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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!
  22. Sep 30, 2010 #21
    Could someone please answer my question? Thanks guys ...
  23. Sep 30, 2010 #22
    Take into account that Harvard takes what, 10 students per year? So basically you WILL need to be somewhere in the top ~20 students in the US. Are you sure those classes are enough to earn you such a spot? I've been pretty much told that I'll need a few math grad classes since at least junior year to have a real chance, and I'm going for physics grad school!
    You really need to do research. Take some of the grad classes but start doing research (all summers etc). If you've started since freshman year, and take only math, there aren't enough courses anyway. And there's no reason to take ALL courses. Take the basic ones, find out which field you like best, take some advanced/specialized ones in that field. Then start doing research with the profs in those courses. Ideally this will happen somewhere around second sophomore semester, so you can get in two summers of research on the topic you like.

    No one is expecting you to do research as an undergrad, but you need to be on the same level with the other applicants. Find grad students at Harvard and look for their resumes to see what you're up against.
    Last edited: Sep 30, 2010
  24. Sep 30, 2010 #23
    Does this post amount to anything more than bragging about your hypothetical accomplishments? If you are so talented, there is no reason not to publish some quality research before you graduate. Certainly you have professors on their knees begging you on a daily basis to work on their projects?
  25. Sep 30, 2010 #24
    "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?"

    Listen to what I say carefully (I hope that doesn't sound too "knowing"), because I have a realistic answer for you.

    Yes, with your approach, you will impress many top grad schools. No, that doesn't guarantee you a spot. It is perfectly possible to get in the high 90s percentile, have taken a ton of insane courses in a top school for undergrad, and get rejected.

    Think about it, Harvard (as someone said) may have 10-ish people in the entering class. It almost is to the point where when you take which graduate course doesn't matter. Yeah, of course your schedule will make anyone think you're a hardcore student, but 10 students is *tiny*, and they will look for people who bring research talent in some field and really know what they are doing. It is NOT, unlike what you seem to believe, important when you take your graduate courses. Real research work is insane even if you've taken every course in your dept, because the courses are the foundation, and then it takes years and years of struggling around poorly documented information in mathematics to start to follow what's going on.

    Spend your time figuring out what you want to study, and being serious. I promise when you take which course isn't going to matter beyond the fact that at the end, you should seem a promising researcher.

    "Does this post amount to anything more than bragging about your hypothetical accomplishments? If you are so talented, there is no reason not to publish some quality research before you graduate."

    I don't even think it's *THAT TALENTED* - people overstate the importance of taking this many or that many courses all the time. I think people misunderstand how lost you will be anyway when you enter and try to research a hard topic - because all you can do is take the few courses that give you the foundation and then you have to rely on your advisor.

    To the original poster, if you want to be *GUARANTEED* admission at Harvard, you should not even be asking these questions, you probably should have been doing high quality PhD level work at some absurdly young age (it's not unheard of, but even at a school like Harvard, it's exceptionally rare, to the point where I doubt anyone could deny you admission).

    I would wager you will get into *a* top school if your letters are fairly good and you do all you set out to, but don't underestimate how hard it is to actually do it (I'm not saying you are, but you might be), and don't believe that this is the most important thing.

    The problem is real research mathematics is insane to succeed at. A professor I know went to Harvard as an undegrad and was a serious, great student, but his true accomplishments shone when he went to grad school. He outdid many people who had traditionally impressive padded resumes.
  26. Oct 2, 2010 #25
    If you do all that and also do research in the summers (which does not necessarily mean getting published results but just attempting to do so at REUs, for instance), then you will have about as high a chance as you could ever have of getting into Harvard, and if you apply to all the top grad schools I'd be shocked if you got rejected from every single one of them.

    Most grad students at Harvard didn't do any really serious research as undergraduates. They all tried, but most didn't get any really noteworthy results. To be a *shoo-in*, maybe it's necessary to have significant results. But to have a good chance, it's not necessary; you just need to have given it a serious attempt.

    That said, I can safely say the chances of not having to take any non-math courses for your entire undergraduate degree are about 0%. How exactly are you planning on pulling that off? One of my friends, who's a freshman at Harvard doing Ph.D. level research, is only taking two math classes this semester, and I've heard of some other extremely talented undergraduates at Harvard who do the same thing.

    Which classes out of curiosity?
    Last edited: Oct 2, 2010
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