Not sure about the strength of my grad application

[jaeliseo]

Not sure about the strength of my grad application (MATH)...

Hi all, Sorry to post another typical grad application question, but I really need some guidance on appropriate math grad schools I should apply to. My advisors don't seem to know much. Could anyone give me a rough idea of where I should apply... Top 20, 30, 40, 50... etc.. I am applying in the fall of this year.
I plan of apply to Pure Math PhD programs.

I go to a large state school in NC without any significant math reputation:

My overall GPA: 3.5 (I had a dismal start... 3.7+ last 2 years)
Math GPA: 3.75
MATH GRE: will take.

RESEARCH EXPERIENCE:
I have been doing a year-long project in Mathematical Biology with a professor, and am currently writing the paper for publication. I will get first name on the paper. I am also a T.A. for the math department, and a member of Pi Mu Epsilon (if that means anything).

I have taken the following courses:

UNDERGRADUATE COURSES:
Single, Multi- Variable Calculus: A
Differential Equations: B
Elementary Linear Algebra: C (not sure what happened here...)
Intro to Abstract Algebra: A-
Intermediate Abstract Algebra: A+
Intro to Mathematical Analysis: A
Discrete Mathematics I and II: B+
Set Theory and Transfinite Arithmetic: A+
Functional Analysis: A

GRADUATE COURSES:
Advanced Linear Algebra and Matrix Theory: A
Mathematical Analysis: A
Advanced Abstract Algebra: A
General Topology: A
Theory of Computation: A

LAST SEMESTER SCHEDULE:
Advanced Linear Algebra and Matrix Theory II (Graduate)
Mathematical Analysis II (Graduate)
Advanced Abstract Algebra II (Graduate)
General Topology II (Graduate)
Complex Analysis

So... what should I shoot for?

 

[Arsenic&Lace]

If it's like physics grad school you should in principle be able to get into a top 10 school, especially if your research advisor is somewhat well known and can provide you with a good letter of rec. But it's not probable that this will happen; there are truly very few students for whom it is probable that they will get into a top ten school.

But that's really immaterial from what I've heard talking to advisors and so on (again, for physics). Basically look for an advisor doing something you think is really cool and apply there, assuming the location and cost of living are compatible. Trying to make overly pragmatic career oriented decisions can be very damaging; if you try to go to princeton because you think that will allow you to become a professor, but it turns out you hate princeton and your advisor there (assuming you get in), that's vastly more damaging to you than going to Georgia Tech and liking the culture/advisor/project.

School ranking shouldn't be a deal breaker.