Exploring Abstract Algebra with Mathematica

Table of Contents for Exploring Abstract Algebra with Mathematica

This subsection gives the Table of Contents for Exploring Abstract Algebra with Mathematica. More details can be found in Full TOC subsection.

• Preface
• Part I -- Group Labs
  • Lab 1. Using Symmetry to Uncover a Group
  • Lab 2. Determining the Symmetry Group of a Given Figure
  • Lab 3. Is This a Group?
  • Lab 4. Let's Get These Orders Straight
  • Lab 5. Subversively Grouping Our Elements
  • Lab 6. Cycling Through the Groups
  • Lab 7. Permutations
  • Lab 8. Isomorphisms
  • Lab 9. Automorphisms
  • Lab 10. Direct Products
  • Lab 11. Cosets
  • Lab 12. Normality and Factor Groups
  • Lab 13. Group Homomorphisms
  • Lab 14: Rotational Groups of Regular Polyhedra
• Part II -- Ring Labs
  • Lab 1. Introduction to Rings and Ringoids
  • Lab 2. Introduction to Rings, Part 2
  • Lab 3. An Ideal Part of Rings
  • Lab 4. What Does Look Like?
  • Lab 5. Ring Homomorphisms
  • Lab 6. Polynomial Rings
  • Lab 7. Factoring and Irreducibility
  • Lab 8. Roots of Unity
  • Lab 9. Cyclotomic Polynomials
  • Lab 10. Quotient Rings of Polynomials
  • Lab 11. Quadratic Field Extensions
  • Lab 12. Factoring in
  • Lab 13. Finite Fields
• Part III -- User's Guide
  • Introduction to AbstractAlgebra
  • Groupoids
  • Morphoids
  • Ringoids
  • Additional Functionality
• Appendices
  • Appendix A -- Installation Instructions and References
  • Appendix B -- Lab 0 Getting Started with Mathematica
• Index