Looking for Math PhD Recommendations

[SeanLikesMath]

Hello, I'm sure none of you have ever seen a recommendation request here before. :)

I'm in a bit of an odd situation; I went to a good technical school a few years ago as an engineering major but left without finishing for personal reasons, mostly due to severe depression. My degree was nearly complete (only non engineering courses remained) and I decided to take them a a nearby state school to finish up. While doing so, I noticed that I was close to a degree in Math as well as engineering. My grades at my first school were not great (like a 2.6) but that was over 5 years ago.

Long story short, I will be ending up with a double major in math and philosophy from a state school. I currently have a 4.0 and will in all likelihood be ending up either staying at that level or going as low as 3.9. I also have some co-op experience as an engineer at a national laboratory. I am also working full time as an athletic coach, have competed internationally for the US and have produced an athlete that has done the same, if that matters at all. I am taking the GRE this week; I hope to score around what I scored on my practice exam, which was a 167 verbal and 167 quant. I will be taking the subject test in the fall. I am also 30 years old.

I would like to pursue my PhD in math, most likely in analysis, number theory or some cross disciplinary area like logic or neural networks. I would like to pursue research and teaching at a college level, work directly for the government or as a contractor, or get involved in medical research. Here are the schools I am currently thinking of applying to:

MIT, Stanford, Berkeley (Reach schools; I know there is an extremely low chance of acceptance but I have been advised to apply anyway just in case. I also have some connections as far as Stanford is concerned.)
Northeastern (Which would allow me to pursue the degree part time and still work)
Tufts
Rutgers (Where a family member was a professor in a different department)
Illinois at Urbana Champaign
Washington University in St. Louis (A few connections here)
University of Colorado at Boulder
Johns Hopkins
Boston College
Dartmouth
Arizona State
University of Missouri at St. Louis (Safety school where I have informally been told I would get in.)

I plan on doing a lot of preparation for my GRE subject test and I already have some solid recommendations lined up from my professors. Since I will be taking the subject test in the spring, I also have some time to kill in between undergrad and grad to either take some classes or get involved in some research.

What would you recommend that I do with my time, and are there any schools I am missing or should not place on my list? Geographically, I would like to stay either around St. Louis, Northern California or the Boston-DC corridor.

Thanks for your replies and I'm sorry about the long post; I just want to lay all my cards on the table.

 

[halo31]

You surely have the grades and your inspiration shows for mathematics. I'd also consider other universities such as Stoneybrook or University of Maryland College Park. I heard they have pretty good math programs and they rank quite high. But also do consider that you have good letters of recommendations and a near perfect on the quanitative portion of the gre as well(shouldn't be too bad to do) as well as some research perhaps. With that said your chances look pretty good and as for your prior degree, I would not think that should affect your acceptance into anyone of these universities.

 

[SeanLikesMath]

I just took the GRE last night; I scored a 167 verbal and a 168 quantitative. The writing has obviously not been evaluated yet. I know those are good scores but I keep hearing that top programs want perfect quantitative; should I schedule a retake?

Also, Halo, thank you for your response and your recommendations!

 

[micromass]

I just took the GRE last night; I scored a 167 verbal and a 168 quantitative. The writing has obviously not been evaluated yet. I know those are good scores but I keep hearing that top programs want perfect quantitative; should I schedule a retake?

Also, Halo, thank you for your response and your recommendations!

I really doubt that grad schools care about the general GRE. If your subject GRE is good enough, then everything is alright.

 

[lucid_dream]

I would recommend taking the subject test GRE in mathematics. A friend of mine scored in the 80 percentile and got rejected from nearly every school he applied to except Dartmouth. He had a 4.0 gpa, published a paper in topology and took many graduate classes. Granted, they were all top 20 schools for PHD programs. Still, I would recommend applying to a couple more safety schools.