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While undergraduates in just about any field do not know everything there is to know about any particular area, there is a long ways to go before you know enough to really publish Doctoral-level research (and that is the way it should be, otherwise everyone would get a Ph.D.), I do believe a reasonable amount of research can be conducted by undergraduates.
Research is new information, or possibly old information rehashed, for the researcher it is new and that is what makes it research - I believe. Book reports are not research and neither are surveys of literature, unless I guess you are studying history and some sort of comparative study was being done on existing literature.
I took a Linear Algebra class at another institution that I can completely bored in, I had already taken Modern Algebra and I tutor mathematics, so the material they covered wasn't new to me. BUT, I went to class anyways, and I did miss a lot. Final grade: 99/100 in the course. Some students can do that, not go to class and understand the material. But I'm also getting ready to apply to graduate school and, after doing summer research at other institutions, realize and understand the importance of letters of recommendation and impressing professors.
Somewhere down the line you need people to speak about how dependable you are and how smart you are. If you answer questions in class right all the time, a professor that really cares might recommend for you to go to XYZ summer program or program on campus and become your research mentor, as was my case.
I could have blown off Calculus 2 or 3, Differential Equations, Modern Algebra, or any other course I've taken within the past 3 years. But, and I have classes of less than 10 students, professors really do pay attention to that and take that into consideration when writing letters of recommendation and when you ask them to do research with you.
New professors might be the best bet for you, it might be the way you might want to go. But the way professors see it, if you don't show up to class now, and seeing as past behavior is a good prediction of future behavior, will you show up to research meetings or, later on, your graduate classes?
In math, you have to work hard to find new proofs, or even to prove things that have already been proven to show you have some proofing ability. But, put yourself in your professors shoes, if that new professor asks one of your current professors how you are in class, what do you think the answer will be?
- Vanes.