Essentials of Modern Algebra
Pub Date: August 2012
Specs:7 x 9 Hard cover
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 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
- Provides 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.
Cheryl Chute Miller holds a PhD in mathematics from Wesleyan University and is currently a professor of mathematics at SUNY Potsdam. She has over 20 years of teaching experience, has written numerous articles, and has received several awards and grants during her career.
SHORT DESCRIPTION OF BOOK
This book is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. Features groups, rings, and fields and provides numerous exercises and projects.