Andrew Gibson ([info]amplimax) wrote in [info]mathematics,
@ 2005-06-07 00:37:00
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a school dilemma

For reasons that are rather long and painful to go into, I ended up settling for a local college without much of a reputation for my undergraduate degree. To be honest, the decision to attend here was less like a decision and more like a resignation against caring anymore.

When I first came here I was solely interested in doing physics; then in my first year I attracted the attention of a graduate student who helped convert me over to mathematics and has since introduced me to the really good professors on staff. Apparently, I got lucky, because this was a frequent hang-out spot for Paul Erdös and his presence attracted a lot of top-notch Hungarian mathematicians, especially in Combinatorics and Graph Theory. They have annual conferences now in Erdös' honor that draw people in internationally (I went to the one this spring where a fly-in from Tel Aviv lectured on the Probabilistic Method in proofs). Next year is UCLA. There are several postdocs here from Cambridge, and I personally know one very young graduate student (my age, actually--I think he started when he was like 14 or something) who placed 2nd in the Putnam a few years back; and he came up here specifically to work with these people. He's stark-raving brilliant. So are the professors who published papers with Erdös; having met some of these professors, I can say that they really are on an entirely different plane of existence -- and what can be better than having incredible professors, right? I'm taking a class on number theory from one of them this summer, and I'm elated at the potential it holds for future placement.

The problem is, the school doesn't even place on the NRC rankings...at all. How do those rankings work? Is there a great deal of politics involved? Do they update often? I can't shake it, despite what I see here.

As an undergrad, I really don't know how to feel about any of this. Is it realistic to expect a school with a pretty shitty undergraduate student-body to have high-quality graduate programs? (Are the two usually indicative of each other?) I only know of one grad student who went here as an undergrad -- they rest chose to come here from somewhere else, and from fairly decent schools, too. Or am I just seeing the fluff and puff of academia? To be quite honest I don't know what constitutes a good program or not; it's hard to see from the outside. By the time next year rolls around, I think I should be developing some idea of where I want to go for grad school, and what I want to specialize in. If I stay here, my choices will be decidedly limited to discrete math (which may or may not be a bad thing).

The biggest problem in all this is my inner voice telling me to dissent: there is simply no way a person can get this lucky. It's the "it's too good to be true" syndrome; I know this, but I can't help it.

For the grad-students among you -- how did you decide where to go? Did you stay put? What's your story?



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[info]tarang
2005-06-07 07:19 am UTC (link)
I just finished my undergraduate degree in Math and CS and wanted to go to pursue a Ph.D. program in Pure Math. Now, I have decided to take a break and go work for a few years and do a part time masters in math before I head off to do a Ph.D.

The most important thing to make sure in your head before you start researching the schools is what branch of mathematics you are most interested in. That is the first step and narrows your research down a whole lot more.

I am most interested in algebraic number theory. Here is what I did. I picked up my favourite books on the subject and jumped straight to the bibliography. If you are lucky, you can find an electronic version of the bibiolography somewhere. I then searched on google for all the books and papers mentioned and searched where those professors were currently. Using that, I populated a list of schools.

With respect to NRC rankings, I think they work based on many different criteria that are weighted differently. Someone else can correct me on this, but I believe their highest weights goto number of papers published, how many of those papers are cited by other papers, the amount of money available per student, Ph.D.s awarded every year etc. This is a pretty good measure from a research standpoint. Especially the 2nd crieterium, ie the number of papers cited by other papers. This is a good measure of how good these papers are. You would want to cite only relevant and well done research.

Now if you are not sure of what you want to pursue in math, there is no need to worry. Everyone can still pick a general branch they like. I personaly like algebra a lot, followed by topology and finally analysis.

Now your school probably falls under the category of schools where there are 3-4 people that are clearly the best in their very specific fields.

Another viewpoint I have heard is that it is generally not a good idea to pursue a Ph.D. in the same school where you did your undergraduate degree. In fact, a lot of schools discourage their undergraduates to apply to the same school. Even the grad schools want people to come from different backgrounds so they can bring something new to the table. I might be wrong about this, but a friend of mine at Univ of Chicago said that Chicago does not even admit its own undergraduates.


I rambled a lot, and as opposed to your request am not a grad student. But I hope my info helped.

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[info]amplimax
2005-06-07 08:25 am UTC (link)
That was extremely helpful.

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[info]jp7010
2005-06-07 12:54 pm UTC (link)
It generally is not a good idea to pursue a PhD in the same school where you did your undergraduate degree.

Having nothing but the same school listed three times on your vita can hurt your job prospects, unless you have some good connections and land a really good post-doc. It will seem your inexperienced, having worked nowhere but at the same school, with the same people, for roughly 9 years of your life.

That's the only input I have to give, having not even started my grad program yet.

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[info]rhohat
2005-06-07 08:02 am UTC (link)
I would take the NRC ratings with (at least) a grain of salt. See also Saunders Mac Lane's rant in the Notices.

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[info]mydivineshadow
2005-06-07 09:09 am UTC (link)
Not that it will help with your dilemma, but a grad student at my school solved an Erdos problem a few years back:

http://www.uga.edu/columns/991011/campnews4.html

The math department made a big deal about it at the time.

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[info]amplimax
2005-06-07 09:40 am UTC (link)
Erdös was insanely brilliant: anyone who independently discovers the existence of negative numbers at age five has some serious innate mathematical abilities -- hell, that was a point of contention for medieval mathematicians for far too long, and he comes along and literally makes child's play out of it. I can't even imagine how that discovery would have gone. Makes you sorta green all over, doesn't it?

