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Abstract Algebra

Structure and Application

  • David R. Finston
  • Patrick J. Morandi

Table of contents

  1. Front Matter
    Pages i-ix
  2. David R. Finston, Patrick J. Morandi
    Pages 1-21
  3. David R. Finston, Patrick J. Morandi
    Pages 23-40
  4. David R. Finston, Patrick J. Morandi
    Pages 41-55
  5. David R. Finston, Patrick J. Morandi
    Pages 57-72
  6. David R. Finston, Patrick J. Morandi
    Pages 73-91
  7. David R. Finston, Patrick J. Morandi
    Pages 93-104
  8. David R. Finston, Patrick J. Morandi
    Pages 105-120
  9. David R. Finston, Patrick J. Morandi
    Pages 121-134
  10. David R. Finston, Patrick J. Morandi
    Pages 135-144
  11. David R. Finston, Patrick J. Morandi
    Pages 145-181
  12. Back Matter
    Pages 183-187

About this book

Introduction

This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.

Applications include:

  • Identification numbers and modular arithmetic
  • (linear) error-correcting codes, including cyclic codes
  • ruler and compass constructions
  • cryptography
  • symmetry of patterns in the real plane

Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject, or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.

Keywords

Cyclic codes Field extension Group theory Modular arithmetic Rings and fields Symmetry

Authors and affiliations

  • David R. Finston
    • 1
  • Patrick J. Morandi
    • 2
  1. 1.Department of MathematicsBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-04498-9
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04497-2
  • Online ISBN 978-3-319-04498-9
  • Series Print ISSN 1867-5506
  • Series Online ISSN 1867-5514
  • Buy this book on publisher's site
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