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<p>Umm, Applied Math also has lots of proofs, and you can definitely go to grad school or get a job straight out of college in either case. If you get a job after having a pure math major though, you probably won’t be doing pure math, but you can definitely get a good job.</p>
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<p>I don’t see why not. I believe that to become an actuary, you need to pass a series of tests that you could probably study for on your own pretty easily if you’re a pure math major. And people go into finance all the time after majoring in pure math. Anyways, applied math is a really broad area, which can include things like combinatorics, theoretical computer science, numerical analysis, etc. which are probably as related to finance and stuff as many classes from pure math.</p>