What are some of the top graduate schools in algebra? I know MIT of course has a great algebra department, what are other possibilities? I'm also considering European universities (that have programs in English), like Bonn, ETHZ, Berlin Mathematical School, and ALGANT (an ERASMUS program).
Posted Jul 30, 2010, 1:23 PM UTC
What kind of algebra? Schools that are strong in group theory might not have anyone that works on rings, commutative and non-commutative research is very different, etc.
Okay, right now I'm more interested in commutative algebra, algebraic geometry, and homological algebra.
Ah, that's definitely something I can say something about. typographicalerror gave good advice above about people to contact. I can name a few schools for you to consider as well. Note that this skews more towards commutative algebra than algebraic geometry.
Michigan and Berkeley are definitely good all-around schools with some great commutative algebraists. U of Kansas (Lawrence), U of Nebraska (Lincoln), are not as good overall, but have very strong commutative algebra programs. There are also some very good commutative algebraists at U of Utah (Salt Lake City), Purdue. There's more but these are some highlights.
You might want to check out http://www.commalg.org and look under "people" to get a feel for where there's a good concentration of people.
Ok, I see so many "where should I do my grad studies" threads in here, and I can't offer you much advice except this:
Is there anyone in your faculty doing similar research? Go talk to that person and find out where the best schools are for that topic. Get advice from someone who has been to grad school, taught graduates, and knows the field.
I guarantee you will get your best advice that way.
Unfortunately there is no one in at my undergraduate university doing anything remotely related to what I want to do (everyone basically does applied math here). Thanks, though.
Thats unfortunate! Im sorry you dont have the resource of an experienced professor of abstract math.
Maybe still ask around if anyone has good advice, but I guess that does change things. This makes me feel lucky that I have an abstract math dept., small as it may be.
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This would be a terrible question for MO.
Actually, questions related to math education seem to be accepted there as long as they are serious questions about serious math education. There's a number of similar questions that have received answers and upvotes.
http://www.ams.org/programs/students/undergrad/undergrad
The Assistantships and Graduate Fellowships guide. Next to each university lists the number of recent Ph.D's in each area of mathematics. This should give you a basic list of possible schools. Then just do some research on the department webpage. Look at how often they teach graduate seminars in areas you are interested in and the research areas of their tenured professors.
Obviously rankings aren't everything, but here's a good place to start:
I don't trust that at all.
Extrapolater's advice is good, but there is a better idea.
Just email some experts in the field and ask them. Don't be intimidated to be e-mailing world-renowned professors; they get much more useless emails than an undergraduate seeking out a good school, and the worst they can do is not reply.
Some recommendations on people to think about emailing: Craig Huneke, David Eisenbud, Mel Hochster, David Cox, William Fulton. There are probably others, but that's a good start. If you have access to mathscinet, you can go to the "Citations" tab, "Search by Subject" and look up the top cited papers in your fields of interest (and investigate a bit to find things that sound interesting to you) and send emails to those people who can tell you useful information.
One school that I personally would strongly consider were I in your situation is Michigan, which has several world-class commutative algebraists and geometers, but you'll certainly hear that from any and all of the people I mentioned.
Thanks a lot!