Undergraduate research experience for top schools

Forum for the GRE subject test in mathematics.
variationofhedges
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Undergraduate research experience for top schools

Postby variationofhedges » Fri Dec 28, 2012 2:01 am

For the top 5-10 programs in pure math, what is the typical amount of research (in number of published papers, for example, factoring in quality) that an entering grad student will have done during their undergraduate years? For top 20?

kuz
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Re: Undergraduate research experience for top schools

Postby kuz » Fri Dec 28, 2012 3:14 am

For this year's incoming Princeton class, about 7 or 8 of the 10 had a publication, and 1 or 2 had more than one publication. I think nearly all those publications were quite decent though, and a lot were sole author.

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Gasquet
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Re: Undergraduate research experience for top schools

Postby Gasquet » Fri Dec 28, 2012 5:53 am

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Last edited by Gasquet on Sat Jan 11, 2014 8:06 am, edited 1 time in total.

vonLipwig
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Re: Undergraduate research experience for top schools

Postby vonLipwig » Fri Dec 28, 2012 11:37 am

My impression is that very very few applicants have a publication. I know people who have been accepted to a wide variety of the top schools with no publications.

(This seems to contradict kuz, above. Perhaps undergraduate theses are looked on favourably here, and this would explain the cases I know of)

dexter
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Re: Undergraduate research experience for top schools

Postby dexter » Fri Dec 28, 2012 2:14 pm

vonLipwig, did you send your undergraduate thesis with all your applications? I'm assuming you haven't published.

gromov
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Re: Undergraduate research experience for top schools

Postby gromov » Fri Dec 28, 2012 6:24 pm

Well, I think admissions styles vary greatly among strong schools. Princeton is a program with an often 4-year track, with no formal course requirements, if I've got that right. As a result, I think they may stress a student's readiness and maturity to jump into research more.

This isn't to say someone without such credentials can't get accepted at Princeton of course. I think very strong letters from reputed faculty, a strong background, and other accomplishments suggesting mathematical talent can also work.

One thing about kuz's experience is that I think he's speaking of those who accepted Princeton's offer, not merely those accepted at Princeton. It is my view that those accepted to Princeton may not always, amidst the applicant pool, all be well suited to its program style, even if they're "strong" enough.

Those who accepted Princeton's offer may be likelier to already be excited about pursuing a certain track, have started along it, and continue in the program this way. I can think of at least one case where this precisely happened.

I think there are plenty of students at Stanford, Chicago, various Ivy Leagues and top US public schools who do not possess a large publication record, and who aren't very sure of what they want to do. Those schools all produce students of exceptional caliber and researchers of exceptional caliber.

General advice: to get into a top program, worry first that your learning, grades, and letters are going to be up to par.
Then add on publications if all is going well, and it could be a bonus to knock you into some of the most hypercompetitive. I think for all but the strongest of the strongest students, it's going to be a bit of luck of the draw, as far as I can tell, to get into schools like MIT, Harvard...

vonLipwig
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Re: Undergraduate research experience for top schools

Postby vonLipwig » Fri Dec 28, 2012 7:13 pm

dexter wrote:vonLipwig, did you send your undergraduate thesis with all your applications? I'm assuming you haven't published.


I mentioned them in my SOP (the topics, etc), but only sent them to Michigan, which for some reason mentioned that they'd like copies of such things.

variationofhedges
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Re: Undergraduate research experience for top schools

Postby variationofhedges » Sun Dec 30, 2012 11:13 am

kuz wrote:For this year's incoming Princeton class, about 7 or 8 of the 10 had a publication, and 1 or 2 had more than one publication. I think nearly all those publications were quite decent though, and a lot were sole author.

Could you give some more concrete description of what the publications are like? (E.g. Journal reputation, length, depth or level of sophistication, relation to student's current research interest, etc.) Could you also comment on the fields of these papers? Thanks in advance.

kuz
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Re: Undergraduate research experience for top schools

Postby kuz » Sun Dec 30, 2012 2:31 pm

vonLipwig wrote:My impression is that very very few applicants have a publication. I know people who have been accepted to a wide variety of the top schools with no publications.

