Exploring Abstract Algebra with Mathematica® (Softcover with CD-ROM)

Condition

GOOD: This book is in good condition, showing some signs of use and wear (mostly on the covers). The book was printed on acid-free paper.
Although the CD-ROM has been removed from its sealed plastic envelope, attached to the inside back cover, it appears to have been unused, or taken very good care of if in use.

Product Details

Continued from the back cover: "This course is often challenging for students because of its formal and abstract content. TheMathematica® labs allow students to both visualize and explore algebraic ideas while providing an interactivity that greatly enhances the learning process. The book and CD can be used to supplement any introductory abstract algebra text, and the labs have been corss-referenced to some of the more popular texts for this purpose.

"The packages are capable of handling most of the types of objects encountered in a first-year undergraduate abstract algebra course, including working with (finite) groups, rings, fields, and morphisms and functions related to each of these objects. There are a larger number of built-in groups (including such standard groups as Z_n, U_n, and D_n, as well as direct products and quotients of these) and rings (including Z_n, Boolean, and lattice rings, as well as polynomial, matrix, and function extension rings). One can also create functions between groups or rings and investigate if these are morphisms. No programming experience in Mathematica® is assumed or necessary; a review of the basic concepts of Mathematica® is included in the book. The enclosed CD contains all the labs, the User's Guide, the AbstractAlgebra packages, and other resources (including useful palettes). The notebooks support versions 2.2 and 3.0-4.0 and are compatible with all platforms that run Mathematica®."

PART I. Group Labs

1. Using Symmetry to Uncover a Group
2. Determining the Symmetry Group of a Given Figure
3. Is This a Group?
4. Let's Get These Orders Straight
5. Subversively Grouping Our Elements
6. Cycling Though the Groups
7. Permutations
8. Isomorphisms
9. Automorphisms
10. Direct Products
11. Cosets
12. Normality and Factor Groups
13. Group Homomorphisms
14. Rational Groups of Regular Polyhedra

PART II. Ring Lags

1. Introduction to Rings and Ringoids
2. Introduction to Rings, Part 2
3. An Ideal Part of Rings
4. What Does Z[i]/< a + b i > Look Like?
5. Ring Homomorphisms
6. Polynomial Rings
7. Factoring and Irreducibility
8. Roots of Unity
9. Cyclotomic Polynomials
10. Quotient Rings of Polynomials
11. Quadratic Field Extensions
12. Factoring in Z[√d]
13. Finite Fields

PART III. User's Guide

1. Introduction to AbstractAlgebra
2. Groupoids
3. Ringoids
4. Morphoids
5. Additional Functionality

Appendices

1. Installation Instructions ● References
2. Lab 0 Getting Started with Mathematica

The book concludes with an Index.