Abstract Algebra: A Geometric Approach

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. It takes a concrete, example-oriented approach to the subject matter.

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.