Worldwide Mathematica Conference • Chicago 1998

Worldwide Mathematica Conference • Chicago 1998

My Favorite Mathematica Projects 
for Teaching Linear Algebra

Murray Eisenberg
University of Massachusetts, Amherst

murray@math.umass.edu
www.math.umass.edu/~Math_236/Chicago

Some of the Mathematica code presented at the Mathematica Worldwide Conference is input that students in a linear algebra course would be expected to supply themselves.  To preserve the integrity of these projects for instructional use, such code has been excised from these files.  Instructors and others with legitimate need to see the code should contact the author directly.

The projects

1. Stretching and spinning a cat:  transformations of the plane

Open Cat

2. Fitting a polynomial by least-squares

Open  Fit

3. Cracking a Hill cipher:  linear algebra over a finite field

Time constraints prohibited presentation of this project at the conference.  Interested parties should contact the author directly.

Comments

Course context

Sophomore linear algebra and linear algebra/multivariable calculus/ODEs courses.

Previous Mathematica experience is not assumed.

In-class instruction including demos; supervised labs; open labs.

Projects involve printed and on-line materials.

Benefits of such projects

Mathematically instructive

Stimulate student interest

Motivate and help teach Mathematica programming

Facilitate collaborative work

Implementation issues

Some parts originally implemented in array processing languages (APL, J)

Can do in other software systems—but Mathematica makes it easier thanks to…

▪ powerful array-manipulating primitives 
▪ easy-to-use functional progamming constructs
▪ superior system for delivering such projects
▪ excellent environment for students' doing and documenting their work

Instructor may need to do advanced programming (or carefully imitate models)

See, for example, the manipulation of contexts in the notebook FitData.nb , which is the source of the package FitData.m that generates data for the  project on fitting a polynomial by least-squares.

Open FitData

Additional notes

These materials altered from form used in courses to better fit the presentation format.  (The projects are plucked from the course context.)

Students' solutions are at times more elaborate or interesting than my own!

These particular projects hardly use symbolic capabilities of Mathematica!