Beginning in the summers of l989 and l990, Boston University will sponsor an intensive six week program in mathematics for ambitious high school students. The students will be advised by l2 mathematically experienced counselors and l0 faculty. The heart of the program is the experience gained by students through their efforts to solve problems in Number Theory and Algebra. To assist them in these efforts, the program provides several sources of aid (beyond the daily lecture). Five problem sessions, directed by senior mathematicians, will meet three times per week in groups of about l0 students. Each student will be supervised by a counselor in residence who is always available to answer questions. The coursework will be supplemented by diverse weekly lectures by faculty preceptors. Students will be assigned a faculty preceptor who will be on hand to offer career guidance and mathematical stimulation throughout the summer.