I have a problem: I learned about a lot of the applications of mathematics from academics. Neither they nor I have had much contact with the "real world" to go and see for ourselves how mathematics are used today (rather than, say, in the pre-computer age).
So if there are non-academics out there reading MO, I would very much like to hear from them about how their use of mathematical tools may or may not differ from the academic training they received. I don't expect we'll get a very representative sample of math-users on MO, but that's quite all right, anecdotal evidence is all I'm after.
Precision: I want to read about the tools being used rather than, say, an underlying mathematical motivation (which is another legitimate role of mathematics, but not really part of my question). So for instance, you may say that Google's PageRank algorithm was motivated by the theory of Markov chains, but (from what I can tell), I would not say it uses Markov chains.