"Interactive mathematics texts from Computer Algebra Systems:
use in teaching engineering students"

Dr. G. Keady and Dr N. Fowkes, University of Western Australia,
Dr J. Ward, Murdoch University

Introduction

The written account in this paper differs somewhat from the presentation. In the presentation real examples of Maple Worksheets and Mathematica Notebooks - the "interactive mathematics texts" of the title - are given. These may include examples which have been published in, or which are in preparation for, the PWS Notebook series. You can find many public-domain examples via WWW sites, e.g. via those of the CAS developers,
http://www.maplesoft.com
http://www.wri.com/WWWDocs/mathsource/ (Address changed)

We believe that the Worksheet/Notebook formats, combined with student editions of CAS running on relatively inexpensive, e.g. home, computers, will result in a massive increase in the use of CAS. CAS are quite old, so it is valid to indicate why there is still scope for the big increase. CAS have been mathematicians' research tools from the 70s. However, in the early period, they were not user-friendly. From the early 80s, the more adventurous introduced CAS into the upper levels of teaching - Honours and later third-year undergraduate. From the late 80s, CAS began to be used in large-class teaching, e.g. to second-year Engineering Mathematics classes. On-line helps in the packages were crucial to this. The large classes also made it essential to produce some printed materials to support the use of CAS. Cooperative efforts - making materials available across the net - enabled the load of preparing such material to be shared. By about 1992, some of the printed materials aimed to bridge between existing text books and the CAS, a development which definitely assists integration of the students' CAS experience with their other experiences of mathematics. Another major change is now in progress, brought about by the Worksheet/Notebook formats, henceforth abbreviated to 'notebook'. Rather than providing extensive printed materials for the CAS, the "disk/electronic-supplement with the text", "interactive text" is delivering the information in a more immediately usable form. The PWS Notebook series of disks began in 1994, PWS distribution via the Web began in 1995. This article explores issues related to these new "interactive text" CAS possiblities.

With or without "interactive texts", we see the computer work is a supplement to, and not a substitute for, more conventional methods of teaching - text, lectures, assignments of exercises from the text, tutors marking these and tutorial discussion.

The two CAS which are now most widely used in engineering and in upper levels of undergraduate Engineering Mathematics teaching are Maple and Mathematica. Both were released in the late 80s, e.g. for Mac in 1987 and 1988 respectively. The PC versions were later than Unix and Mac versions, because Maple and Mathematica both needed more than the 640K common in early DOS machines. As new versions appear, the two 'Ma-' packages leap frog in their capabilities and features. Both have good on-line help. Both provide very good support for graphics and animation.

There are at least three factors which will cause rapid development of CAS "interactive texts".

  1. Notebooks now look good enough so that a 10 or 20 page mathematical document can be written in them in a way which is pleasant to read.
  2. About half the students have access to home computers with 4Meg RAM - enough to run the Maple Student Version. This fraction will increase. Access to machines at home encourages students to use the CAS when they have a problem to tackle - from an engineering course or wherever -, not just when their mathematics lecturer asks them to do a particular mathematics assignment.
  3. Several publishers of mathematics texts understand that the provision of CAS materials supporting their texts will enhance their market share.

There remains a lot of uncertainty. Will formats more akin to Matlab's Notebook structure, which build on existing word-processors, using DDE or OLE or OpenDoc become more popular? In March 95, Maple released MathOffice which combines, via DDE, MSWord and Maple. Will it be a CD- ROM which accompanies the mathematics book, rather than a disk with the book? Will it be distribution via the Web? Irrespective of the answers to these questions, CAS notebooks are tools worth exploiting. Given the various uncertainties though, it would seem prudent to "keep notebooks simple" so that they can be maintained.

Background

Curtin and Murdoch Universities and UWA have all successfully used Maple in large-class engineering mathematics teaching since 1989. Mathematica and its predecessor, SMP, have been used at various campuses in Perth since 1984, but primarily for research - even regular Maple users turn to Mathematica for those problems which it does better than Maple (e.g. some definite integrals). In 1995, UWA began using Mathematica in its 2nd year Mathematics course for EEE (Electrical and Electronic Engineering) students, as this was requested by the EEE departments. (From 1990, Edith Cowan University has used DERIVE - a good, smaller CAS - in its teaching.)

The leading CA-in-teaching sites in Australia are now UNSW and RMIT, both of which use Maple. The leading Mathematica-in-mathematics-teaching sites are Tasmania and Otago. There can be more to CAS than just presenting mathematics: UNSW and Tasmania use CAS for marking assignments.

There are Australian user groups associated with the packages. The Maple e- mail based one is
maple-news@solution.maths.unsw.edu.au

GK, and Rod James, from UNSW, have pre-Worksheet linear algebra course materials on the Maple Share Library. These are at the level of 2nd year Engineering Mathematics courses. Like the "interactive text" items described below, these materials supplement established texts.

Click here to go to the ACEC95 links page.

Click here to go to G.Keady's homepage.