Participating in an undergraduate research project can be a wonderful opportunity for any mathematics major. It is a great way to learn new mathematics, to experience the joy of discovery, and to see what it is like to be a research mathematician. It is also important for getting into a good graduate program in mathematics.
To get a sense of some of the possibilities, see some samples of research reports by past University of Rochester students.
Two main ways to get involved in undergraduate mathematics research are:
- Work with a Mathematics Department faculty member. Simply knock on the door of a faculty member or email them, and ask them about conducting math research. This could be a past teacher or someone who works in a field in which you may have an interest. Alternatively, you may contact Professor Gonek, chair of the Undergraduate Research Committee, at email@example.com. He will arrange a meeting with you to discuss your interests and background, and then try to find an appropriate faculty member with whom you can work. Although there are no hard and fast rules, it would be best to have first taken MTH 161, 162, 163 (or 165), and 164, as well as a proof based course at the 200 level. Alternatively, MTH 171-174 will do.
- Participate in one of the many REU (Research Experience for Undergraduates) summer programs across the country. Many of these are 8-10 weeks long and give students a stipend. An excellent place to see what is available is on the website of the American Mathematical Society (AMS): http://www.ams.org/programs/students/undergrad/emp-reu
Important note: Most REU application deadlines are in February and March. Also, programs funded by the NSF generally require students to be US citizens or permanent residents, though they sometimes have extra funding to support a few non-US citizens.