Exploring Abstract Algebra with Mathematica

Overview of Exploring Abstract Algebra with Mathematica

The book, Exploring Abstract Algebra with Mathematica, is intended for anyone trying to learn (or teach) abstract algebra (a difficult course for some students). Perhaps one of the reasons this course is often challenging is because of its formal and abstract nature. While some people are quite adept at thinking abstractly, many are helped by also thinking visually or geometrically. To this end, where possible, the Mathematica labs are designed to appeal to visualization of various algebraic ideas (as pioneered by Ladnor Geissinger in his software package Exploring Small Groups). Additionally, the nature of the Mathematica notebooks encourages an exploratory environment in which one can make and test conjectures. Viewing the notebooks as interactive texts allows an environment that can not be replicated by lecture alone. While many of the labs are designed to prepare the way for in-class discussion/lecture, they can also be used to extend examples seen in class.

There is no assumption about being able to program in Mathematica; users only need to know the basic concepts of using Mathematica, which are reviewed in Lab 0. Every lab starts with a set of goals as well as prerequisites, listing both mathematical assumptions as well as any assumptions about having used previous labs. Most labs are independent, though a few assume some experience with a previous lab. Although the labs are presented with the ring labs following the group labs, they can be just as easily used by those who prefer to do rings first (as one of us does). Questions are interspersed through the lab at the points where it is natural to ask. As with any text, one does not need to complete every question (although a few have dependency on previous questions). While the length of the labs vary from 40 minutes to 90 minutes in length, they typically require about 60 minutes. (Of course, this is a function of how many of the questions are assigned.) For adopters of the book, there are provisions for suggested minimal questions to be included, as well as which ones could be considered optional. Additionally, notebooks containing just the questions are available, as are partial solutions upon request by an instructor. Finally, a number of palettes for 3.x users are available to facilitate the use of the labs and the implementation of the packages.

The book comes with a CD containing all the labs, the packages, additional palettes and other related materials. It began shipping January, 1999. Note: the labs make no assumptions about what main text is being used; they should be suitable to accompany any text. See the Cross References subsection to see how a number of standard texts can be used with EAAM.

 

Prepared by Al Hibbard. Most recent update: 6/16/2006. This page has been viewed 295 times since June 16, 2006. The entire EAAM web site has had 669,454 hits since July 23, 2002.