There are a lot of different kinds of mathematical experiences students can have over the summer. Many students engage in research either on- or off-campus, others attend programs where they essentially take classes, and a few find internships that have a mathematical sciences flavor.
Research Experience for Undergraduates: Many colleges and universities have REU programs sponsored by the National Science Foundation. Students get paid to spend 6-10 weeks working on a research project given to them by the faculty participating in the REU. Usually students spend a couple of weeks at the beginning of the program learning their topic area, then work in groups on the research. Some REU programs are designed for rising seniors who are very serious mathematics students, while others are designed for rising juniors and even younger students who do not yet have a lot of mathematics courses under their belts. Unfortunately, you'll need to wade through a lot of links to find the right program for you.
- NSF Sponsored REUs: This is a list of schools currently receiving funding for REU programs from the NSF.
Research at St. Olaf: There is some funding for students to stay on the hill and work with St. Olaf faculty over the summer. Similar to the REUs described above, students get paid to spend 10 weeks working on a research problem in mathematics, statistics, or computer science. The formal process for obtaining one of these positions is under reconstruction, so ask a professor or the chair of MSCS if you want to know more about doing research on campus. You can also dig around the Collaborative Undergraduate Research and Inquiry (CURI) website for summer research information.
Other Summer Programs
- Summer Program for Women in Mathematics at Carleton College. This program is designed for rising sophomore and junior women mathematics majors. Students get paid to spend 4 weeks taking two courses.
- Summer Program for Women in Mathematics at George Washington University. This program is designed for rising junior women mathematics majors. Students get paid to spend 5 weeks taking two courses.
- Park City Mathematics Institute in Park City, Utah. This is a 7 week program involving undergraduates, graduate students, faculty, and researchers. The topic changes every summer.
Internships: This section will be appearing asap.