Exploring Abstract Algebra with Mathematica

Al Hibbard - Central College - e-mail homepage

Ken Levasseur - UMass-Lowell - e-mail homepage

Outlines of each lab/chapter

Lab 0. Getting started with Mathematica

Group Lab 1. Using symmetry to uncover a group

Group Lab 2. Determining the symmetry group of a given figure

Group Lab 3. Is this a group?

Group Lab 4. Let's get these orders straight

Group Lab 5. Subversively grouping our elements

Group Lab 6. Cycling through the groups

Group Lab 7. Permutations

Group Lab 8. Isomorphisms

Group Lab 9. Automorphisms

Group Lab 10. Direct products

Group Lab 11. Cosets

Group Lab 12. Normality and factor groups

Group Lab 13. Group homomorphisms

Group Lab 14: Rotational groups of regular polyhedra

Ring Lab 1. An introduction to rings and Ringoids

Ring Lab 2. An introduction to rings: part two

Ring Lab 3. An ideal part of rings

Ring Lab 4. What does look like?

Ring Lab 5. Ring homomorphisms

Ring Lab 6. Polynomial rings

Ring Lab 7. Factoring and irreducibility

Ring Lab 8. Roots of unity

Ring Lab 9. Cyclotomic polynomials

Ring Lab 10. Quotient rings of polynomials

Ring Lab 11. Quadratic field extensions

Ring Lab 12. Factoring in

Ring Lab 13. Finite fields

User's Guide

1. Introduction to AbstractAlgebra

2. Groupoids

3. Ringoids

4. Morphoids

5. Additional functionality

6. Appendices

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