Second year, looking for advice

Forum for the GRE subject test in mathematics.
Deltadesu
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Joined: Sun Dec 18, 2011 3:52 pm

Second year, looking for advice

Postby Deltadesu » Sun Dec 18, 2011 4:04 pm

Short version: I'd really like to get in to the very best universities for graduate school. I think I've got a decent shot, but my math score (77%ile) scares me. Should I worry?


Long version:

I'm a second-year student at a quite good public university, double majoring in math and computer science.

I took both the subject and general GRE tests this quarter, basically on a whim. Got perfect score in quant and verbal on the general test, but 77%ile on Math. I have excellent academics - this year I'm taking more than twice the typical workload, including two graduate classes in math per quarter (the Algebra and Topology full-year sequences), and have, at the moment, a 4.0 GPA.

I'm going to apply for Budapest Semesters for next fall, and will hopefully get in. I'm also applying for REUs this summer, although I don't know if I can get in as a rising junior.

I got a 19 on the Putnam last year.

I'm going to retake the math GRE next fall after some serious studying. I'm basically going to have to re-learn all of Calculus. With luck, I'll improve my score. If I don't, am I automatically out of the running for the top tier? If I do, do I have a good chance? Is there anything I should be doing that I'm not?



Thanks much.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Sun Dec 18, 2011 10:30 pm

If you took the subject test cold and got a 77th percentile score, you can probably get into the 90s with adequate preparation. You'll be fine.

Is there anything I should be doing that I'm not?

You are probably already doing these but just in case:

1. Make sure to talk to your professors. This will help with letters of recommendation for REUs or funded summer school programs like PCMI or the Princeton Program for Women in Math. They might also offer to work with you over the summer, which is in many ways better than an REU.

2. Go to seminars. This is where you learn what math people are actually working on, and it also helps you foster relationships with professors and graduate students in the department.

I'm going to apply for Budapest Semesters for next fall, and will hopefully get in.

Just out of curiosity, what are you hoping to get out of the program? I considered applying as an undergrad, and then I realized that I had way more mathematical opportunities at my own university or several dozen other study abroad programs.

ANDS
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Joined: Wed Aug 10, 2011 8:41 pm

Re: Second year, looking for advice

Postby ANDS » Sun Dec 18, 2011 11:04 pm

There's definitely a cautionary tale here.

1. Relax

2. Get some internships under your belt.

3. Review the profile information in the Accepted/Rejected threads. People DO get into top tier schools with beating 90% of all Subject GRE takers, despite what folks would have you think. 77th percentile is hardly a bad score - just ask my PhD professor who got in the 50's and was accepted to Chapel Hill (her undergrad and willingness to take graduate classes sealed the deal).

Deltadesu
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Joined: Sun Dec 18, 2011 3:52 pm

Re: Second year, looking for advice

Postby Deltadesu » Mon Dec 19, 2011 12:12 am

owlpride wrote:Just out of curiosity, what are you hoping to get out of the program? I considered applying as an undergrad, and then I realized that I had way more mathematical opportunities at my own university or several dozen other study abroad programs.


My school does a lot of topology and analysis but very little discrete mathematics, an area in which I've always been interested and an area in which Hungary is traditionally very strong. Plus, everyone I've ever talked to says studying abroad was one of the best things they've ever done.

Thanks for the reply!

ANDS wrote:Review the profile information in the Accepted/Rejected threads.


See, that's part of what scares me. Very few people with scores below the 80th percentile get in to the likes of Princeton, and those who do tend to be like mathgrad31455 in the 2010 thread - published papers, went to an Ivy, STILL didn't get in to MIT or Princeton (but did get in to Yale).

ANDS
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Re: Second year, looking for advice

Postby ANDS » Mon Dec 19, 2011 3:48 pm

Well what schools are you looking to get into? I can tell you, from speaking to grad co-ordinators, your 77% is going to be a cherry on top of a solid undergraduate career; especially with excellent marks in graduate courses.

Plus you have (presumably) two more years left - there's plenty of time to retake this exam if you feel especially worried, but all A's will trump a good (no matter what people say) score on the subject any day.

