The National Science Foundation makes possible a number of opportunities for undergraduates to join research projects each summer. This allows students to experience first-hand how basic research is done, and to contribute consequentially.
This is a nicely presented page of some of the sites which held REU programs during the summer of 1998. Most of them will have similar programs this summer. This is a good place to start your search.
Lists all of the NSF Research for Undergraduate Education (REU) programs in all of the sciences. Many of the listings are for the summer of 1998, but most of these programs will be available this summer as well. You don't have to major in a particular field to attend an REU summer program in that field.
MORE UNDERGRADUATE RESEARCH PROGRAMS IN MATHEMATICS:
The Math Forum hosts a growing database of announcements for undergraduate math research programs, including:
Summer 1995 -- Carnegie Mellon University summer program
" I had an internship in the Minnesota Supercomputer Institute of the University of Minnesota in the summer of 1996. This internship program accepts students for a variety of projects in computing, math, chemistry and several other areas. Many projects deal with mathematical models or other areas of applied math. In this internship, I had a chance to participate in actual research. The project that I worked in was application of fractals to geophysics. It was very interesting and I learned a lot that summer. If you are interested in information regarding this program, my e-mail is email@example.com."Elizaveta has continued to work with the Minnesota SuperComputer institute during this fall semester. She can connect to the institute from the U of R campus, and has been flown out to Minnesota for consultation. Information on the summer institute for 1997 is available at http://www2.msi.umn.edu/Programs/uip/uip.html