Mathematics Graduate School Admissions

[blerg]

I am hoping to apply to graduate schools in mathematics this fall, and I am in the process of deciding where I'm going to apply.

I have a 3.95 GPA (overall and in math). I go to a top 30 math school. I've taken upper division in pretty much every topic (about 15 undergraduate) and have taken 5 graduate course (and plan to take about 10 by the time I graduate). I consider my coursework one of the strongest points of my application.

My GRE scores are General: 800 Quantitative, 590 Verbal. Subject: 810 (87%).
As a side question, should I retake the subject test? I was scoring near perfect on all the practice tests, so I believe I could do better, but is my score good enough?

I did one REU last summer and have submitted results for publication. I've been to several major conferences where I gave a talk on these results.
I did independent study with a famous mathematician last semester and am continuing this work this summer, which will lead into a senior thesis with him this coming year.

I've also been a TA for the past two semesters (not sure if this is worth anything)

My letters of recommendations should be good to great, being from professors I did research with and professors I have had multiple grad classes with.

My interest is in topology, specifically algebraic topology.


Right now my list of schools I want to apply to are as follows:
Berkeley
Chicago
Columbia
Michigan
UPenn
Washington
Harvard
MIT
Northwestern


I would like to have my list critiqued. Do I have a chance of getting into these school? Is my list too top heavy, i.e. should I add some lower ranked school? Any opinions on these schools with regard to my research interests?

Thanks for any type of input!

 

[deRham]

You should have a good shot at some of those schools, if your letters of recommendation are good.

I don't think you need to take your subject GRE again at all - that's a very good score. Of course any embellishment can possibly help, but at this point, I don't think a higher GRE subject test score will help you.

Anything can happen in the application process, but I wouldn't worry too much about keeping the application like it is.

 

[deRham]

Err, keeping the list like it is.

I would be very surprised if you got rejected from all those schools.

 

[blerg]

Thanks for the advice.

I suppose the stress only gets worse from here.