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Mathematical Institutes?


Hey guys, this is an opinion question. I will be graduating soon and want to go on to doctoral studies. As part of my research (my homework) I want to ask some people here what are some of the best schools to work in math. I am studying Applied Mathematics and Statistics and I am talking about schools in the Western United States. I know that schools like California Institute of Technology and UCLA are perfect but what about other school like in California, Arizona, Texas, New Mexico and etc. Instead of JUST prestige, I am talking about other factors such as financial aid and the cost of living.

Any useful comments or links will be welcomed. Thanks in advance!

If you search you can find an NRC web site which adreseses some of your questions like the average length of study, diversity and etc in national doctoral programs. Appearently NRC also comissioned a new study of the doctoral programs this summer as the last survey was done in 1995.

Whatever the results of that survey will be, here are my best advices to you.

1) Go to a school with prestige. It does not necessarily have to be the highest ranked school that takes you in but you can not compare Stanford to University of Arizona.

2) Of course if you know a stellar researcher who promises to take you as a PhD student in University of Arizona, the first rule might not apply, but even then look for guarantees. What if you don't get along, is there someone else you can work with? Will he help you find a job when you graduate?

3) Living conditions are important, but not as important as being able to find a job when you graduate. So among the schools of similar prestige, go for the one in a nicer city, otherwise don't bother.

4) As an extension of the above, don't bother about the cost of living. Financial aid is not an issue, as almost noone pays for grad school in math. Not in US currency anyway. You pay by being a TA and for that you get a small stipend too. Whatever it is that you are paid as a TA, you can live on it. I know people who started families with a single TA salary.

5) You tend to get more personal inetraction in small departments which may be good or bad depending on your personality.

6) When you apply to graduate schools, try to diverisfy. It costs 50-100$ to apply to a school so you can't just apply to everywhere. High ranking private schools are a little harder to get in, as there are many who want to get in and few jobs for TAs. Large public universities need TAs and so it is easier to get in, but except for places like Berkeley or Michigan, they tend to rank lower than private universities. On the other hand if it is a too teaching intensive environment, you may find it difficult to concentrate on your research.

7) Pay attention to the size of the research group you want to get in. If it will be just you and your professor, you won't get much exposure to other people and their research. This may be very costly when you start looking for jobs.

8) If you are graduating with reasonably good grades and if you are an american citizen or a resident, then you can probably get a VIGRE or GRAAN grant. The department will let you know whether you will be getting it when they accept you. That will exempt you from teaching duties for a year or two. It is nice to be paid for doing nothing but I would not go to a place with considerably low ranking for something like that. Also teaching experience comes in handy when you apply for jobs in academia.

9) Also, some departments put the list of their recent alumni and their first jobs on their web page, look to see if anything related to your career goals are there.

I probably can think of many more advice to give but it will take too long and I think I covered the most important ones. As for which schools to go for applied mathematics, I would consider (in roughly this order) the following schools:

Berkeley
Stanford
Caltech
UCLA
University of Washington

Then in no particular order, Uni Arizona, USC, Uni Oregon, UC Santa Barbara, UC San Diego, UC Irvine,...

Although a little outdated (1995), the list in the following link (AMS notices) will give you the rankings of doctoral programs in prestige. Use it wisely.
http://www.ams.org/notices/199512/nrctab...

Edit: It looks as if I did put too much emphasis on the prestige rankings, so let me clairfy my point. I definetely do believe that there are many good mathematicians coming out of middle and low ranked schools every year, and you can find many talentless people coming out of top schools too. This is even true at the PhD level. However, academia is a very elitist place and many people just can't help but think in terms of rankings. So if you are from one of the top universities (say top 10-15 in the rankings) you definitely have an edge over someone from a school ranked in 40s when you start looking for jobs. Even outside of academia, this is so. I have seen a few job advertisements for math PhDs at some financial institutions which were only for Ivy League school graduates... Any serious mathematician would brush of such a qualification requirement, and it was just a handful of firms that said it, but if you want to be in financial markets, that is the reality of life.

Also, top ranked places are themselves centers of attraction and therefore in terms of quality research going on, seminars and colloquia, and personal contacts, being at one of those places can make all the difference in your career, at least initially.

Hi.

Think carefully about what you want to apply your applied math to. Most schools probably apply it to the sciences. What if you want to apply it to something else such as finance? Also, what if you decide you really like statistics and want a doctorate in statistics? You may find that the so-called perfect school does not offer either of these things.

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