Abstract Algebra
A Geometric Approach
Published on 31. August 1995
Book
Paperback/Softback
432 pages
978-0-13-319831-7 (ISBN)
Description
Appropriate for a 1 or 2 term course in Abstract Algebra at the Junior level. 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.
More details
Content
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.
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.