I have no research experience and I'm in my junior year of college. I'm very interested in doing research in any field at this point (combinatorics or linear algebra would be especially preferred) and I fully intend to apply for math grad school during my senior year.
I have a decent amount of coursework (abstract algebra [groups, rings, fields and special topics], analysis [real, complex, functional, measures], linear algebra, topology, combinatorics, number theory, partial differential equations, and more). I want to do research this summer (even without funding if need be) and throughout my senior year (I was declined to every REU that I applied for, unfortunately) and I plan to work alone since I have no other options (that I know of).
There aren't any student projects going on at my own college (except for one on wheels) and my professors (5 total though one is leaving and another will be on sabbatical) only seem willing to help if I provide a research topic and if that topic is related to their own expertise (I don't fit in this category) which means that I've had no help so far. I don't know where to look since most journals and blogs seem to be deeply invested into very complicated projects where my ability is likely not high enough to understand. There is no graduate program at my college so there are no grad students.
My questions is this: Where can I find potential research projects or at least a start? How does one decide on what they want to do? I know people from other colleges but they were simply given projects to work on so they didn't know how to find on otherwise.