Domains, codomains, ranges, images, preimages, inverse images « Gowers's Weblog

Tim Gowers explains aspects about functions in a very clear way. Much of the stuff can be applied wholesale to many programming concepts. Every programmer, actually every job remotely involving math should really know this stuff.

As an abstraction tool the concept of function is powerful. It basically came into its modern form hand in hand with Calculus and not surprisingly was popularized by Euler.

Even as a programmer having a firm understanding of the function abstraction from Math will have real benefits in terms of reasoning about basic structure of code.