Using Mathematica to Explore Abstract Algebra
Using Mathematica to Explore Abstract Algebra
Abstract of article: By augmenting Mathematica with the AbstractAlgebra packages, one can effectively explore many concepts found in an abstract algebra course. These packages encode the functionality to work with groups, rings, and morphisms. Where possible, visualizations of many of the algebraic concepts are also available. Although the Mathematica program is required to use the packages, no experience with it is required. After indicating how to obtain, install, and implement AbstractAlgebra into a classroom setting, this article gives an overview of the basic structures and capabilities included in the packages. Following this, we illustrate how to create an exploratory environment using AbstractAlgebra. We do so by showing how typical questions from abstract algebra can be answered by using these packages.
About the author: Al Hibbard is Professor of Mathematics at Central College in Pella, Iowa. He did his undergraduate work at St. John's University (MN) and obtained his Ph.D. from the University of Notre Dame. Since 1990 he has been investigating various ways of incorporating technology and other innovations in the teaching of abstract algebra (and other courses). One outgrowth of these pursuits is that he and Ken Levasseur have created a suite of Mathematica packages (and lab notebooks based on them) that enable one to work with groups, rings, and morphisms. These AbstractAlgebra packages are the foundation of their book Exploring Abstract Algebra with Mathematica. When not teaching, programming, or writing, he can be found in a "committee meeting" in a racquetball court at the athletic facilities.
Software used: Mathematica and AbstractAlgebra
Files to download: The Notes volume could only be printed in black-and-white. However, many of the graphics in this article are best viewed in color. Here are three versions of all the Mathematica content in this article. Each can be found below.
html version
pdf version
Mathematica version (Requires either Mathematica or Mathematica Reader to view the content. To modify the code, the AbstractAlgebra packages need to be installed into Mathematica.)
Other links: web site to support the Exploring Abstract Algebra with Mathematica book and project