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About this book :-
A Book of Abstract Algebra (2E) written by
Charles C. Pinter .
This book addresses itself especially to the average student, to enable him or her to learn and understand as much algebra as possible. In scope and subject-matter coverage, it is no different from many other standard texts. It begins with the promise of demonstrating the unsolvability of the quintic and ends with that promise fulfilled. Standard topics are discussed in their usual order, and many advanced and peripheral subjects are introduced in the exercises, accompanied by ample instruction and commentary.
The first few exercise sets in each chapter contain problems which are essentially computational or manipulative. Then, there are two or three sets of simple proof-type questions, which require mainly the ability to put together definitions and results with understanding of their meaning. After that, I have endeavored to make the exercises more interesting by arranging them so that in each set a new result is proved, or new light is shed on the subject of the chapter.
As a rule, all the exercises have the same weight: very simple exercises are grouped together as parts of a single problem, and conversely, problems which require a complex argument are broken into several subproblems which the student may tackle in turn. I have selected mainly problems which have intrinsic relevance, and are not merely drill, on the premise that this is much more satisfying to the student.
Book Detail :-
Title: A Book of Abstract Algebra
Edition: Second Edition
Author(s): Charles C. Pinter
Publisher: Dover Publications
Series:
Year: 2010
Pages: 394
Type: PDF
Language: Englsih
ISBN: 0486474178
Country: US
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About Author :-
The author Charles Pinter , Professor Professor of Mathematics, Emeritus, Bucknell University, US.
His interest is the specific problems involved in modeling structures arising in neuroscience.
He is interested in perceptual mechanisms and especially the process of perceptual learning.
He has worked on the theoretical aspects of training neural networks
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• Download PDF A Book of Abstract Algebra (2E) by Charles C. Pinter
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Book Contents :-
A Book of Abstract Algebra (2E) written by
Charles C. Pinter .
cover the following topics.
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:
33. Solving Equations by Radicals
Appendix A. Review of Set Theory
Appendix B. Review of the Integers
Appendix C. Review of Mathematical Induction
Answers to Selected Exercises
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