You say:

"I am a junior at the moment and taking: One Dimensional Real Analysis, Intro to Numerical Methods, and Abstract Algebra".

Based on this information, I think it is a complete waste of your time even to consider research seriously at this stage; you need several more years of study as a minimum. Right now, you are still learning the basic language of mathematics. It's similar to, say, a student who wants to begin reading classical German literature, but only knows 100 words -- premature, to say the least. The maths you know right now is probably less than 1% of what you will need. Even after my Ph.D., I feel that my knowledge is very limited in comparison to most good researchers.

But do you really mean "research", i.e. new, original, nontrivial and interesting, and publishable in a good quality journal, i.e. one which your professors would publish in?

Or do you mean a kind of "investigation" or "project" instead? These are not required or expected to contain anything new or original. This would be highly worthwhile -- but only for your personal interest and satisfaction.

The question is, what do you expect to get out of it? If you're at a good university, their lecture courses should already provide you with all you need.

Please don't take offense, and apologies if I've formed the wrong impression, but it sounds to me (from your statement "I have begun speaking with professors about their research also") like you might be the kind of student that irritates professors, always bugging them and asking them questions about their own research, but lacking the knowledge to understand the answers. (But it's not your fault you lack knowledge - that's what you're at university to learn!) As an analogy, imagine a ten-year-old, knowing nothing more than how to add fractions, constantly harrassing you to teach them about calculus; my response (unless I were in a very good mood that day) would be: "go back to school and stop bothering me, for at least another 3 years!" Unless you're an exceptionally good, enthusiastic student, or your professors are far more patient than me, that might be what they're thinking also, but are too polite to tell you.

But just my opinion, don't take my word for it; why don't you ask them directly if that's what they're thinking?!