Help in switching from physics to math

[quasar_4]

So, as I kind of expected, after not studying much for the physics subject GRE I did very badly, ~20th percentile. I'm still applying to some schools, but with limited hope. I now have to decide - I can do a year-long MS in physics or math, then retake the subject GRE. I'm thinking about changing to math (not sure yet), because I'm slightly better at it, but have some questions:

1) will it hurt to have bombed the physics GRE if I do okay on the math GRE in a year? or, since it was physics, will it not really matter at all?
2) how different is mathematical physics for a mathematician than it is for a physicist? I was planning to to gravitational physics, but it's specifically the math in GR that excites and drives me, so I am pretty sure I'd be happy doing math. But I'm not sure how different the emphasis is, and also, all my research has been more from the physics side, so I'm not sure what research in math is like or if I'd be good at it. I think I can handle math classes; I have taken some graduate math classes as an undergrad and immensely enjoyed them.

And also, I don't need any responses telling me to give up because I'm not smart enough. There is a tendency for people to do that on these forums. I am quite smart enough, just didn't spend the time necessary to prepare. (And I hadn't taken several core classes when I took the physics GRE, so I think that's part of the score as well).

 

[rodigee]

A few questions for you! What kind of math have you taken? And what kind of math are you interested in? (I don't know much... well hardly any physics so "math in GR" means nothing to me ;) )

 

[quasar_4]

Let's see, in terms of upper div. courses (you know, past all the requirements for calculus, linear algebra, ODEs, etc.), I have had:

Undergraduate level -

Differential Geometry - A
Abstract Algebra- A
Modern Algebra (Groups + Galois theory) - A
Linear Algebra - A
Intro. Analysis - B
Real Analysis I - still waiting, but I think an A- or B+.

Graduate level -

Differential Geometry - taking this spring
Multilinear Algebra and Representation Theory - A

I also got an A in a physics class this semester called "Methods of Theoretical Physics" - we covered come topics from complex analysis including Cauchy's integral formula and contour integrals, ODE's (solutions with power series, Green's functions, etc.), PDE's (method of characteristics, sep. of variables, etc.), more linear algebra, special functions (Bessel, Legendre, Hermite, etc.), so at this point I feel like I've been exposed to a lot.

Except Topology, because it hasn't been offered at my school since I declared myself as a math major!

I REALLY love differential geometry and algebra. Basically, linear/abstract algebra and group theory are wonderful, and they appear everywhere. Linear algebra is also a foundation of differential geometry, so maybe that is why I like geometry so much. I love how it relates to things in physics, especially in general relativity (this is what I meant by GR!). I will say that I didn't much enjoy doing Galois theory problems, but the theory is interesting. And we didn't cover much representation theory in my one class (only made it a small way into Fulton & Harris's book, but it was interesting too).