Nice breakdown Bostonian. I kept trying to come up with something you missed and then would find where it would fit in. The only things I wonder if you would add separately (though they may fit under another topic) are Linear and Nonlinear Programming and Game Theory. You have some things listed very specifically and others pretty broad (Data Mining)
I don't think people realize the how much of the amazing "computer" programs, simulations, models etc are mathematical models just programmed into a computer. Somebody has to understand the math that drives those things.
