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Exploring Abstract Algebra With Mathematica®

  • Textbook
  • © 1999

Overview

Authors:
  1. Allen C. Hibbard

    1. Department of Mathematics and Computer Science, Central College, Pella, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Kenneth M. Levasseur

    1. Department of Mathematics and Computer Science, University of Massachusetts Lowell, Lowell, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Presentation is highly visual, and includes a full-color insert of significant algebraic concepts and images
  • The multi-platform CD-ROM contains Mathematica version 2.2 and 3.0 notebooks and animations
  • Includes MathReader, the public domain software enabling users to view the content without having access to the Mathematica software package itself
  • Includes illuminating exercises
  • The authors provide a "Users Guide" for the data structures and commands of this package
  • Includes supplementary material: sn.pub/extras

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Group Labs

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Using Symmetry to Uncover a Group

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 3-10

    3. Determining the Symmetry Group of a Given Figure

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 11-16

    4. Is This a Group?

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 17-19

    5. Let’s Get These Orders Straight

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 20-31

    6. Subversively Grouping Our Elements

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 32-44

    7. Cycling Through the Groups

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 45-52

    8. Permutations

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 53-63

    9. Isomorphisms

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 64-73

    10. Automorphisms

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 74-80

    11. Direct Products

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 81-87

    12. Cosets

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 88-94

    13. Normality and Factor Groups

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 95-100

    14. Group Homomorphisms

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 101-110

    15. Rotational Groups of Regular Polyhedra

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 111-116

  3. Ring Labs

    1. Front Matter

      Pages 117-117
      Download chapter PDF

    2. Introduction to Rings and Ringoids

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 119-126

    3. Introduction to Rings, Part 2

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 127-133

    4. An Ideal Part of Rings

      • Allen C. Hibbard, Kenneth M. Levasseur
      Pages 134-139
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Keywords

About this book

• What is Exploring Abstract Algebra with Mathematica? Exploring Abstract Algebra with Mathematica is a learning environment for introductory abstract algebra built around a suite of Mathematica packages enti­ tled AbstractAlgebra. These packages are a foundation for this collection of twenty-seven interactive labs on group and ring theory. The lab portion of this book reflects the contents of the Mathematica-based electronic notebooks con­ tained in the accompanying CD-ROM. Students can interact with both the printed and electronic versions of the material in the laboratory and look up details and reference information in the User's Guide. Exercises occur in the stream of the text of labs, providing a context in which to answer. The notebooks are designed so that the answers to the questions can either be entered into the electronic notebook or written on paper, whichever the instructor prefers. The notebooks support versions 2. 2 and 3. 0-4. 0 and are compatible with all platforms that run Mathematica. This work can be used to supplement any introductory abstract algebra text and is not dependent on any particular text. The group and ring labs have been cross­ referenced against some of the more popular texts. This information can be found on our web site at http://www . central. edu/eaarn. htrnl (which is also mirrored at http://www . urnl. edu/Dept/Math/eaarn/eaarn. htrnl). If your favorite text isn't on our list, it can be added upon request by contacting either author.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Central College, Pella, USA

    Allen C. Hibbard

  • Department of Mathematics and Computer Science, University of Massachusetts Lowell, Lowell, USA

    Kenneth M. Levasseur

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