<p>I am currently taking Analysis II, PDEs, and Stochastic Processes, Modern Physics, and Intermediate Mechanics. Next semester I plan to take Abstract Algebra, Grad Linear Algebra, Topology, and Grad Probability. However, my application will be in before next semester. Below are the courses I have taken and the grades I've recieved. I know I haven't taken that much math, but I changed majors late in the game. Should I even apply now or wait and take more classes and apply next year? I'm primarily interested in PDEs and mathematical physics. Thanks for your input.</p>
<p>My grades so far
1.Calc I A
2.Calc II A
3.Calc III A-
4.Linear Algebra A
5.Differential Equations A-
6.Probability B
7.Programming and Computing A
8.Number Theory A
9.Numerical Methods B+
10.Graph Theory A
11. Mathematical Analysis I A</p>
<p>Physics
Mechanics A
Electricity and Magnetism A</p>
<p>You are good to apply to App Math. I suggest to take Complex Analysis, Galois Theory and/or Math Logic for the next semester, instead of those grad courses, if you want to do the theory.</p>
<p>I think your schedule for this year is good as it is. Topology, advanced linear algebra and abstract algebra are all essential topics, which you should definitely see before you get to graduate school. Logic is a rather esoteric topic within mathematics and galois theory might be too advanced without a background in abstract algebra. Complex analysis would be useful and it is certainly relevant to mathematical physics and harmonic analysis, but don’t worry if it’s not offered or does not fit into your schedule.</p>
<p>I think whether you apply depends on what your goals are. Do you just want to get a Ph.D. somewhere, or do you want to get into a top-20 program? </p>
<p>Also, I think we need more information on things like:
*What did you score on the GRE Math? (I’m assuming you’ve taken it already since you’re thinking about applying.)
*What kind of research experience do you have? (REU, thesis, etc.)
*What do you want to research? (If you’re doing Mathematical Physics, you’ll be considered very prepared. If you want to research Analytic Number Theory though, you might not have the same preparation).</p>
<p>If you just want to get into any program, then I’d say you’re good to go. You’ll have the solid foundation you need to go to grad school.</p>
<p>If you want to get into a top-20 program, however, I definitely recommend you stay. You really need to have 2 semesters of Algebra, 2 semesters of real analysis, complex analysis, topology, and differential geometry as a <em>foundation</em>, as well as a handfull of graduate-level courses like Algebraic or Analytic Number Theory, Algebraic Topology, 2nd-semester Complex Analysis, Representation Theory, Functional Analysis, Measure Theory, Dynamical Systems, … the list goes on. The classes like that that you’d take sort of depend on research interests. The extra year would also give you a chance to get more research in, which is critical for these programs.</p>