Should I stay and complete a physics degree on top of my math degree?

[James Wine]

My situation is different than most people who come to this board; I think anyways. I'm currently in my 4th year of school and can complete my mathematics degree next May. I can also choose to stay one more year and complete a physics degree on top of the math degree.

However here's where I introduce the reasons why I'm stuck on my decision.

1. I'm a 9th grade high school drop out, aka I didn't learn math really until I started college after working long painful nights in a warehouse. Also when I did start I wasn't the best student so my GPA suffers from my first few semesters, but all my upper division classes are A's and a few scattered B's however there is a notice-able paradigm shift after I took Calc II where my grades went up. So my math skills are "scattered" at best. I started out in Algebra I. Now if it's stochastic processes or real/complex analysis I have a firm grip on that. However abstract algebra on the other hand I haven't taken the formal class on it and am reviewing it over the summer. Although I did score on the Putnam this year(10 made me very happy, proofs were bad for the other 3 I had "correct" answers for).

2. As of right now I have no publications, but I do have 3 research projects going on with some of my professors in the following areas; univalent functions, fractals in nonlinear dynamics, and numerical methods for SDEs. If I stay I have a reasonable shot at getting published while I finish up some my remaining physics classes(semi-light load they gave me a break on theoretical mechanics since I essentially have my math degree already).

3. I'd like to go to graduate school doing some kind of cross-departmental research in mathematical physics, and having upper division classes besides statistical mechanics(took it at the same time as Calc-Physics II that was an experience) would probably be beneficial in that environment.

4. If I do decide to take the route of graduating this year I need to start preping for my GREs now before I actually take a class on abstract algebra or topology.

5. I have strong recommendations from the professors I do research with, my study partners graduated this semester and are going to Stanford,Georgia Tech, and NYU on full rides. Our school is not ranked for mathematics but is for physics(low but I believe it's ranked, and if not it should be).

I'm taking these comments very seriously so please answer wholeheartedly

 

[micromass]

If I were you I would stay another year. I notice from your post that this is also what you want.

Topology and abstract algebra are too important not to have seen, so take the classes. Complete the physics degree and get published. You'll have a far better chance at grad school with these things!