iceman99 said:
That is an impressive list.
Yeah but I doubt I'll get into any of those schools. I choose my school list to reflect my interest in geometry (differential geometry, geometric analysis, ricci flows, geometry of PDEs) and mathematical physics (mostly how geometry is used in quantum field theories, general relativity and possibly grand unified theories like string theory).
From my research on grad schools I believe that the better schools for math-physics are: Harvard, MIT, Berkeley, Columbia, Yale (even though it is small, there are some good people for representation theory and they have a general relativity guy), UPENN, Duke (really really impressed me with the emphasis they place on geometry and physics), Texas, Rutgers (seems to have a great quantum department).
For geometry, it is the usual suspects. Stanford in particular sticks out with just the sheer percentage of professors who research geometry. However, again Duke really impressed me with their faculty and they even have a geometry/physics track for PhD. I cannot tell you how exciting it is to see a math PhD program list General Relativity as a regularly offered graduate course.
And I would like to give some advice for potential grad applicants:
1) Do not judge a program squarely based on it's overall rankings. Columbia is lower ranked than Berkeley, but if you want to study Ricci flows, it is one of THE places to be. Likewise, UC-San Diego has an excellent geometric analyst in Chow.
2) Do apply to a wide array of schools. I applied to Yale, which is a smaller department but I also applied to Berkeley, Texas, Rutgers, etc. which all have very big faculty (all also happen to be public, which is another thing to keep in mind). Harvard has a 15 member senior faculty but it also only admits 8-10 students a year, so you get to interact with top notch faculty.
3) I tried to make sure each school had at least 4-5 faculty members that I would have no qualms doing a thesis under, at least material wise. This way I have a sizeable pool of possible thesis advisors and I can choose which one I mesh the best with.
4) I also applied to a school in an area that isn't necessarily as appealing, but I kept the option open. Considering most applications cost $60-70 for the fee, $15 for extra GRE scores and $10 to send a transcript, you figure at most $100 to keep an option open.
If I could apply all over again I would:
1) Apply to "realistic" reach schools. I know reach schools are supposed to be unrealistic, but I don't think I have a shot at the top 6 (Harvard, MIT, Berkeley, Stanford, Princeton, Chicago). I would probably apply to 1-2 super reaches, 2-3 reaches, 2-3 comfortable admits and 2 safety schools. My list does not really have any safety schools, even the lowest schools are top 25 ranked and ranked top 10 in specific research areas. I might very well end up not getting into any PhD program.
2) Write a better grad school essay. My statement of purpose was not so great. I stated what I wanted to study in grad school, but they were all rushed because I wanted to get my applications in so early, which did nothing since some of my recommenders took so long to send in letters.
3) Definitely study more for the GRE and the GRE subject. I thought I could take an honors thesis on an open problem, an independent study in general relativity, an independent study in topology, a course on measure theory, a seminar on geometry of physics, write all my grad school essays AND study for the GRE and the GRE subject exams. Big mistake. I have a great GPA, good letters but a terrible GRE score. It is the one blotch on my application and it might potentially hold me back from a better school. If I could do it again, I would have set aside 2-3 months during the summer of my sophomore year and studied regularly (nothing crazy) for the GRE and have taken itduring the fall of my Junior year, allowing me to completely focus on upper-upper division math courses, grad courses, independent studying, an honors thesis, etc. during my Junior and Senior years, the most crucial years in the grad school application.
Yes math is about working hard and being a good mathematician, but getting into grad school is not 100% about being the best math student. You have to be on your heels and be able to stay on top of deadlines as well as being able to convey what kind of math student you are, on paper.
As I type this, I am going insane waiting on grad decisions.
). No info on fin aid yet.
