Symbolic Computation Group

The derivative of a function at a point is defined as the slope, or more formally as the Cauchy Limit, and so on. But, when we actually calculate derivatives, we behave like a computer algebra system and push symbols around (Chain Rule, Product Rule etc.). This talk will claim that there are actually two theories of calculus, the analytic and the algebraic, with an interpretation that OFTEN works between them, and that the failures in the interpretation are interesting challenges for computerised mathematics.