Engaging in mathematical research can be a fun, intense, and rewarding experience. It is also an excellent means to reach beyond your coursework and "do mathematics."
Undergraduate students at Michigan have a variety of research options. For example, students who participate in the Department's REU program work on questions at the frontier of modern mathematics, and the Inquiry Based Learning course Explorations in Mathematics (MATH 389) provides students with a gentle introduction to mathematical research.
Additionally, the Undergraduate Research Opportunity Program (UROP) creates research partnerships between undergraduate students and University of Michigan researchers. All schools and colleges are active participants in UROP, which provides a wealth of interesting research topics for program participants.