I've been considering graduate school in math. I go to a small liberal arts school with no math reputation, but a recent graduate got into Ohio State University for statistics. I have a lot of research experience in physics/chemistry/biology making mathematical models, and I'm just beginning to partake in topology and differential geometry research for my senior thesis with a professor. I sit around all day and study manifolds and I freaking love it. I'm a math/chemistry major with a 4.0, junior year in school. I will graduate with calc I-III, linear algebra, ODE, complex variables, tensor analysis, statistics, probability theory, and abstract algebra. My school doesn't offer graduate level courses, so that's out of the question. I also missed number theory. I REALLY enjoy research in topology/geometry so I plan to apply to a math REU this summer (I've had 2 REUs in biophysics so far). Am I too late in deciding I like math research to pursue a competitive mathematics PhD program? What do these programs usually require?