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**About this book :- **
**A First Course in Abstract Algebra: Rings, Groups, and Fields (2E) ** written by
** Marlow Anderson, Todd Feil **.

Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be some what lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there is more natural-and ultimately more effective. Authors Anderson and Feil developed A First Course in Abstract Algebra: Rings, Groups and Fields based upon that conviction.
The text begins with ring theory, building upon students' familiarity with integers and polynomials. Later, when students have become more experienced, it introduces groups. The last 'of the book develops Galois Theory with the goal of showing the impossibility of solving the quintic with radicals. Each section of the book ends with a "Section in a Nutshell" synopsis of important definitions and theorems. Each chapter includes "Quick Exercises" that reinforce the topic addressed and are designed to be worked as the text is read.
Problem sets at the end of each chapter begin with "Warm-Up Exercises" that test fundamental comprehension, followed by regular exercises, both computational and "supply the proof" problems. A Hints and Answers section is provided at the end of the book. As stated in the title, this book is designed for a first course--either one or two semesters in abstract algebra. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex numbers.

**Book Detail :- **
** Title: ** A First Course in Abstract Algebra: Rings, Groups, and Fields
** Edition: ** SEcond Edition
** Author(s): ** Marlow Anderson, Todd Feil
** Publisher: ** Chapman and Hall/CRC
** Series: **
** Year: ** 2005
** Pages: ** 345
** Type: ** PDF
** Language: ** Englsih
** ISBN: ** 1584885157,9781584885153
** Country: ** US

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**About Author :- **

The author ** Marlow Anderson ** , is a graduate of Whitman College (1972), and received his Ph.D. in 1977 from the University of Kansas, US.

The author ** Todd Feil ** , Denison University, Granville, Ohio, USA.

**All Famous Books of this Author :- **

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** • Download PDF A First Course in Abstract Algebra: Rings, Groups, and Fields (2E) by Marlow Anderson, Todd Feil **

** • Download PDF A First Course in Abstract Algebra: Rings, Groups, and Fields (3E) by Marlow Anderson, Todd Feil **

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**Book Contents :- **
**A First Course in Abstract Algebra: Rings, Groups, and Fields (2E) ** written by
** Marlow Anderson, Todd Feil **.
cover the following topics.

**Part-I Numbers, Polynomials, and Factoring**

1. The Natural Numbers

2. The Integers

3. Modular Arithmetic

4. Polynomials with Rational Coecients

5. Factorization of Polynomials
**Part-II Rings, Domains, and Fields
**

6. Rings

7. Subrings and Unity

8. Integral Domains and Fields

9. Polynomials over a Field

Part-III Unique Factorization

10. Associates and Irreducebles

11. Factorization and Ideal

12. Principal Ideal Domain

13. Prime and Unique Factorization

14. Polynomials with Integer Coecients

15. Euclidean Domains

Part-IV Ring Homomorphisms and Ideals

16. Ring Homomorphisms

17. The Kernel

18. Rings of Cosets

19. The Isomorphism Theorem for Rings

20. Maximal and Prime Ideals

21. The Chinese Remainder Theorem

Part-V Groups

22. Symmetries of Geometric Figures

23. Permutations

24. Abstract Groups

25. Subgroups

26. Cyclic Groups

Part-VI Group Homomorphisms

27. Group Homomorphisms

28. Structure and Representation

31. Cosets and Lagrange's Theorem

32. Groups of Cosets

33. The Isomorphism Theorem for Groups

Part-VI Topics from Group Theory

34. The Alternating Groups

35. Fundamental Theorem of Abelian Groups

36. Solvable Groups

VII Constructibility Problems

37. Constructions with Compass and Straightedge

38. Constructibility and Quadratic Field Extensions

39. The Impossibility of Certain Constructions

Part-VIII Vector Spaces and Field Extensions

40. Vector Spaces I

41. Vector Spaces II

42. Field Extensions and Kronecker's Theorem

43. Algebraic Field Extensions

44. Finite Extensions and Constructibility Revisited

Part-X Galois Theory

45. The Splitting Field

46. Finite Fields

47. Galois Groups

48. The Fundamental Theorem of Galois Theory

49. Solving Polynomials by Radicals

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