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SOME ELEMENTARY MATHEMATICS REVISITED AND REVISED

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The developers of computer algebra systems have had to reconsider, and sometimes rewrite, results in elementary mathematics in order to use them reliably. This talk describes several topics that most mathematicians would consider elementary and «solved», but which have had to be modified for use in a computer algebra system. For example, quadratic, cubic and quartic equations should not be solved following the standard books. Inverse functions could be implemented more easily in computer algebra systems if they were formulated differently. The changes, and the background to the changes, will be described. Demonstrations in Derive and Maple will be given if possible. Teaching Error-Correcting Codes, Discrete Mathematics and Modern Algebra with Computer Algebra.

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