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[info]mydivineshadow
2005-06-07 11:13 am UTC (link)
They were all like that. Gauss, Euler, Ramanujan, etc. I'm beginning to think that being a childhood prodigy is prerequisite to being worth a damn.

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[info]zivis
2005-06-07 09:22 am UTC (link)
Not a math major, but I can relate to you story of a lackluster alma mater.

Did a BSE in CS&Egr at Northern Arizona. Just finished an OpRes MS at Berkeley. I was in the PhD program and finished most the coursework, but just decided I don't like abstract math that a Berkeley PhD in OR does enough to make an academic career (I'm hoping for a tenure track post on graduation), so I just transfered to Business and Public Policy PhD prog, which brings me to why I chose Cal in the first place. There is no place like it on earth for finding the best in the field, no matter what field you pick from politics to mathematics. It fit me well because I like academic wandering and the post-graduation placements are great.

BTW my other options were Cornell and Stanford. Weather killed Cornell for my wife and Stanford was so damn condescending on the interview I couldn't take it. I assume test score made the difference in my acceptance to all three because I didn't have a pedigree and I'm a mediocre writer. You should not discount the quality of students the top programs draw either. I breezed through my undergrad, helped few students out, but never really got much stimulation out of them. At Cal, you have the full blown 5 sigma IQ'ed freaks of nature for classmates and if you want to see your peers do some neat shit and aren't intimidated by not being the smartest guy in class anymore, you can be pretty energized at the elites. Money (especially tuition) is not an issue for PhD students either. They are all, always, everywhere to my knowledge paid for.

My recommendation if you decide to stay is preview your advisors now and ask yourself 1) if they can guide you well enough on a topic that you are going to have to love for 2/3 years straight, 2) if you can just plain get along with them and 3) if they will be able to write really solid, name-recognized recommendations for the next decade because it sounds like the institution granting the degree won't open doors for you.

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[info]szymanowski
2005-06-07 10:37 am UTC (link)
I'll be starting grad school at UC San Diego this autumn. I'm pretty happy but I could have done a better job in the grad school application/selection process.. though there isn't exactly a next time.

In my case I thought I was fairly sure that I'd be going into a field involving lots of algebra, but I've been working on an analysis-oriented research project recently as well as taking complex analysis classes, and this has made me less and less sure of my original intent. I'm starting to think that it would be a really bad idea for me to choose a specialty field until I've seen quite a bit of math, especially the really hard stuff where you see the more gritty and unpleasant aspects of what you'd have to do while writing a thesis.

So I can definitely see the value of being in a large department, though I planned originally to look only at small to medium size departments. UCSD, while not huge, still has a pretty wide range of faculty so I have flexibility of not having to choose a subfield until I'm a few years into grad school, which is very nice.

This is not to discourage you, because if you're into discrete math, it sounds like your school would be an excellent place to go. (Just make sure you've seen other parts of math until you decide.) From what I've seen, it can happen that a school has an excellent group working in a particular area but has a low overall rank because they aren't strong in other areas.

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[info]39orangestreet
2005-06-07 11:58 am UTC (link)
It sounds to me like your school has a great department for a few subdisciplines and not so much for others. It is more important to go to a school that is strong in what you want to study (if you know what you want to study, which indeed is the issue...) than a school which is strong overall.

That said, I think most people -- including myself -- would strongly discourage someone from going to grad school the same place they went to undergrad. ESPECIALLY in your situation, I think it would be really important to expose yourself to more of the breadth of mathematics, as well as to work with a wider range of professors.

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recommendations
[info]vokzal
2005-06-07 05:40 pm UTC (link)
Get recommendations that are really good from some of these really spiffy professors. Preferably saying that you've been doing some sort of research thing with them.

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generalities
[info]swiftset
2005-06-09 02:00 pm UTC (link)
I've been considering how to approach grad school also, and here's what I've gathered. From the mouth of a guy on an admissions committee, and innumerable profs: the strength of your applications depend upon the classes you took (e.g. did you take a two semester analysis course and a two semester adv. linear algebra course) and most of all recommendations (e.g. did you impress any of your profs with dedication and brilliance, or do respectable research?, does the person who wrote the recommendation have a good name, or even know you?); so it's a bad idea to get a recommendation from a dean, for instance, unless the dean taught you a class. My feeling is that it's best to take one prof for at least two classes, impress them, if possible do research with them, then get a recommendation.

For choosing grad schools, the best thing to do is talk to professors (at your school or not) in the fields you're interested in to get a feel for what places suit your interests. Now that I heard about checking bibliographies, that sounds like a neat idea, because mostly you hear about big named schools, instead of the smaller ones that might be exactly what you're looking for. The NRC rankings are useless: if you know what you want, and the school meets your requirements, then go for it; even if the school ends up being one that is low ranked by the NRC, you (probably) chose one that maximizes your opportunities in your field of interest, while the NRC rankings consider factors that may not affect you. Also, apply for independent grants; never expect schools to meet all your need, even if they say they will; it also makes it possible to move between schools if you change interests (not to mention schools love the fact that you have your own funding).

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[info]pixie_of_spite
2005-06-13 05:31 pm UTC (link)
So something that may not have been mentioned:

I had a choice between two schools for pursuing a PhD in math last year (I just finished my first year), UIUC or Dartmouth. I chose UIUC. I had an old cs prof berate me for this: wouldn't I like the beautiful campus, the proximity to Boston, the urbanity? Wouldn't I like the entering class size of 6 or 8? (can't remember exactly what it was).

Not really. Our incoming class of people here was 34 new PhD students. We have about 85-90 faculty. We have a castle for a math building and a great sense of community.

I think the "mathematical climate" should be considered when choosing a grad school. Visits are good things to make if you have the time and money.

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