I frequently take on undergraduate students for research projects.
My primary interest is differential equations and have found that some of the basic inverse problems are quite approachable at the advanced undergraduate level.
Math 412 or equivalent would be good background course; this together with M417 would be better, the addition of M446 would be optimal.
I have NSF funding to support students in this area during the summer and would be happy to talk to anyone with interest.
I also will take students on in the topic of mathematical cryptography. Required background here is M470.