I just need the research to get into graduate school (Phd program) in math, because my school is not even on the map (it doesn't even have a college profile on USNews). I only have the minimum math classes I can take (because my school doesn't offer many upper-level or advanced math courses), and then there's the math subject GRE which I should obviously aim for a perfect score. But considering that's all I have, I don't think it will land me into the school of my choice, so I think research is my only advantage here. Will it matter if my research is performed in a field other than the branch of math I apply to? (e.g., if I apply to a geometry PhD program, and my research has absolutely nothing to do with geometry or math.)
I'm staying within REUs because I have no money to travel anywhere. I live at my school (and my school doesn't have any dormitories, mind you) so it'd be difficult to travel anywhere out of town without funding from an REU program.
Transferring to another school is not an option because schools want the tuition paid before the beginning of the semester, and I don't have any credit to take out a bank loan. Since there is a maximum amount of government loans I can take out, it doesn't cover the tuition so I wouldn't be allowed to attend the school. I have a full scholarship at my current institution which is the only reason I am here.