Below are links to various summer research programs for undergraduates. Many programs target students in the summer between their junior and senior years. Some programs are open to students following their sophomore year (with appropriate background) and a few programs specifically target students in the summer following their sophomore year.
To apply for a Summer Research Award, you will need to write a research proposal. Generally, this will involve finding a faculty member who is willing to guide your research. Many faculty members in the department have ideas for student research projects. If you are interested, start asking around.
Note that these awards are sometimes referred to as "Murdock awards" for historic reasons.
Follow the "Search for an REU Site" link. Many of the individual REU sites are not updated for the upcoming summer until early that same year. In some cases, you can figure out if the program is funded for an upcoming summer by going to the "Abstract of Award" link for the program.
Each national lab has student internship programs, some of which include mathematics or computer science. In particular, the Pacific Northwest National Lab has SulI internships that are open to mathematics and computer science students.
The MAA Undergraduates page has links to research opportunities along with information on undergraduate MAA membership.
The AMS undergraduate page is a good resource for information about graduate work and careers in mathematics in addition to having some information on summer research opportunities.
This page was last updated January 15, 2012.