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My GPA here is pretty poor, due to 16 hours of F's (all one semester). In terms of core coursework, things aren't so bad but still a bit spotty.

A: Analysis 1, Algebra 1, Probability, Topology, Linear Algebra, Vector Calc

B: Algebra 2, Knot Theory, Number Theory, Diff Eq

C: Complex Analysis

This semester I am probably gonna get an A in Analysis 2 (measure & integration, hilbert spaces), A or B in an "applied linear algebra" class (mainly spectral theorem and applications to problems of physics) and a C in a numerical methods class.

I'm really lazy when it comes to some classes, if it doesn't interest me I have a bad habit of just not doing the work. That's a pretty gaping character flaw of mine. However, when I am interested in something I'm pretty dedicated to it, I think I would find phd level mathematics rewarding and would even be pretty good at it (relatively speaking... not a superstar but able to do good work).

Next semester I'm gonna take the undergrad PDE and Diff Geometry courses, and I'll probably get A's in both of those.

I missed the GRE deadline so I'm gonna apply next fall, but I expect I should have a pretty good score. So with the above mentioned grades, and 3 mediocre reference letters ("he was a top student in my class but I don't know much about the guy"), what sort of school should I be shooting for? I hope to be able to continue some independent studies this summer (if I manage to land a job somewhere around here) with a professor on topics in analysis & geometry, so it's possible that I could get at least one interesting letter.

If anyone read this far, I'd appreciate some advice. I'm probably gonna go talk with a professor about this same issue to see what he has to say.

Thanks