Symbolic Computation Group

Friday, January 5, 2001, at U. of Western Ontario.

Abstract:

For at least 2 centuries now mathematicians have routinely written down expressions such as sin(2*Pi*x) + arctan(y) and called them "functions". In this talk we will examine what it could mean to treat an expression as a function and, more specifically, different ways to give a semantic/functional interpretation to expressions with an eye towards exceptional cases such as x/x, x*sin(1/x) and diff(sqrt(x^2),x). In particular, we will consider pointwise, local and global interpretations, and show that all of them lead to undesirable behaviour in certain circumstances.