Abstract Algebra: A Geometric Approach / Edition 1

by Theodore Shifrin

Overview

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

Product Details

ISBN-13:	9780133198317
Publisher:	Pearson Education
Publication date:	08/14/1995
Edition description:	New Edition
Pages:	432
Product dimensions:	7.00(w) x 9.10(h) x 1.00(d)

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.

Editorial Reviews

A textbook that presents the basic ideas of modern algebra, its problem-solving skills and basic proof techniques, and some of its elegant applications. The link with geometry comes from understanding a geometry by means of its group of motions. There are over 225 substantial examples and some 750 exercises. These include computations, proofs varying from the routine to the challenging, and open-ended problems. Assumes some experience with linear algebra (with exposure to matrix algebra and naive vector space theory) and the language of proofs. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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