<p>Here are some options:</p>
<p>1) actuary – things to do with risk management. A math major with knowledge of things like statistics and some programming is probably best equipped, and a graduate degree isn’t really part of the culture. Rather, you take lots of exams after college and passing them lets you get to a higher position.</p>
<p>2) financial maths in general – there are master’s programs in this. Check out, for example, that of UChicago, which is very good I think. Very competitive to get into, requires a maths or other technical degree, familiarity in basic things like linear algebra, calculus, basic analysis, stochastic processes, and some programming helps again. Work experience is usually a huge plus to get into these programs. A graduate degree in a technical field can help.</p>
<p>3) engineering – you can choose to major in engineering as well or take some classes alongside the maths concentration and go on to do a graduate degree that trains you in mathematical modeling or something. Operations Research uses plenty of mathematics. Things like optimization techniques, if you’re interested. EE’s signal processing is structured so that you study signals and systems at my school; the signals are functions, and the system is some kind of space of functions on which there are operators. This obviously lends itself to linear algebraic language. </p>
<p>4) computer science – plenty of mathematics goes into algorithms. </p>
<p>5) research mathematician – go to get a PhD and then become an expert in some area of mathematics, with the goal to solve the current problems in the field. For this, use undergrad to get a very solid exposure to different topics in maths in order to have strong background to decide what you want to contribute to most in the future. You have to know a TON of different things to be able to tread this path realistically, because seeing the connections among different fields is one of the only ways you can solve problems people might care about.</p>
<p>6) maths teacher – pure teaching.</p>
<p>7) law school – maths folk are very strong in logical reasoning and assuming you don’t mind reading, you’ll be able to ace the LSAT and get into a good law school. Someone I know did it. </p>
<p>… I’m sure there are more, but this is a good start and lists many plausible tracks.</p>