I would love to talk to the folks who were rejected from campuses because of their MGRE score specifically. I bet those folks are hard to find.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Mon Dec 19, 2011 5:20 pm

just ask my PhD professor who got in the 50's and was accepted to Chapel Hill

No offense, but Chapel Hill is not a top (pure math) program in many people's books.

There is evidence that the top programs do pay attention to subject GRE scores. Berkeley and Penn have explicit cut-offs, for one.

bloopbeep
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Re: Second year, looking for advice

Postby bloopbeep » Mon Dec 19, 2011 10:56 pm

Could you please provide links to their explicit cut offs?

quinquenion
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Joined: Fri Nov 04, 2011 12:34 pm

Re: Second year, looking for advice

Postby quinquenion » Mon Dec 19, 2011 11:26 pm

I think owlpride is referring to these links:

http://www.math.upenn.edu/grad/graddata.html
http://math.berkeley.edu/programs/graduate/phd-program

They aren't "explicit cut-offs" per se, but are at the very least strongly suggestive.

Deltadesu
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Re: Second year, looking for advice

Postby Deltadesu » Tue Dec 20, 2011 4:18 am

ANDS wrote:Well what schools are you looking to get into?


The likes of Princeton, Stanford, Cal, and MIT. Like I said, the very best. That's why I'm worried.

ANDS
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Re: Second year, looking for advice

Postby ANDS » Wed Dec 21, 2011 2:58 pm

Deltadesu wrote:
ANDS wrote:Well what schools are you looking to get into?


The likes of Princeton, Stanford, Cal, and MIT. Like I said, the very best. That's why I'm worried.


I think EVERYONE should be worried when applying to those schools regardless of their academic performance; It's sad that a 77% is considered worrisome for such an arbitrary exam, but that's simply the nature of the beast when you are chasing a doctoral and prestige.

Knowing this I say take it again with the caveat that they'll see your prior performance.


quinquenion wrote:I think owlpride is referring to these links:

http://www.math.upenn.edu/grad/graddata.html
http://math.berkeley.edu/programs/graduate/phd-program

They aren't "explicit cut-offs" per se, but are at the very least strongly suggestive.


Well sure, most programs will toss their averages on there. Without information on the distribution though - those are almost meaningless.

quinquenion
Posts: 57
Joined: Fri Nov 04, 2011 12:34 pm

Re: Second year, looking for advice

Postby quinquenion » Wed Dec 21, 2011 3:17 pm

ANDS wrote:
quinquenion wrote:I think owlpride is referring to these links:

http://www.math.upenn.edu/grad/graddata.html
http://math.berkeley.edu/programs/graduate/phd-program

They aren't "explicit cut-offs" per se, but are at the very least strongly suggestive.


Well sure, most programs will toss their averages on there. Without information on the distribution though - those are almost meaningless.


I agree that the average over matriculated students' scores is almost meaningless and that the full distribution would be a lot nicer to have, but I wasn't referring to that. UPenn and Berkeley give explicit numerical guidelines for what applicants are generally expected to have:
UPenn wrote:Scores on the Advanced Math Subject Test of the GRE should be at least 750, though applicants with somewhat lower scores may be admitted if the rest of their application is sufficiently strong.

Berkeley wrote:A score below the 80th percentile suggests inadequate preparation and must be balanced by other evidence if a favorable admission decision is to be reached.

Naturally the wording leaves enough wiggle-room that they can let in outstanding applicants who might be below that number, and the OP might well fit that characterisation. Still, I think it's safe to say that for at least some students, GRE scores were a significant factor in admissions decisions.

Of course, I'm not on an adcom, so I can't say for certain. Maybe I'll be more informed in a couple decades. :P

Addendum addressing the OP: you seem like a very solid applicant and I'm sure you'll blow the GRE away after a bit of practice. Because of the amount of competition, it's impossible to say anything for certain at the level you're aiming for, but you'll have a good shot. Apologies for the thread hijack.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Wed Dec 21, 2011 4:46 pm

I happen to know the graduate director at Penn personally. He said that Penn started to pay a lot of attention to Math Subject GRE scores because they found it to be a good predictor of students' performance on the preliminary exam (covering undergraduate algebra and analysis).

