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The sort of experiences we have
had doing mathematics interactively has persuaded us of several
conclusions. It is necessary to develop good context dependent
intuition. It is useful to take advantage of the computer to do the easy
--- many unimaginable hand-calculations are trivial to code. (So trivial,
in fact, that one has to resist the temptation to compute mindlessly.) The
skill is to recognize when to try speculative variations on a theme and to
know when one has actually learnt something from them. The mathematical
opportunities are virtually unlimited but only in a relatively painless to
use high level and multi-faceted environment.
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Previous: THE CUBIC ARITHMETIC