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I am currently a math major in college and my main problem is that it feels directionless. My college offers little in term of variety in undergraduate math so I moved on into taking graduate courses and I am actually loving it. But at this point I am just randomly taking courses that looks interesting and was wondering if there was specific directions to take within math. And even past that where will it lead.

Thanks

EDIT
After reading the comments I decided to add extra info. On the courses that I like, I have taken Abstract Algebra and Linear Algebra and really enjoyed them and also Number theory. I have also taken the typical three semester Calculus courses, Differential Equations, Discrete Math, Probability, Numerical Analysis and Real Analysis. On these courses I like them though I am not as enthusiastic about them as I am for the other courses I have mentioned. Though I find their applications very interesting.

And more specifically on the question it is on what paths are there to take in school and also what paths are there to take after graduation.

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    I am quite sure that math can lead to more math, which can lead to more math, *ad infinitum* (but not *ad nauseam*, for the most part). I have heard tell that it can lead to other pleasant careers as well, but I have no personal experience with this. Seriously, this is yet another question that you should ask in person to someone at your particular institution. The anonymous internet is a poor substitute.2011-03-04
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    You sound kind of directionless, could you edit your question and tell us some things you like or are interested in? Perhaps things you don't like?2011-03-04
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    The first question you need to ask yourself is whether you want or need to make a lot of money. The second question might be whether you like real-world applications. If the answer to both of those questions is no, then you can pretty much go anywhere you want to go.2011-03-04
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    @Qiaochu: if we ever have the great fortune to hire you in my department, remind me never to nominate you for union rep. (Wait, did you edit that part of your answer? It seems more balanced now, and this comment correspondingly less funny.)2011-03-04
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    @chaire: It would help if you tell us (i) what courses you have taken and *really* enjoyed; (ii) what other courses you have taken. Yes, there are specific directions within math, and subfields within fields, etc. But to put them in context, it would help to know where you are (not just where you want to go) before we start giving you directions.2011-03-04
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    @Pete Some people just don't have that type of relationship with anybody in their department. One could go around asking people questions. Although, who wants to get a reputation for being the lost and confused guy that doesn't know why he's in mathematics? These are the same people that are needed come recommendation time. They also might not want to discuss your "feelings" about mathematics with you or their own feelings for that matter, especially if they don't know you very well.2011-03-04
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    @Henry: probably it's true that some people have no one they feel comfortable talking to, but that's a big problem in need of a remedy independent of this particular question. What students seem not to realize is that as faculty, it is *expressly part of our job* to answer their questions, give them advice, try to allay doubts, and other such things. If you don't know anyone well enough to be at all candid with them, I don't like your chances of getting good recommendations later on.2011-03-04
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    Pete: it may be expressly part of our job, but that doesn't mean that students necessarily think we're willing to do it. (This is totally separate from whether we are or not.)2011-03-04
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    @Michael: right, hence my attempts to let them know that we are...2011-03-04
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    @Pete: I went to talk to a few professors and one of them recommended this site as source of information. Also on the general conversation it does feel like there is a wall between students and professor but that's just something that needs to be overcome.2011-03-08

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