What exactly constitutes "math research"? I'm an incoming second-year, majoring in pure math, and I'm trying to get involved in research this upcoming Fall. I recently asked my advisor and he said the only option during the school year would be an Independent Study, where you have a faculty sponsor/supervisor, and it will basically be a self-paced reading course. Would you consider this "research", or "research with a professor"? Isn't it basically the same as a standard course, with the exception of the self-pacing? I'm doing an REU next summer, but as far as research during the school year, the only option is the Independent Study. So I'm considering either the Independent Study or a grad course (maybe PDEs), in addition to 3 grad courses as my Fall schedule. Which would you guys recommend? I'll have plenty of grad courses by the time I graduate, and having an Independent Study could potentially help my research aspect. But would you really consider it "research"? Maybe I could try producing a paper/project by the end.