He conceded that neither grades nor GRE scores predict a student's success as a mathematical researcher, but that's hard to judge at the undergraduate stage anyway. Since they cannot predict which applicants will write a successful dissertation, they try to do the next best thing and admit applicants that will be successful in the coursework and exam stage of the graduate program. And apparently GRE scores help them do that.

gromov
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Joined: Sun Feb 13, 2011 6:49 pm

Re: Second year, looking for advice

Postby gromov » Wed Dec 21, 2011 5:31 pm

It is safer to try raising your subject GRE scores, because ultimately you don't want something to hurt you, if you are at all borderline. If a school really wants you, it will take you regardless, but only in a few cases is it clear that it really wants you. Whenever a school is at all nervous, these loose ends start hurting.

One thing I have found though is that a top program refers generally to how competitive admissions is, and the average student quality drawn. The experts who publish great stuff in various fields are scattered to an extent, although the so-called tippy top programs have professors doing some of the "hottest" research. The admissions process has sufficiently many soft variables that aside from the truly prodigious students, who basically have zero weaknesses and are hitting the roof in terms of nearly all measures of success, students do seem to end up in a variety of places for varying reasons.

My advice is thus to find out schools of varying competitiveness that you would actually be happy at. As already stated, it is often not the quality of your dissertation which competitive programs are selecting for in any exact way, so you can get rejected for many reasons. Just because a school is more competitive does not mean you will do your best at it. Those who are prodigies probably would succeed regardless of where they went. Only, be sure that the school you eventually attend has some strong students with whom you can have dialogue about mathematics, because this is said to be important to your development.

ANDS
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Re: Second year, looking for advice

Postby ANDS » Thu Dec 22, 2011 3:55 am

owlpride wrote:I happen to know the graduate director at Penn personally. He said that Penn started to pay a lot of attention to Math Subject GRE scores because they found it to be a good predictor of students' performance on the preliminary exam (covering undergraduate algebra and analysis).

He conceded that neither grades nor GRE scores predict a student's success as a mathematical researcher, but that's hard to judge at the undergraduate stage anyway. Since they cannot predict which applicants will write a successful dissertation, they try to do the next best thing and admit applicants that will be successful in the coursework and exam stage of the graduate program. And apparently GRE scores help them do that.


Now that I can buy into, and certainly would accept as a reason for rejecting a students application. One of my old professors has a fun story about a former student of his at a top tier school who quite simply stunk at exams, but because he had published so many papers and was actively working as a mathematician, when he appealed to NOT have to take his qualifiers, and be given the PhD - they said "Sure. . ."

But in this day and age, with the level of competition being what it is schools can be as arbitrarily selection as they want.

Final advice to the OP - try and recall the problems you flubbed so you can have some facility with where you might need a bit of polish, and then knock it out of the park in a few months. You have time, no reason to start beating yourself up with so much time left.

gromov
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Re: Second year, looking for advice

Postby gromov » Thu Dec 22, 2011 2:40 pm

A question based on the last few posts seems to suggest itself: is there any truth to a claim that schools without general mathematical prelim exams pay less attention to scores on standardized tests? If the school's requirement is just to pass several courses, it would make most sense to see if the student has had success in courses at a similar level, would it not? Further, there are surely schools which only require an oral examination on topics in preparation for starting dissertation work. I would think such examinations have fairly high passing rates, and are primarily intended to see if the student can be in dialogue with mathematicians in areas neighboring and in what she/he wishes to work in.

I leave the question open, as the above is about all the thoughts I have on it.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Thu Dec 22, 2011 5:47 pm

is there any truth to a claim that schools without general mathematical prelim exams pay less attention to scores on standardized tests? If the school's requirement is just to pass several courses, it would make most sense to see if the student has had success in courses at a similar level, would it not?

Do such programs exist? All of the programs I have ever run into tested students either on undergraduate or first-year graduate material.

gromov
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Re: Second year, looking for advice

Postby gromov » Fri Dec 23, 2011 2:06 am

I could be mistaken, but schools such as U. Chicago (I think it is very rigid about its graduate students taking certain year-round courses, but does not seem to mention a single written preliminary exam type system); MIT (a large, but flexible course requirement plus a special topics oral examination).

These seem to have requirements for first year graduate students, but not written preliminary exams.

