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I don't know if this is the right place for such a question, so please redirect me to a more appropriate place if necessary.

My main question is, if you go to a small school, are you doomed to fail right from the get-go? My secondary question is, what are my options then, if I am indeed doomed to "fail"? The following is more of a personal description, so obviously it doesn't apply to everyone, which would make the question "not general enough", but I suspect that there are many others caught in a similar situation.

I'm going to be a senior (fourth-year) in the fall (August) and am currently doing my "homework" on graduate school admissions. I go to a small liberal arts college you've probably never heard of. From what I've read and heard, I'm extremely discouraged and I'd say I'm borderline depressed about my future, but the truth is, I don't really want to do anything else other than learn more math (and get a PhD in the process if I'm capable of it).

I like to think that I've worked very hard (but everyone says the same thing). Classes I've taken include topology, complex analysis, algebra, real analysis, statistics, graph theory, number theory, and Galois theory. I've been told that none of my coursework means much to graduate schools because my school is relatively unknown. Furthermore, much as I can get some good recommendation letters, I've heard that since none of my letter writers is "relatively well-known" in their area, and everyone who applies to graduate schools gets glowing reviews anyway, I can't compete with other applicants at all.

I've gone through all of Herstein, a little more than half (i.e., as much as I could) of Rudin, most of Hoffman/Kunze, and the first half of Munkres. None of these texts are actually used at my school. In other words, I don't think I've given any less than I'm physically capable of in the last three years, and if that isn't enough, I really shudder to think what is.

I haven't taken the GRE yet but am currently studying for it. But it's no secret that the GRE is a relatively silly measure of grad school success. A bad score would condemn me to eternal hell, but a good score isn't a direct ticket to success.

I've heard the "anything can happen ... who's to say that you can't succeed ... people from small schools have gotten into big schools" argument, but in all realisticness, there's absolutely no reason to pick me over a Princeton graduate who has the exact same credentials, and there are tons of them. So what are my best options given this reality?

Any advice/encouragement/experiences would be very much appreciated. Thank you.

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    No one, at no stage in life, is doomed to fail.2012-07-07
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    "there's absolutely no reason to pick me over a Princeton graduate who has the exact same credentials" - that is, unless you find a way to make yourself distinctive from those other people you speak of. Find that distinction.2012-07-07
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    Doesn't happen to be Coe, does it?2012-07-07
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    Being condemned to eternal hell sounds terrible. Let's hope you do well on the GRE!2012-07-07
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    Don't neglect the GRE's. You don't need a perfect score, but you have to pass some threshold to be considered. Don't get sub 50th percentile! Ironically, top ten math graduate schools may accept you with poor gre scores, but you may get rejected from all your safeties. Not something you want to depend on. Many schools use them as a filter.2012-07-07
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    You may find that admissions committees are less biased against small liberal arts schools than you think. Anyway, if you love mathematics, then you have your answer: you must try and study it no matter what. Do your best to interact with others in the mathematics community. Apply to an REU. Read the notices of the AMS, the college mathematics journal, the American Mathematical Monthly. Start reading/participating in MSE. Interacting with the mathematical community is a great way to avoid depression of this kind. By the way, a 21 on the Putnam exam is a good score!2012-07-07
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    I went to a small liberal arts college in the midwest and I didn't study Herstein, Rudin, Hoffman/Kunze, or Munkres on my own. My best score on the Putnam was 10. My GPA was around 3.30. I did get 81st percentile on the Math subject GRE and I had an REU where I got a paper (though most of the paper was written by the adviser and the student work was added in). And, I got into a grad school that is in the top 70 on US News list. And, I will be graduating in a few months with a PhD. So, you should be able to do quite a bit better than that.2012-07-07
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    You'll also be competing with applicants from outside the US, who usually have two additional years' worth of training (masters level). I would recommend also applying to masters programs outside of the US. Some of them even have funding for students, making the option much more realistic.2012-07-07
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    Well, you can always expand your horizons, see if there are schools in other countries, where admission is easier?2012-07-07
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    @paul: The first step would be to edit this post to put it into the form you'd like to have it in. After that I can see if a comm team member would be able/willing to comply with your request.2013-10-31
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    You need to distinguish yourself with a truly original idea.2017-05-09
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    There is a reason to pick you over a Princeton graduate. Princeton students are almost universally overachiever types.2017-05-09

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