TITLE: What are some research problems that fit as a good candidate for undergraduate research?
QUESTION [7 upvotes]: 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.

REPLY [3 votes]: I know this is not what you want to hear, but when I was in school the following recipe worked for me:

Find an interesting open problem. (One of these worked for me http://www.math.ucsd.edu/~erdosproblems/)
Find a recent survey on the problem. Read it.
Get the papers referenced by the survey, read them.

You'll have the rest of your life to look at the problem if you still care, and in the meantime you will have started learning how to read research level math.