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 can also be 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 students.
Two main ways to get involved in undergraduate mathematics research are working with a mathematics faculty member or participating in an REU, (research experience for undergraduates) summer program.
Working with a Faculty Member
For students who would like to work with a specific faculty member, the best way to do this is just to ask the faculty member that you would like to work with about conducting math research. This could be a past teacher or someone who works in a field in which you may have an interest. Most professors will be happy to mentor you if they have the free time, and if not, to give you suggestions about who might.
Another option is to contact Professor Jonathan Pakianathan, chair of the Undergraduate Research Committee. He’ll 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.
While there are no set prerequisites for assisting with research it is best if students have completed a calculus sequence and a 200-level proof based course first.
Summer research opportunities for undergraduates are available all around the country. These programs are usually 8-10 weeks long, and usually pay for living expenses and a little more. An excellent place to see what is available is on the American Mathematical Society (AMS) website. Students should apply early as most REU application deadlines are in February and March. 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.
REU at University of Rochester
Each summer at UR we have a mathematically focused REU coordinated by Professor Alex Iosevich in partnership with the Data Science program, namely the TRIPODS NSF and Stem-For-All programs. This year's program will focus on neural networks. For more information, see the program page here: TRIPODS/STEM-FOR-ALL PROGRAM PAGE.
The following MathOverflow responses can help give you an idea of what to expect from math research as an undergraduate.
Here are some links with detailed information: