Importance of prestige of math grad school?

[murmillo]

I'm currently trying to decide where I want to apply for math grad school. Many of my professors recommended places that were not as selective as the top grad schools but still had what they thought were strong programs in the field I want to go into (algebra). I was wondering whether going to a school that's not as selective will hurt my ability to get a job in academia in a top/very good university. A friend of mine told me that what happens is that since the PhDs from the very best math programs can't get job offers where they went, they will end up landing research positions at the very good (but not top) universities. Then those who got their PhDs from very good (but not top) universities will get the jobs at the OK universities, and things will sort of go down from there. Is there any truth to that?

At first you might be thinking, Why does it matter to him? If he wants a PhD he should go wherever he gets in. But what it boils down to for me is that I would like to go to grad school right after I graduate, but I think my chances of getting into the very strong programs will be better if I wait a year.

 

[deckoff9]

I just had this talk with my professor recently. I was shocked to learn that even academics who should know about the strength of a program at a school sometimes fall for the name appeal of the more prestigious schools. However, he did say that while big name grad schools are good for getting your foot in the door, after a couple of years no one cares about that anymore and you become identified by your work. The caveat to that is if you go to a school where the professors are all super hot shots and don't care about their students and don't give you interesting problems to solve, your grad school experience could be a fairly terrible one. Again, all his words. So, he recommended to apply to a bunch of places, see where you get in, and then when you go visit, make sure to knock on professors' doors and speak to them. Make sure they're friendly and seem like they would be interested in helping you. It doesn't matter how prestigious a name is if you don't actually learn anything when you're there, right?

 

[deRham]

I was wondering whether going to a school that's not as selective will hurt my ability to get a job in academia in a top/very good university.

This is a good question, overall. The answer, as far as I can tell, depends how much less selective we are talking. The truth is that there are silly lines drawn by places like US News as to how top ranked a certain school is, but in reality, this does not determine the quality of employment for any individual. For instance, while UPenn is lower on the rankings than, say, Stanford, it's hardly fair to say that one has a low chance to reach a very good academic position comparable to that reached by many Stanford students by being strong at UPenn.

What you'd want is an advisor who is renowned in your field and with whom you click enough to produce really good stuff.

The truth is that the less selective schools have students who may not go quite as far in academia only because the most selective schools do tend to have a lot of the strongest students. Let me also note that selectivity and being top-ranked are technically two different things. For instance, I would hardly say Caltech qualifies as significantly less selective than schools ranked above it.

The main thing to remember is that the measures used by PhD programs to admit you often will not really say who will and won't be the strongest mathematicians, because they are judging you at that time. Some people show signs of extreme promise much earlier, and those are some of the ones who just get in everywhere. Others take a longer time to bloom.

After all, academia isn't just about being smart at math and being able to ace exams and learn lots of stuff in great detail. It ultimately involves sitting down and grinding out the details to something that ends up being considered important by the academic community. Some people will have ideas and put forth the work to make the cut, and others simply won't for varying reasons.

 

[deRham]

the very best math programs

Let me just again emphasize: a lot of programs even in the top 25 offer some of the "very best" in terms of what kinds of research people do there. It is important to go somewhere that is quite hardcore, and will push you to work, but most important is that you'll churn out good work under the right kind of advisor.

If you have to be worried about something, do NOT worry about getting into a top 10 vs top 15 school or a similar comparison. You should worry about ever getting to be a good mathematician, because whether in the top 10 or top 15, it will actually end up being pretty hard.

When people say a PhD needs to make an original contribution, and thus is tough, they are in fact selling short the difficulty of making an academic career, because ultimately you will have to make several contributions which win you the respect of the academic community in order to remain in it at all.

 

[deRham]

The caveat to that is if you go to a school where the professors are all super hot shots and don't care about their students

I would say that being a super hot shot and caring about students hardly need be exclusive. The key is they will want very strong, motivated students. But seriously, a lot of hot shots are pretty understanding, and even will encourage the student to go above and beyond what they're doing. The other thing is that you will find super hot shots spread through a ton of good schools, not just a small subset which people tend to identify first. I do agree it is possible that working with a hot shot at a school where not everyone is quite as strong as you as a student could be good.

 

[deluks917]

There is a very significant difference between the average graduate student at a school ranked 15-25 and one ranked 1-10.

 

[deRham]

^ I don't disbelieve you necessarily, but how do you know?

I would argue that perhaps the difference starts dropping quite a bit after you leave out schools like MIT, Harvard, Princeton. This is from my view of who seems to get into these schools, and who seems to get into other schools.

For example: US News ranks UPenn and Brown below UCLA. The former two are roughly in the 15 to 25 range, and UCLA is in the top 10 according to US News. Is there a significant difference in graduate quality at UCLA as opposed to Brown and UPenn?

 

[deluks917]

This is a really enlightening read:

http://math.stackexchange.com/questions/8652/does-it-ever-make-sense-not-to-go-to-the-most-prestigious-graduate-school-you-ca"

I based my opinion mostly on reading the course descriptions of the graduates courses offered. The level these courses are taught reveals something about the "level" of the students. I think there is a difference.

 

[deRham]

I looked through a bit of that link. The main comment I have is that one needs to define prestige. I don't think markers like US News properly capture that really. For instance, US News ranks MIT as the top in 2010. I would scoff at the idea that MIT is more prestigious than Harvard for math.

I think assuming all other factors are equal (when there are faculty you can enjoy working with, and decent living conditions, etc) yes, it is good to attend a very prestigious program.

The ONE exception I might make is if one is a strong student admitted to a school such as Princeton, but would really be better suited to a different program. Princeton is a school where there are basically no intro courses and people jump straight into research. Getting admitted there and not being quite ready can be disastrous. Also, you'll be overshadowed by those who are ready. Taking an extra year or two to do your PhD in 5 years instead of 3 or something and doing it at a very highly ranked but not-as-selective-as-Princeton school is not necessarily a bad idea if you plan on graduating with stellar recommendations and credentials and publications.

As for your remark about coursework: I am not sure I truly see the difference you are talking of, except in the cases of schools like Harvard/Princeton. The fact that Princeton ONLY has specialized research seminars and Harvard has the biggest, scariest list of topics courses in insane topics makes a lot of sense, because Harvard's and Princeton's selectivity are a cut above most places. But I still see no evidence of, say, UCLA's department having significantly higher level courses overall than, say, University of Pennsylvania.

In fact, UCLA is weak in some areas of mathematics and strong in others, and even its course offerings may show that. For instance, I'm sure their analysis coursework is a lot more intense than some of its algebra coursework.

 

[Mépris]

The ONE exception I might make is if one is a strong student admitted to a school such as Princeton, but would really be better suited to a different program. Princeton is a school where there are basically no intro courses and people jump straight into research. Getting admitted there and not being quite ready can be disastrous. Also, you'll be overshadowed by those who are ready. Taking an extra year or two to do your PhD in 5 years instead of 3 or something and doing it at a very highly ranked but not-as-selective-as-Princeton school is not necessarily a bad idea if you plan on graduating with stellar recommendations and credentials and publications.

Okay, that's interesting. I'm curious as to how the students pull that off though? Do they do an MS elsewhere first?

 

[deRham]

If you are asking about how people complete Princeton's graduate program - well, they probably entered in having already done research in stuff they are interested in, and just want to continue at Princeton because they feel it has the right resources (i.e. faculty) to help them. In an extreme case, a student may have already written a PhD thesis level paper, and use that to graduate from Princeton without having to go through a host of requirements.

This isn't really anything to do with an MS. In reality, coursework can relate only vaguely to the ultimate topic of research, and a student who is just ahead of the game in terms of knowing what they want can graduate Princeton extremely strong without ever needing to take a course in graduate school. Doing an MS isn't required to go to Princeton or any other school in the US, as far as I know (within mathematics).

 

[Mépris]

If you are asking about how people complete Princeton's graduate program - well, they probably entered in having already done research in stuff they are interested in, and just want to continue at Princeton because they feel it has the right resources (i.e. faculty) to help them. In an extreme case, a student may have already written a PhD thesis level paper, and use that to graduate from Princeton without having to go through a host of requirements.

This isn't really anything to do with an MS. In reality, coursework can relate only vaguely to the ultimate topic of research, and a student who is just ahead of the game in terms of knowing what they want can graduate Princeton extremely strong without ever needing to take a course in graduate school. Doing an MS isn't required to go to Princeton or any other school in the US, as far as I know (within mathematics).

I see. I was under the impression that doing coursework for one-two years and then passing the pre-lims were essential to proceed into the research part of the program. I got this right, one can come in with just a BS degree, pass the prelims the minute they get in, and proceed directly to research?

 

[deRham]

At Princeton, there is an oral qualifying exam on both fundamental subjects and subjects of one's choice (related to research). Most of the preparation for this stuff is supposed to be done on the student's own time. If already prepared to take the exam, it is possible to take it early on during the first year, and just research otherwise.

Yes, your model for taking courses and passing the prelim is more standard, but isn't the Princeton model.

 

[Mépris]

You doing graduate work there, by any chance?

This sure explains a lot. I was on Wikipedia a while back, reading up on some mathematicians, forgot who, but many of them already had their PhD at 25. Spivak, I think, had his by 24! (he did it at Princeton, I think) I never thought 6 years of study, post-high school would be enough.

 

[deRham]

Nope :)

You're right that that's why a lot of people can graduate there super early. Although this is really just a function of already being very focused on something early on, and just needing the right environment to take the next step in an efficient way.

 

[Mépris]

Are there other grad programs in the USA, that you know of, which are similar? It would seem the UK follows a somewhat similar model - the downside is funding for non-EU citizens is barely existent.

Let's say one wants to do research in one subfield of algebra or another - before beginning research, they are to get up to speed with everything that's been happening in the said field, yeah? Is this not something anyone with a decent level of math and an internet connection can do? Why should this be part of a graduate program when a senior (undergrad) could just do it on his own? :S