I'm in my junior year in college and I hope thag I can do some original research in while being in college. Sadly, my departement is not large and most professors are elements of one of the following types:
1.They are available but they have not done research for a long time.
- They are doing good research but either they don't come much to the uni or have a view against undergraduate research.
So it seems that it would be difficult to get involved in research with some faculty member in my college. Nevertheless, I want to do some research.
I'd be satisifed if the problems are in any topic: algebra, analysis, combinatorics, graph theory, logic etc ...
More Importantly, I have the interest and passion to study and work through the required background if I don't fully have it as long as I find an interesting problem that I worlk work on.
It would be even better if you think that the problem is suited to undergraduate research.
I know that it is hard to indicate some problems without knowing the background of the student, but generally, as an indicatiin, you assume that the student has a good background in algebra (groups, rings, fielda, modules,universal algebra, category theory), in logic (FOL, completness, incompletness, set theory,forcing, boolean algebras) etc ...
If needed I can provide more details regarding my background in a specific area if needed.