During my high school career, I had the unique opportunity to take multiple mathematics courses at my local university, and after graduating, I took two graduate level math courses: Measure theory, and a class on topological manifolds. This was a great experience, but it has left me in a shifty situation.
I asked the department head if I could be admitted into the program since I took a full time course load receiving a B+ and A respectively, but it was denied due to the fact that I did not have a bachelors. The only option given to me at this university would be to enroll in the undergraduate program and take graduate courses.
I would be open to that idea, but it has multiple pitfalls. First of all, I am not guaranteed any research opportunities, which view as highly restrictive on my growth as a mathematician. In addition, I am not guaranteed funding opportunities like I would be in the graduate school. This in combination with the fact that I would have to take 50% more credit hours of course work would mean I would end up having to take out more loans than I would like. This is all very disappointing for me.
Instead of enrolling in courses again, this semester I began independent study in algebra and differential topology using Aluffi's and Lee's book respectively on the subjects. In addition, I have been exposing myself to more theoretical physics, such as Yang-Mills theories and Supersymmetry. Because these subjects are capturing my interest as well, it seems natural that I take my studies towards Algebraic Geometry and String Theories. I really want to get involved with a program to help enable me with my studies, but I do not think an undergraduate program would be adequate. For those of you who are still reading, how can I work towards getting into a program which would enable my studies an empower me with supervised research?
I did not think my undergraduate work would to be too relevant, since most of it was not rigorous; that is, calculation based. I took undergraduate courses in ODE's, PDE's, probability theory, analysis, mulitvariable calculus, and linear algebra. Unfortunately, I did not do well in the ODE, calculus, and linear algebra courses because they were during the summer, and I had not yet acclimated to the required amount of work. In this specific program, my course work is nearly equivalent to a bachelors degree, sans single variable calculus and a class in discrete math.