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I am slightly confused as to whether or not it's worth my time to apply to top tier math PhD schools. I don't know whether I have a viable chance at what are considered "top tier" schools, or if I should "stay in my place" where I am now. The reason why I ask is because professors have told me that I have a glimmering shot at good schools, but my academic past has been a slow start. I haven't talked too much to advisers, and have recently considered getting a PhD. I am interested in discrete structures.

My academic past involves starting off at a smaller community college and taking remedial courses in mathematics after a bad high school start. My math SAT is on my CC transcript, and it's pretty poor. However, I worked my rear off and got a CC GPA of 4.0/4.0 and after summer classes, I worked my way up to the Cal I-III series before I transferred to a university. I also took CS courses at the CC, and tutored calculus mathematics as an employee there.

At my University, I earned a transfer scholarship as well as a scholarship from the DoD, in exchange for going to the DoD lab in the summer for research in constructing algorithms.

I have 2 REUs in discrete structures, one with applications in physics from a top 20 school. The dean of admissions there told me when I went there over the summer that I was the only CC student there in the history of the school's REU program. He said my statement of interest was well written.

I will graduate 3 semesters from now due to taking interdisciplinary coursework. I have finished most of my math requirements, including netting A's in linear algebra, the real analysis sequence, and a graduate discrete course. My GPA is ~ 3.85 as of now (slightly higher).

My question is, do I have a shot at a top tier school, or should I just stay in my place and stick around at my uni? Does my CC past and my remedial courses poison my application? My thinking is, I've already made it this far as an aspiring mathematician, and I believe I could have more in store.

How do schools view students who have turned over a new leaf? My current uni isn't prestigious, it's an average school, probably only the 3rd most notable state school in my state.

closed as off-topic by gman, jakebeal, Enthusiastic Engineer, David Richerby, scaaahu Sep 23 '15 at 2:56

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  • Your question will almost certainly be closed as the answer depends too much on your particular circumstances. If this information came to me as in a cover letter on an application, I'd be interested enough to look further at the application. There's nothing you've said that would kill your chances of admission, but someone evaluating your application would also want to see strong letters of recommendation, know the undergraduate program you've been in and see GRE general and subject test scores. – Brian Borchers Sep 22 '15 at 16:10
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    I am a mathematician on the faculty at a state research university, and I'm not exactly sure what you mean when you say you want to study "discrete structures". A quick google shows that this term is used in computer science departments much more commonly than in math departments. Relatively few of the top tier math PhD programs have substantial offerings in discrete mathematics: the one which first comes to mind is Princeton, which has top graph theorists. At many top places applied math / engineering is a different department entirely. Could you say more about your interests? – Pete L. Clark Sep 22 '15 at 16:56
  • This is not an answer to your question, just a remark. If a professor says "I think you have a shot at School X", you should take it significantly more seriously if that professor is writing a letter for you -- not because they have more insight into the admissions process, but because the biggest determiner of whether you'll get into School X is whether you have letters that say you'll do well at a school like X. From the other side: if 10 professors think you should get into School X, but the 3 who write letters for you don't, then you won't get into School X. – Tom Church Sep 23 '15 at 2:51
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I would need to know more information about your file -- more than is appropriate for a question on a site like this perhaps -- to speak with any confidence about your admissions chances. But here are some broad strokes:

Applying to a top tier school isn't any harder or any different than applying anywhere else. It just involves some more mouse clicks and paying some application fees. If your local academic advisors think you have any chance at getting into a top place, why not apply? In general you should apply to 5-10 places and include "several tiers". If the top places show no interest, there's no harm done. They're not going to give you any negative feedback.

At my University, I earned a transfer scholarship as well as a scholarship from the DoD, in exchange for going to the DoD lab in the summer for research in constructing algorithms.

That sounds very impressive...for some graduate program. A top program centered in pure mathematics may not give you that many points for working at the DoD or constructing algorithms. But other departments would.

I have 2 REUs in discrete structures, one with applications in physics from a top 20 school. The dean of admissions there told me when I went there over the summer that I was the only CC student there in the history of the school's REU program. He said my statement of interest was well written.

I am puzzled that the dean of admissions was involved in an REU. In my experience these are sponsored by the NSF and all the admissions work is done by the faculty PI and/or her hand-picked co-PIs / assistants. Was this in a math department?

I will graduate 3 semesters from now due to taking interdisciplinary coursework. I have finished most of my math requirements, including netting A's in linear algebra, the real analysis sequence, and a graduate discrete course. My GPA is ~ 3.85 as of now (slightly higher).

FYI, except for the graduate discrete course -- what topics did you cover there? -- this is all coursework that candidates admitted to top math PhD programs have done in the first year or two of their undergraduate career, or in some cases in high school. (I for instance did my PhD in a top three math department. I took linear algebra in high school. In my freshman year I took a real analysis sequence which included metric spaces, Lebesgue integration, some Fourier analysis and calculus on manifolds. I was admitted in 1998...before there were treasure troves of mathematics available on the internet. Nowadays a small but non-negligible percentage of people arrive at university knowing most of what I did when I graduated.)

This is not meant to discourage you, but only to tell you that you have just begun to take the appropriate coursework. You should load up in the coming semesters to have a reasonable shot.

Does my CC past and my remedial courses poison my application?

While it would be hard to argue against a strong pedigree, the answer to this is a clear no. Even the brightest admits to a PhD program still have much to learn...as in long years ahead of them. Most admissions faculty are interested in your trajectory as well as your position. From that perspective, if you are doing rather well now then the knowledge that you came from very humble beginnings makes your trajectory look better. Nobody cares about what you did in high school because you need to have moved far beyond it anyway. Graduate admissions packages almost never include information about SAT scores, so even if the admissions personnel saw them they would almost certainly ignore them. They can do that because they will have your GRE scores to look at.

To be honest, I suspect that perhaps you do not know what it takes to get into a "top tier math department". Maybe some faculty around you do; if so, they can be a great help to you. It is not even clear to me that you really want to pursue a PhD program in mathematics: maybe also CS or engineering / applied sciences? That's worth serious consideration. Anyway, even a third tier PhD program is a serious place and could launch you into a promising academic career. You should apply relatively widely, get into the best program that admitted you and is a good fit for your interests, and take it from there.

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