, and take notes all in one place, even when offline. Seamlessly integrated videos and interactive figures allow students to interact with content in a dynamic manner in order to build or enhance understanding. Educators can easily customize the table of contents, schedule readings, and share their own notes with students so they see the connection between their eText and what they learn in class — motivating them to keep reading, and keep learning. And, reading analytics offer insight into how students use the eText, helping educators tailor their instruction. Learn more about Pearson eText. 


NOTE: Pearson eText is a fully digital delivery of Pearson content and should only be purchased when required by your instructor. This ISBN is for the Pearson eText access card. In addition to your purchase, you will need a course invite link, provided by your instructor, to register for and use Pearson eText. 


0321390369 / 9780321390363  PEARSON ETEXT -- FIRST COURSE IN ABSTRACT ALGEBRA, A -- ACCESS CARD, 8/e

Table of contents

Instructor's Preface 

Dependence Chart 

Student's Preface 


0. Sets and Relations 


I. GROUPS AND SUBGROUPS 

1. Binary Operations 

2. Groups 

3. Abelian Groups 

4. Nonabelian Examples 

5. Subgroups 

6. Cyclic Groups 

7. Generating Sets and Cayley Digraphs 


II. STRUCTURE OF GROUPS

8. Groups and Permutations 

9. Finitely Generated Abelian Groups 

10. Cosets and the Theorem of Lagrange 

11. Plane Isometries 


III. HOMOMORPHISMS AND FACTOR GROUPS

12. Factor Groups 

13. Factor-Group Computations and Simple Groups 

14. Groups Actions on a Set 

15. Applications of G -Sets to Counting 


IV. ADVANCED GROUP THEORY

16. Isomorphism Theorems 

17. Sylow Theorems 

18. Series of Groups 

19. Free Abelian Groups 

20. Free Groups 

21. Group Presentations 


V. RINGS AND FIELDS  

22. Rings and Fields 

23. Integral Domains 

24. Fermat's and Euler's Theorems 

25. Encryption 


VI. CONSTRUCTING RINGS AND FIELDS 

26. The Field of Quotients of an Integral Domain 

27. Rings and Polynomials 

28. Factorization of Polynomials over Fields 

29. Algebraic Coding Theory 

30. Homomorphisms and Factor Rings 

31. Prime and Maximal Ideals 

32. Noncommutative Examples 


VII. COMMUTATIVE ALGEBRA 

33. Vector Spaces 

34. Unique Factorization Domains 

35. Euclidean Domains 

36. Number Theory 

37. Algebraic Geometry 

38. Gröbner Basis for Ideals 


VIII. EXTENSION FIELDS

39. Introduction to Extension Fields 

40. Algebraic Extensions 

41. Geometric Constructions 

42. Finite Fields 


IX. Galois Theory 

43. Introduction to Galois Theory 

44. Splitting Fields 

45. Separable Extensions 

46. Galois Theory 

47. Illustrations of Galois Theory 

48. Cyclotomic Extensions 

49. Insolvability of the Quintic 

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