Essentials of Modern Algebra (Mathematics)

This book is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. It follows that basic plan, using the axioms or rules to understand structures such as groups, rings, and fields, and giving the reader examples to help, but leaving many theorems and examples for them to try. The unique feature of the text is the list of 'projects' at the end of each chapter that can be used in the classroom (with students solving them), alone, or in groups with the aid of an instructor. Because of their interactive nature, the projects are designed to understand concepts or to lead the student to new ideas they will encounter later.

Features:

Provides a logic-based presentation, with the structures of groups, rings, and fields presented in similar ways through objects, subobjects, mappings between objects, and quotients of objects

Follows a fairly straight path without many of the side areas, such as modules, in order to introduce Galois Theory and solvability of polynomials

Includes numerous examples, exercises and the inclusion of 'projects' in each chapter

Instructor s resources available upon adoption

Brief Table of Contents:
Preliminaries.
1. Groups.
2. Special Groups.
3. Quotient Groups.
4. Rings.
5. Quotient Rings.
6. Domains.
7. Polynomial Rings.
8. Factorization of Polynomials.
9. Extension Fields.
10. Galois Theory.
11. Solvability.
Bibliography.
Index.