John Auer - Ten years of teaching linear algebra using Maple V at Brock University

Since the late 1980s, Brock University has offered a freshman linear algebra, one-semester course for a wide audience, using the Maple V CAS. This led to the publication of my first linear algebra text (Prentice Hall, 1990) containing Maple V supplementary material for use in solving linear algebra problems in a weekly, compulsory one hour laboratory-tutorial. A second, fully integrated text entitled``Essentials of Linear Alegebra Using Maple V'' (1999) has been published and is used as the text and laboratory manual for this course.

A CAS like Maple V or Mathematica is an ideal environment for solving problems and exploring concepts in linear algebra. My talk will discuss our course content and the integration of Maple V, concentrating on the following features provided by CASs:

(i)  The facilitation of focusing on concepts and methods, without the distraction of numerical mistakes in lengthy calculations. A case in point is the learning of row reduction of matrices, where CASs contain individual commands for the three elementary row operations. Of course, CASs also have ``canned'' commands to produce the final result (e.g., a row echelon matrix), but these should be avoided, except as noted in (iii) below.

(ii)  The exploration of theoretical results using CASs' symbolic manipulation capabilities. One simple example is provided by the exploration of the structure of the formulas for the determinant of a matrix W traditionally bewildering for many students.

(iii)  The checking of numerical and symbolic calculations. I think this is very beneficial in building students' self-confidence.