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Abstract Algebra : A Geometric Approach

Abstract Algebra : A Geometric Approach - 96 edition

Abstract Algebra : A Geometric Approach - 96 edition

ISBN13: 9780133198317

ISBN10: 0133198316

Abstract Algebra : A Geometric Approach by Theodore Shifrin - ISBN 9780133198317
Cover type: Print On Demand
Edition: 96
Copyright: 1996
Publisher: Prentice Hall, Inc.
Published: 1996
International: No
Abstract Algebra : A Geometric Approach by Theodore Shifrin - ISBN 9780133198317

ISBN13: 9780133198317

ISBN10: 0133198316

Cover type: Print On Demand
Edition: 96

List price: $118.00

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Summary

This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many unusual applications, and the interplay between algebra and geometry. It takes a concrete, example-oriented approach to the subject matter.

Features

  • Provides sample foundational material - both at the beginning of the text and in the appendices - while not avoiding calculus.
  • Features a "rings" first approach to make abstract concepts more accessible. Over 225 substantial examples and 750 exercises (many having multiple parts) are provided.
  • Geometry is slowly integrated through the text to make the abstract concrete and permit more structures to play with.
  • Culminates in Chapter 8 with the true integration of geometry and algebra.
  • Encourages the use of geometric models to discover the relations between group theory and geometry.

Table of Contents

Table of Contents

1. The Integers.
2. From the Integers to the Complex Numbers.
3. Polynomials.
4. Homomorphisms and Quotient Rings.
5. Field Extensions.
6. Groups.
7. Group Actions and Symmetry.
8. Non-Euclidean Geometries.


Appendix A. A Logic Review, Sets and Functions, and Equivalence Relations.
Appendix B. Miscellaneous Facts from Linear Algebra.

Supplementary Reading.
Table of Notations.
Index.

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