A Book of Abstract Algebra / Edition 2

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Overview

Long-considered one of the best-written titles on the subject, this text is aimed at the abstract or modern algebra course taken by junior and senior math majors and many secondary math education majors. A mid-level approach, this text features clear prose, an intuitive and well-motivated approach, and exercises organized around specific concepts.
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Product Details

  • ISBN-13: 9780072943504
  • Publisher: McGraw-Hill Higher Education
  • Publication date: 5/6/2003
  • Edition description: New Edition
  • Edition number: 2
  • Product dimensions: 6.00 (w) x 8.80 (h) x 0.90 (d)

Table of Contents

1. Why Abstract Algebra?

2. Operations

3. The Definition of Groups

4. Elementary Properties of Groups

5. Subgroups

6. Functions

7. Groups of Permutations

8. Permutations of a Finite Set

9. Isomorphism

10. Order of Group Elements

11. Cyclic Groups

12. Partitions and Equivalence Relations

13. Counting Cosets

14. Homomorphisms

15. Quotient Groups

16. The Fundamental Homomorphism Theorem

17. Rings: Definitions and Elementary Properties

18. Ideals and Homomorphisms

19. Quotient Rings

20. Integral Domains

21. The Integers

22. Factoring into Primes

23. Elements of Number Theory (Optional)

24. Rings of Polynomials

25. Factoring Polynomials

26. Substitution in Polynomials

27. Extensions of Fields

28. Vector Spaces

29. Degrees of Field Extensions

30. Ruler and Compass

31. Galois Theory: Preamble

32. Galois Theory: The Heart of the Matter

33. Solving Equations by Radicals

Appendix A: Review of Set Theory

Appendix B: Review of the Integers

Appendix C. Review of Mathematical Induction

Answers Selected Exercises

Index
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