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Mathematics Grad. School Application Harvard

  1. Sep 23, 2010 #1
    I'm interested in applying to a top mathematics grad. school like Harvard, Chicago, or Princeton. I'm wondering what my chances are and I'm especially interested in what would happen in the following scenario:

    I've taken only math courses my entired undergrad. education and I've taken grad. level math courses since my first year of undergrad. I've also taken lots of independent study courses on advanced topics in many areas of mathematics. Like in 4-manifold theory, algebraic geometry, algebraic group theory, representation theory, noncommutative ring theory, harmonic analysis, C* algebras, several complex variables ... well you get the picture. Not only that, I've got A's in all these math courses. I've also got a near perfect score on my GRE. And the undergrad. and grad. program in this university is very strong so all the courses are advanced.

    I know there are other factors to grad. school like letters of recommendation and personal statements, but would I be a shoo-in to grad. school if I had such a transcript - full of advanced math courses, only math courses, with only A's? Or would grad. schools in math frown upon me not taking other subject courses and reject me? Suppose I hadn't done very much research either. Does anyone know about how such a situation would be viewed?

    This is a hypothetical situation but I'm interested in knowing how grad. schools would view it and whether it'd guarantee admission. My gut feeling is close to yes since I don't know whether anyone has such a transcript full of A's and advanced (and this is *really advanced*) math courses. But the big question is how grad. schools would view the "not done research" and the "not done other courses in other subjects". Bear in mind that "not done research" also come with "done advanced math subjects that provide nearly all the background necessary for reading papers in numerous areas of math. I'd think grad. schools would think highly if someone had the background to do research in numerous areas of math (we're talking algebra, analysis topology and geometry - the knowledge is broad) but I could be wrong. Also bear in mind that the courses are highly fast-paced and very difficult grad. courses. (BTW, I'm taking top grad. schools like Harvard here.) Thanks guys ...
  2. jcsd
  3. Sep 23, 2010 #2
    A hypothetical situation? So you're *not* actually going to do all that? What a tease.
  4. Sep 23, 2010 #3


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    There is never such a thing as a "guaranteed admission". What if everyone applying that year has a similar transcript but with research experience too?
  5. Sep 23, 2010 #4
    No I am. But it's still early in the undergrad. education to do all that so at this stage it's hypothetical. But it won't be after a while. I'm still eager to know how it'll play a role in the admissions decisions. Could someone please tell me?
  6. Sep 23, 2010 #5
    OK and thanks for your answer. I get that there's no such thing as "guaranteed admission". But the point is that obviously people get accepted without having such a transcript. I'm interested to know what transcript of the average applicant to Harvard (say) looks like and whether admissions committees will strongly consider accepting someone if he's got such a transcript.
  7. Sep 23, 2010 #6
    From browsing this forum I'd say a "normal" strong applicant (good research, some grad classes, 900+ GRE, well known university) is enough to get in somewhere in the top-15. MIT/Harvard seem to reject even extremely strong appplicants.
  8. Sep 23, 2010 #7
    What year are you? I think you're getting ahead of yourself, which is something easy to do , and something I do often. Just take the most challenging classes you can, do as well as you can in them, and see what happens. Whether or not someone on a forum says "yeah you could for sure get in" means nothing unless they are on the admission committee at one of those schools.

    One more minor thing: in your list of advanced topics, what is algebraic group theory? Typo? Otherwise it's sort of redundant/vacuous.

    Also: I've known people who've come in with about as many hours as one can, but how can you possibly only take math courses for 4 years? Surely your degree has requirements which can only be satisfied by classes at your institution.
    Last edited: Sep 23, 2010
  9. Sep 24, 2010 #8
    Do you know what an algebraic group is? You can look it up on Wikipedia or on the internet I think. It's basically an algebraic variety that has the structure of a group. Elliptic curves and abelian varieties are examples. Algebraic group theory is the study of algebraic groups.

