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Exploring Abstract Algebra with Mathematica® (Softcover with CD-ROM)
"Exploring Abstract Algebra with Mathematica®, a book and CD package containing twenty-seven interactive labs on group and ring theory built around a suite of Mathematica® packages called AbstractAlgebra, is a novel learning environment for an introductory abstract algebra course." — From the back cover
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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.
Continued from the back cover: “This course is often challenging for students because of its formal and abstract content. The Mathematica® 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 Zn, Un, and Dn, as well as direct products and quotients of these) and rings (including Zn, 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
- 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 Though the Groups
- Direct Products
- Normality and Factor Groups
- Group Homomorphisms
- Rational Groups of Regular Polyhedra
PART II. Ring Lags
- Introduction to Rings and Ringoids
- Introduction to Rings, Part 2
- An Ideal Part of Rings
- What Does Z[i]/< a + b 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[√d]
- Finite Fields
PART III. User’s Guide
- Introduction to AbstractAlgebra
- Additional Functionality
- Installation Instructions ● References
- Lab 0 Getting Started with Mathematica
The book concludes with an Index.
- Hibbard, Allen C. and Kenneth M. Levasseur
- Publish Date:
- 1999 (First Printing)
- Softcover with CD-ROM
- Weight (pounds):
- Dimensions (W”xL”xH”):
- Grade Level:
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