I imagine there are other schools in the so-called top 25 who do not seem to make mention of such testing as part of the program. Almost all programs have special topics qualifying exams, although these have higher pass rates and offer considerable flexibility to the student to select what topics he/she wishes to pursue.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Fri Dec 23, 2011 4:30 am

MIT's oral exams are quite extensive and do require a fair bit of preparation. (Quote from an MIT professor: Gotta be tough or else too many students will ask you to be on their committee.)

I am not familiar with Chicago's program so I cannot comment. Is it Chicago where all grad courses are pass/fail and the threshold for passing is so high that grad students do actually fail their courses? If so, the final exams for the first-year courses could easily function like a preliminary exam in other departments.

But now I am wondering: why is it that grades in coursework are not a near-perfect indicator for performance on preliminary exams or the math subject GRE? Is it solely the time pressure? The unavailability of reference material on exams? Do courses reward effort more than understanding? Does an exam designed by someone other than the instructor of your course require a higher level of mastery? The first two wouldn't be much of a concern, but the last two would seem to justify some sort of comprehensive exam?

gromov
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Re: Second year, looking for advice

Postby gromov » Fri Dec 23, 2011 5:55 am

There is no denying those schools all have extremely rigorous requirements. For one thing, Princeton has only an oral qualifying exam, but it is supposed to be quite exceptionally intense, even for a batch of very strong students. Chicago's classes are supposed to be fairly intense, and perhaps even more intense than most first year sequences.

You are right that I was getting at the question as to why a strong showing in classes seems to correlate with something different. Some of my thoughts:

A class focuses on systematically developing a topic. Usually, one is aware of what piece is being worked on. In a class, the instructor is deliberately preparing you to succeed. This may or may not (depending on the particular circumstance) be the case for an arbitrary exam written by someone else.

Both situations can present problems requiring deep thinking about difficult ideas. However, it is less likely time pressures will be a negative factor with the classes, because for most of the requirements, one is aware of what piece is being worked on, and is thinking more closely about it already. Some on the spot presence of mind is necessary for almost all mathematical endeavors. However, much more seems to be needed for one requirement than the other.

Last, in a class, an instructor probably wants to help the class succeed. Whereas at times, preliminary exams for graduate programs can have poor passing rates, despite the student body being quite talented. This seems like a slightly more cynical version of a point I already tried to make.

As for standardized testing, I think it is safer to say that the style of testing is of quite a distinct flavor, and suits some much more than others. Nevertheless, a very high showing on those exams is not meaningless, contrary to what some may attempt to argue, but I think lots of care is to be taken to analyze how strong any given student is, and in what sense(s).

As for possible advantages to a comprehensive exam: I think one of the main ones is that it is an official departmental standard, as opposed to leaving things to the whim of a given professor. In a single word, standardization, internal to the given graduate program.

owlpride
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Re: Second year, looking for advice

Postby owlpride » Fri Dec 23, 2011 6:28 am

A class focuses on systematically developing a topic. Usually, one is aware of what piece is being worked on. In a class, the instructor is deliberately preparing you to succeed. This may or may not (depending on the particular circumstance) be the case for an arbitrary exam written by someone else.

I have a conjecture that many high-achieving (measured in terms of coursework) students do poorly on the math subject GRE because they don't recognize the utility of their mathematical tools out of context. For example, a student may know how to solve linear algebra problems on a linear algebra exam, but they may not even realize that they are looking at a linear algebra problem when the problem occurs "naturally" and is not stated in terms of matrices. Or they may be able to solve a linear algebra problem knowing that it's in the chapter on Jordan Normal Forms but not without that information.

It just seems way to easy to do well in a course without a working knowledge of the material involved. That's why I *personally* think that "external" (to any specific course) exams are so valuable, both in evaluating applicants and to motivate real learning.

gromov
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Re: Second year, looking for advice

Postby gromov » Fri Dec 23, 2011 1:58 pm

I think you are right, although I do think that surviving final exams to hard classes tends to require some of the same out of contest thinking. Such thinking also becomes useful in advanced classes drawing upon several bodies of knowledge, which need to be used in ways which are unclear to someone who does not give sufficient thought.

The main trouble arises when coupling time pressure and asking for such out of context recognition. I think solving a hard problem with several unobvious steps over a reasonable amount of time is not quite the same skill as solving a hard problem with one unobvious step under relatively high time constraint.




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