    Yup I'm in my second year and I've already taken some of the classes I listed. So I've been taking lots of advanced grad. courses in my first and second year. My question I guess (which I think was misunderstood) is that: does the typical very strong applicant to a top grad. school have this kind of transcript?
  10. Sep 24, 2010 #9
    Could someone please answer my question? Thanks.
  11. Sep 24, 2010 #10

    Regarding your main question: yes, absolutely that's what they look for. I'm still an undergrad, but everyone I've talked to (peers, grad students, professors, etc.) says this. Take the most challenging (and don't forget interesting!) courses you can, and do well in them. If you're making good grades in courses like this beginning from your freshman year, then you're doing all the right things I would say. Of course you'll want to consider doing other things like research, etc. but I'm sure you're doing that too.

    Unrelated: I had no idea algebraic groups existed. I assumed that since you already have a variety, which has more structure than a group, you wouldn't be interested in what other structures you can attach to it. Very interesting. http://en.wikipedia.org/wiki/Algebraic_group
  12. Sep 24, 2010 #11
    Grad classes since freshman year?
  13. Sep 24, 2010 #12
    To the original poster, you do have a very good shot at schools, but I would not get hopes too high up. I don't think it is uncommon to have your kind of transcript at the highest caliber schools, probably not at Harvard.
  14. Sep 24, 2010 #13
    *No one* is a shoo-in at the top schools.

    I would about your lack of research experience as well... students who get into the top schools tend to have great grades *and* some experience... so having just great grades makes you a below average candidate.

    The good news is there is still time for you to do something about that!
  15. Sep 24, 2010 #14
    I don't know about research. It doesn't have to be on there for top schools and I don't think it will help you much unless you do something really significant, which is unlikely for math theory.
  16. Sep 25, 2010 #15
    wait, so you haven't actually done any of this stuff? where along this timeline are you? what have you actually done and what is hypothetical?

    and if you haven't started university yet, what makes you think you can take (and succeed) in graduate level classes?
  17. Sep 25, 2010 #16
    I have nothing constructive to say.... just to point out that he's in second year, see Reply 8 above.
  18. Sep 26, 2010 #17
    You should just be proud of the fact that you're doing such advanced courses at such an early stage in your education!

    Good things come to those who wait =]
    Last edited: Sep 26, 2010
  19. Sep 28, 2010 #18
    What university is this that has an excellent undergraduate and graduate math program where it's possible (and manageable) for you to be taking only math courses for all four years and to be taking graduate math courses freshman year? Just curious.
  20. Sep 30, 2010 #19
    Obviously, the only reason I can do grad. classes in math is if I've already done math before going to university which is what I've done. So I finished the undergrad. program for math (on my own) before going to uni. For reasons of "annonymity" as I'm called Annonymous111, the only information I can give you is that the university is in the top 10 (probably much better than 10th) math departments in the world and is located somewhere in the US.
  21. Sep 30, 2010 #20
    I don't understand. So suppose someone has published multiple papers to a top mathematics journal and has great grades, and he gets rejected? There's a lot of hype about Harvard being a great university and all but surely they have some sort of maximum standard and surely there can't be too many people publishing papers to top math journals applying.

    Anyway as I said I haven't published anything. But I'm interested in what people mean by "research". Does this mean original research that is published in a journal? Or does this just mean library research or survey articles that survey some highly advanced topics in a given sub area of math but that don't really constitute original research? Does the latter count as research experience?

    Surely Harvard doesn't expect people to publish original research before going for a PhD? And math is something that it's really difficult to get some original research done without having a specialized enough background.

    So what kind of research is expected of me when I apply? Could someone please clarify? I've also read plenty of forums of top grad school applicants and none of them seem to have taken more than so-many grad. classes. Besides, surely there can't be too many people who've had enough math background to be able to take advanced grad. classes in their freshmen year?

    Suppose also the grad. classes contain material that's more advanced than and subsumes every single one of the grad. classes offered at Harvard and you've got A's in them. Does *that* make you a shoo-in?

    Thanks for all the answers so far. I appreciate them!
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