> And (in maths, at least) one maps something onto something else.

Yes, but that's the opposite of what you said earlier. You might map x onto 2*x, for example. Or, if you're talking about a collection, you might map the integers 0..10 on to double their value. Data first, then the way you're manipulating it. I'm a mathematician and this is what makes sense to me.

I would only say "map this function..." if the function itself is being manipulated somehow (mapped onto some other value).