Read more about Elementary Abstract Algebra: Examples and Applications

Elementary Abstract Algebra: Examples and Applications

(2 reviews)

Justin Hill, Temple College

Chris Thron, Texas A&M University-Central Texas

Copyright Year: 2019

ISBN 13: 9780359042111

Publisher: Justin Hill and Chris Thron

Language: English

Formats Available

Conditions of Use

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CC BY-NC-SA

Reviews

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Reviewed by Mark Koester, Associate Professor, Metropolitan State University of Denver on 3/26/21, updated 5/26/21

Extensive index is included. The book includes more topics than a semester course could study. read more

Reviewed by Diana Morris, Assistant Professor, University of Virginia on 12/13/20

At almost 1000 pages, this book certainly covers the basics comprehensively. You might not find the Sylow Theorems or Jordan Canonical Form, but it accomplishes what it sets out to do, covering the basic background of numbers and set theory, the... read more

Table of Contents

  • 1 Preliminaries
  • 2 Complex Numbers
  • 3 Modular Arithmetic
  • 4 Modular Arithmetic, Decimals, and Divisibility
  • 5 Set Theory
  • 6 Functions: Basic Concepts
  • 7 Introduction to Cryptography
  • 8 Sigma Notation
  • 9 Polynomials
  • 10 Symmetries of Plane Figures
  • 11 Permutations
  • 12 Introduction to Groups 
  • 13 Further Topics in Cryptography
  • 14 Equivalence Relations and Equivalence Classes
  • 15 Cosets and Quotient Groups (a.k.a. Factor Groups) 
  • 16 Error-Detecting and Correcting Codes
  • 17 Isomorphisms of Groups
  • 18 Homomorphisms of Groups
  • 19 Group Actions
  • 20 Introduction to Rings and Fields

Ancillary Material

  • Ancillary materials are available by contacting the author or publisher.
  • About the Book

    This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.

    About the Contributors

    Editors

    Justin Hill, Temple College

    Chris Thron, Texas A&M University-Central Texas