Exploring Abstract Algebra with Mathematica is intended as an upper-division laboratory supplement for courses in abstract algebra. It consists of several Mathematica packages that the authors have programmed as a foundation with two collections of labs for group theory and ring theory built on this base. The Mathematica labs allow students to both visualize and explore algebraic ideas while providing an interactivity that enhances the learning process. The accompanying multi-platform CD-ROM contains both Mathematica Version 2.2 and Version 3 notebooks of all the labs along with additional resources.
Group Labs | Using Symmetry to Uncover a Group | Determining the Symmetry Group of a Given Figure | Is This a Group? | Let's Get These Orders Straight | Subversively Grouping Our Elements | Cycling Through the Groups | Permutations | Isomorphisms | Automorphisms | Direct Products | Cosets | Normality and Factor Groups | Group Homomorphisms | Rotational Groups of Regular Polyhedra | Ring Labs | Introduction to Rings and Ringoids | Introduction to Rings, Part 2 | An Ideal Part of Rings | What Does Z[i]/ Look Like? | Ring Homomorphisms | Polynomial Rings | Factoring and Irreducibility | Roots of Unity | Cyclotomic Polynomials | Quotient Rings of Polynomials | Quadratic Field Extensions | Factoring in Z[[square root of]d] | Finite Fields | User's Guide | Introduction to AbstractAlgebra | Groupoids | Ringoids | Morphoids | Additional Functionality | Installation instructions, References | Lab 0 Getting Started with Mathematica |