Choosing a Math Grad School: Factors and Considerations

[InbredDummy]

So I will be applying for math grad schools this upcoming Fall, and I made a list of factors that are important to me in choosing a grad school, and I tried to grade it on a 1-5 scale, 5 being ideal.

I created the following rubric for myself:
- Location
- Weather
- "Prestige"/Rankings
- Strength in Geometry and Topology
- Strength in Mathematical Physics
- Realistic chances of admission (i.e. I have a better chance of admission to UC-San Diego than I do to Berkeley)
- Size of the Department
- Guranteed Support for all admitted students?

I know certain schools are almost great in everything, like Berkeley, Harvard, Princeton and certain other schools ave particular strengths, like Urbana has a good algebra program, etc. But I wanted to go to school for mathematical physics, specifically in the quantum, string or relativity aspects. Now some schools that are highly ranked have little math-physics, even the highly ranked ones like Chicago. They have people who research the mathematical groundwork, but they don't actually seem to delve into it.

My questions for you guys:
1) What do you think of my list? Is there anything you would add or subtract?

2) With the whole "Prestige" angle I am very concerned with. Like I said, some schools are very good in certain areas and they aren't top ranked overall. I believe Rutgers has a very highly regarded discrete math program, but I also noticed their mathematical physics faculty is outstanding, yet I never hear it mentioned from any of my professors.

Seriously, check it out: http://www.math.rutgers.edu/grad/interests.html
they have an amazing group for strings and quantum theory mathematics.

Let's say I get into a good program that isn't as strong in mathematical physics and I also get into Rutgers, which should I pick? Do I go with the top 10 school or the school that has my research interests? I ask this because it seems that prestige and schooling have a big say on your future career as a mathematician. For example Stanford is a great program for both topology and geometry, but they only have 2 or 3 faculty members doing mathematical physics, and Stanford is Stanford, but I believe Rutgers has a better math-physics department due to the fact that Stanfords is almost nonexistant.

3) How many schools should you apply to? I hear from some professors, apply to 2-3 dream schools, 2-3 reaches and 2-3 safety schools others say 2 dreams and 2 schools you can get into. I guess it all depends on what your application is going to look like. I have a really high GPA, a lot of research experience and I can probably get 2 really good letters of reccomendation. My GRE scores are TBD, but I'm studying pretty hard for them right now.
Oh and I come from a well known mathematics school.

Thanks

 

[LazyLlama]

Well for your list, you may want to add price, if that's a factor. Location and Weather don't really matter in my opinion, it's not like you have to live there forever. As for how many schools to apply for, it depends how confident you are that you are going to meet (preferably exceed) the requirements for that school, 2 first choices and 2 backups seem good to me.

 

[mathwonk]

my experience may be out of date, but probabl not totally.

most decent schools support all their admitted students for phd programs. so price should not be too big a deal.

prestige should not be that big either, since most reasonable schools are very good, and the more important thing afterwards is how good you are rather than how good they are.

so i would suggest trying for a school where you can get in, and one which has a good representation in the field you like best, as well as some other fields so you can make some choice if you change your mind.

5-10 applications is plenty if well chosen. i only applied to two, and got in both.