Qualify Matt G's advice somewhat?
matt grime said:
There are special schools/exams for that kind of thing.
matt grime said:
model things for BP, say, or any other industrial company...work for IBM or similar, the telecommunications industy employs mathematicians
That is, Ph.D. mathematicians with a strong background in PDEs, information theory, etc., or programmers of proven ability who also know about those things.
matt grime said:
the office of national statistics
But they will probably want strong statistics and computer science background.
This might have come out wrong: I am trying to say that what degree(s) you have probably don't matter so much, but you would need to show evidence of strong ability in mathematical modeling, especially computer models.
This is based on my conversations with people who work at Boeing and elsewhere in aerospace in the U.S.; it was a bit of a shock to me to find that what people who actually work in industry say is important is quite different from what my math professors said was important!
I'd another important possibility: genomics. You can look for a printed talk by Eric Lander which attempts to recruit bright math majors into this field. But notice that again there is already a lot of specialized knowledge and expertise you'd probably need to demonstrate to be a competitite candidate.
Yet another possibility: the financial services industry employs some Ph.D. mathematicians who know about such things as stochastic differential equations; see
http://en.wikipedia.org/wiki/Black-Scholes to get some impression.
It is important to understand that the number of mathematicians employed in industry is not as large as some would expect, compared to the number employed in academia. In my day, the AMS suppressed this fact, which did some of us a disservice.