Essentials of Modern Algebra

Overview

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 ...

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Overview

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
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Editorial Reviews

From the Publisher
Algebra forms the basis of many mathematical topics, but there are untold depths to the core discipline itself. "Essentials of Modern Algebra" seeks to more comprehensively explain the basics and importance of the algebra aspect of modern mathematics. Designed to teach educators on how to better present the topics to their students. Each chapter outlines a core concept of mathematics, expands upon the depths of the topic, helps infuse the mindset needed to tackle the dilemma, theories of algebra, and breaking through the idea of typical solvability. "Essentials of Modern Algebra" is an absolute must to any community and college library collection focusing on higher level education the mathematical sciences, highly recommended.
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Product Details

  • ISBN-13: 9781936420186
  • Publisher: Mercury Learning and Information
  • Publication date: 11/30/2012
  • Edition description: New Edition
  • Pages: 400
  • Product dimensions: 7.10 (w) x 9.20 (h) x 0.80 (d)

Meet the Author

CHERYL CHUTE MILLER holds a Ph.D. 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.
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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

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