(This seems to contradict kuz, above. Perhaps undergraduate theses are looked on favourably here, and this would explain the cases I know of)


Certainly most people at other US universities that I know tend not to have publications. So Princeton is a bit of an outlier in that respect, for exactly the reasons that gromov wrote.

gromov wrote:Well, I think admissions styles vary greatly among strong schools. Princeton is a program with an often 4-year track, with no formal course requirements, if I've got that right. As a result, I think they may stress a student's readiness and maturity to jump into research more.

This isn't to say someone without such credentials can't get accepted at Princeton of course. I think very strong letters from reputed faculty, a strong background, and other accomplishments suggesting mathematical talent can also work.

One thing about kuz's experience is that I think he's speaking of those who accepted Princeton's offer, not merely those accepted at Princeton. It is my view that those accepted to Princeton may not always, amidst the applicant pool, all be well suited to its program style, even if they're "strong" enough.

Those who accepted Princeton's offer may be likelier to already be excited about pursuing a certain track, have started along it, and continue in the program this way. I can think of at least one case where this precisely happened.

I think there are plenty of students at Stanford, Chicago, various Ivy Leagues and top US public schools who do not possess a large publication record, and who aren't very sure of what they want to do. Those schools all produce students of exceptional caliber and researchers of exceptional caliber.

General advice: to get into a top program, worry first that your learning, grades, and letters are going to be up to par.
Then add on publications if all is going well, and it could be a bonus to knock you into some of the most hypercompetitive. I think for all but the strongest of the strongest students, it's going to be a bit of luck of the draw, as far as I can tell, to get into schools like MIT, Harvard...


This is spot on. A lot of my fellow classmates are pretty ready to start research. We have to pass a general exam at the end of our first academic year, but then it's research all the way after that; furthermore, there are no requirements to take classes (though most people audit some classes in their first year, and even in their later years if there are interesting advanced classes on offer). So it's a shorter degree (by US standards) that is aimed towards students who are mathematically mature in their ability to do research. Of course this doesn't necessarily mean having already been published.

variationofhedges wrote:Could you give some more concrete description of what the publications are like? (E.g. Journal reputation, length, depth or level of sophistication, relation to student's current research interest, etc.) Could you also comment on the fields of these papers? Thanks in advance.


Not sure I can go into so much detail, as I haven't read half of my fellow students' papers. And bear in mind that at the time of application for Princeton, a lot of these papers may not have even been completed, or were just on the arxiv but hadn't been accepted for publication in a journal as yet (my sole paper at the time fell into the latter category). So I'm guessing the advisory committee either read the papers on the arxiv (if they were up there) or took into account letters of recommendation detailing the applicant's research, rather than looking at the reputation of the journal.

I think a couple of the papers were from REUs and the like, and a couple of others were from senior theses (as mine was). The journal reputation varied; one guy had a (2-part) paper accepted in a top combinatorics journal (and this was a long 2-part paper). Others (from minor REU projects) had short papers accepted in average journals. In all cases, the research involved certainly wasn't mediocre (as many papers are!) but most papers weren't impressively sophisticated.

As far as fields go, I think all of them were related to the respective student's current research interests, but it's first year so too early to tell whether someone's interests might change. Of course there was a broad scope of fields: combinatorics, graph theory, analytic number theory, algebraic number theory.

quinquenion
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Re: Undergraduate research experience for top schools

Postby quinquenion » Sun Dec 30, 2012 3:05 pm

Gasquet wrote:Does anyone have the numbers for Applied Math programs at any school?


Applied math means any number of things, depending on where you go. At MIT, very "pure" combinatorics falls under applied, whereas PDEs, probability, and statistics count as pure. Also, you run into the confounding factor of determining what counts as a "math" publication. For example, I had (and still have) no proper math papers, but have several publications in analytical biochemistry/molecular biology (with nary an equation in sight). That's obviously not math, but what about an engineering or physics paper?

kuz wrote:And bear in mind that at the time of application for Princeton, a lot of these papers may not have even been completed, or were just on the arxiv but hadn't been accepted for publication in a journal as yet (my sole paper at the time fell into the latter category). So I'm guessing the advisory committee either read the papers on the arxiv (if they were up there) or took into account letters of recommendation detailing the applicant's research, rather than looking at the reputation of the journal.


