The Bryn Mawr-Spelman Summer Mathematics Program is a six-week summer research program for freshman and sophomore women from Bryn Mawr, Spelman, and area colleges, with the goal of identifying and encouraging talented women to pursue careers in the mathematical sciences. The program would build on and be modeled after a "pre-REU" program that has taken place at Bryn Mawr for the past three summers and would complement the Scholars in Mathematics Program at Spelman. Eight students would conduct research whose primary focus is experimentation and exploration using the computer; they would be aided by alumnae mentors who are just beginning graduate programs in the mathematical sciences. Other features of the program include weekly roundtable discussions on issues in mathematics research and teaching, employment as teaching assistants in the students' respective departments during the academic year, travel to a national AMS-MAA meeting, encouragement to participate in an REU or summer internship program the following summer, and mentoring and advice regarding the decision to attend graduate school as well as the choice of an appropriate graduate program. The Summer Program will be held for the next two years on the campus of Spelman College. The program builds on and complements existing undergraduate programs at both Bryn Mawr and Spelman Colleges and enhances an exchange program between the colleges that began in 1984. It is anticipated that this program would serve as a model for other early intervention and exchange programs at the undergraduate level.