My original plan for this book was to write a ``lab book'' for Linear Algebra, but work with students in the computer lab showed me that the lab book approach---which organizes an obstacle course for students to run---fails to take advantange of the greatest opportunity computers offer: the opportunity for play. Why set up an obstacle course, when the natural landscape is already filled with interesting hills to climb, canyons to explore, and caves to discover?
Consequently, my model shifted from a lab book to a hiker's guide. Linear Algebra describes the territory the student is to become acquainted with; this Matlab Guide describes specific places in that territory and interesting walks connecting them. I hope I have succeeded in choosing and describing those walks well enough to get the student to try them out and even to wander from them and find places of his/her own.Just as a good game pushes us to much higher levels of exertion than any exercise plan can, an entertaining exploration using Matlab will provoke much more vigorous mathematical thinking than any set of exercises could. That, at any rate, has been my premise.
I urge you to approach these explorations with a spirit of adventure in the literal sense. Try things out and see what comes. Play with the ideas. Change a number and see how the outcome of the computation changes. Do a larger example and see whether the algorithm you are using takes it in stride or becomes impossibly long and has to be interrupted. See if you can improve on the procedures that are suggested or find new procedures or patterns that are not suggested.
The educational psychologist Gertrude Hendrix, writing about The Psychological Appeal of Deductive Proof, assigned a role to the ``fundamental human desire for the ability to foretell.'' Everyone enjoys, I hope, putting the computer through a long computation to find a simple result that was known in advance. Sometimes the prediction turns out to be wrong, which may at first be annoying, but which usually turns out to be even more enjoyable, because it leads to a better understanding of the mathematics.
Let your motto be the words of a song from the Student Prince: ``Education should be scientific play.''
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