This is a very important factor to remember. Academics know that publications can take years to actually get to press. I would say that of the MIT first years (pure and applied), about half have a publication in some field (most in math) and a chunk of the others have an arXiv preprint. However, those of us who took the time to do a masters degree (e.g. Part 3 at Cambridge) are *much* more likely to have published. I strongly suspect that at the beginning of our respective senior years, *far* fewer of us would have had publications to our name.

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Gasquet
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Re: Undergraduate research experience for top schools

Postby Gasquet » Mon Dec 31, 2012 4:05 am

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Last edited by Gasquet on Sat Jan 11, 2014 8:06 am, edited 1 time in total.

quinquenion
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Re: Undergraduate research experience for top schools

Postby quinquenion » Mon Dec 31, 2012 11:40 am

Gasquet wrote:I am aware of that. I was looking for similar numbers as kuz mentioned for Applied Math programs, irrespective of which area the students are in. A publication need not be a math one.


Unfortunately, I honestly am not sure which of my classmates are "applied" and which are "pure", which is why I gave combined numbers counting publications from all fields.

(At MIT, once admitted, as far as I can tell, the only practical difference is that applied kids are allowed to count 1 non-math class towards their 11 required classes.)

variationofhedges
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Re: Undergraduate research experience for top schools

Postby variationofhedges » Wed Jan 02, 2013 1:56 pm

quinquenion wrote:(...) However, those of us who took the time to do a masters degree (e.g. Part 3 at Cambridge) are *much* more likely to have published. I strongly suspect that at the beginning of our respective senior years, *far* fewer of us would have had publications to our name.

If possible, quinquenion, could you give a rough estimate of the number of current first-year math PhD students at MIT who have already completed a Master's degree?
Also, for the benefit of all of us applicants, could the numbers also be given from those enrolled in other top programs? Many thanks in advance.

quinquenion
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Re: Undergraduate research experience for top schools

Postby quinquenion » Wed Jan 02, 2013 3:51 pm

Everything in this post *only* applies to domestic students. I really can't say for international students, since educational systems are so different.

My uninformed guess is that, of the domestic students, between a quarter and a third completed a masters degree in some field. Several points to keep in mind:
  • The sample size is extremely small, so percentages can be misleading.
  • Many (most?) American students who do masters degrees overseas (especially part 3) have already been accepted to top American graduate programs and are just deferring their matriculation.
  • In all the cases I know of, these masters degrees were either done in a combined BS/MS program, or at an overseas institution (usually on a fellowship).
  • I strongly suspect that most of the domestic students with overseas masters degrees would have been accepted even without doing the masters degrees.

Again, none of this post applies to international students, and this is just one uninformed graduate student's two cents. Take everything with a grain of salt (or better yet, an entire shaker).

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Gasquet
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Re: Undergraduate research experience for top schools

Postby Gasquet » Thu Jan 03, 2013 3:11 pm

This may answer some questions.

In the U.S., in mathematics, it is a bit unusual to have a peer-reviewed publication from an undergrad, despite the recent years' push for "Research Experiences for Undergrads". In some cases there are group-written papers in second or third-tier journals, but nothing too serious. Or the undergrad gets to be the tag-along on an applied-math research "team". Indeed, it is exceptional, and only rarely happens, that an undergrad in mathematics has adequate background (disregarding future potential) to make a serious contribution. It does happen, but rarely, and is not at all "expected". Evidently the situation is much different in other fields.

In terms of literal admission to good-but-not-elite programs, the usual "publications" we on admissions committees see are "nice", but not really evidence of future potential so much as enthusiasm, ... which is a good thing, for sure! ... but the level of focus and effort required for these little papers is far, far different than the level of commitment required to do a Ph.D., with or without "talent".


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