Essentials of modern algebra / Cheryl Chute Miller.

Format:

Book

Author/Creator:

Miller, Cheryl Chute, author.

Language:

English

Subjects (All):

Algebra.

Physical Description:

1 online resource (356 pages)

Edition:

Second edition.

Place of Publication:

Dulles, Virginia ; Boston, Massachusetts ; New Delhi : Mercury Learning and Information, 2019.

Summary:

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: A logic-based presentation, with the structures of groups, rings, and fields presented in similar ways through objects, sub-objects, mappings between objects, and "ients of objectsFollows a fairly straight path without many of the side areas, such as modules, in order to introduce Galois Theory and solvability of polynomialsProvides numerous examples, exercises, and the inclusion of “projects” in each chapterAdds more, varied examples to use when illustrating ideas such as order of elements, direct products, and subgroupsIncludes 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

Contents:

Frontmatter

Dedication

Contents

Preface to Second Edition

Preface to First Edition

Photo Credits

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

Notes:

Description based on print version record.

ISBN:

9781683922810

1683922816