Essentials of Modern Algebra 2E

This new edition is intended for the undergraduate one or two semester course in modern algebra, also called abstract algebra. It follows a logical path, 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 reinforce previous concepts. Features +Features a logic-based presentation, with the structures of groups, rings, and fields presented in similar ways through objects, sub-objects, 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 +Adds more, varied examples to use when illustrating ideas such as order of elements, direct products, and subgroups +Includes new material on the history of mathematics with vignettes of mathematicians +Provides instructor’s resources with solutions and PowerPoint slides for use as a textbook Brief Table of Contents 0. Preliminaries. 1. Groups. 2. Subgroups and Homomorphisms. 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. Hints for Selected Exercises. Bibliography. Index. About the Author Cheryl Chute Miller holds a PhD in mathematics from Wesleyan University and is currently a professor of mathematics at SUNY Potsdam. She has over 30 years of teaching experience, has written numerous articles, and has received several awards and grants during her career. Read more