I'd like to ask any seasoned math researchers, professors, and/or students to share some appropriate ideas for independent research a recent college graduate (but not yet a grad student) could do, so as to stay in the habit of participating in academia outside of campus. I could even specify the topics within mathematics.
Though the question is specific enough for MSE users to answer, there would be an inherent level of opinion in each response. Furthermore, one might argue that this question would belong on Academia.SE; on the other hand, one could also argue that the question would get more exposure being on a site where the main focus is Mathematics (you know, MSE).
Would such a question be on-topic?