
Abstract Algebra: A Geometric Approach, 1/e
Theodore Shifrin, University of Georgia
Published August, 1995 by Prentice Hall Engineering/Science/Mathematics
Copyright 1996, 416 pp.
Cloth
ISBN 0133198316

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Abstract AlgebraMathematics

This book explores the essential theories and techniques of modern
algebra, including its problemsolving skills, basic proof techniques,
many unusual applications, and the interplay between algebra and geometry.
It takes a concrete, exampleoriented approach to the subject matter.
provides ample 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.
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.
