Exploring Abstract Algebra With Mathematica® / Edition 1

by Allen C. Hibbard, Kenneth M. Levasseur

Overview

• What is Exploring Abstract Algebra with Mathematica? Exploring Abstract Algebra with Mathematica is a learning environment for introductory abstract algebra built around a suite of Mathematica packages enti­ tled AbstractAlgebra. These packages are a foundation for this collection of twenty-seven interactive labs on group and ring theory. The lab portion of this book reflects the contents of the Mathematica-based electronic notebooks con­ tained in the accompanying CD-ROM. Students can interact with both the printed and electronic versions of the material in the laboratory and look up details and reference information in the User's Guide. Exercises occur in the stream of the text of labs, providing a context in which to answer. The notebooks are designed so that the answers to the questions can either be entered into the electronic notebook or written on paper, whichever the instructor prefers. The notebooks support versions 2. 2 and 3. 0-4. 0 and are compatible with all platforms that run Mathematica. This work can be used to supplement any introductory abstract algebra text and is not dependent on any particular text. The group and ring labs have been cross­ referenced against some of the more popular texts. This information can be found on our web site at http://www . central. edu/eaarn. htrnl (which is also mirrored at http://www . urnl. edu/Dept/Math/eaarn/eaarn. htrnl). If your favorite text isn't on our list, it can be added upon request by contacting either author.

Product Details

ISBN-13:	9780387986197
Publisher:	Springer New York
Publication date:	02/19/1999
Edition description:	Softcover reprint of the original 1st ed. 1999
Pages:	467
Product dimensions:	6.69(w) x 9.61(h) x 0.04(d)

Table of Contents

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 Through the Groups.- 7 Permutations.- 8 Isomorphisms.- 9 Automorphisms.- 10 Direct Products.- 11 Cosets.- 12 Normality and Factor Groups.- 13 Group Homomorphisms.- 14 Rotational Groups of Regular Polyhedra.- II Ring Labs.- 1 Introduction to Rings and Ringoids.- 2 Introduction to Rings, Part 2.- 3 An Ideal Part of Rings.- 4 What Does—[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—[?d].- 13 Finite Fields.- III User’s Guide.- 1 Introduction to Abstract Algebra.- 2 Groupolds.- 3 Ringoids.- 4 Morphoids.- 5 Additional Functionality.