I am not necessarily endorsing any programs that's listed. I am simply give a helping hand by listing the possible outlets for mathematically/scientifically inclined students.
Awesome Math — A program designed for students ages 12 to 17 with the mission of providing a fun, intellectually stimulating environment to learn math, inspiring a love of mathematics and learning that lasts into college and beyond. It helps students significantly improve their performance in mathematics competitions and makes mathematics itself and the entire camp experience highly enjoyable.
Berkeley Math Circle — The Berkeley Math Circle (BMC) is a weekly program for over 100 San Francisco Bay Area high and middle school students. The program is jointly sponsored by the UC Berkeley Math Department, the Mosse Foundation For Arts and Education through the Mathematical Sciences Research Insitute (MSRI), and Parents' Contributions.
COSMOS — COSMOS is a four-week residential program for talented and motivated students completing grades eight through twelve. Students work side-by-side with outstanding university researchers and faculty exploring advanced topics that extend beyond the typical high school curriculum. COSMOS courses are hands-on and lab intensive emphasizing current research underway at the University of California.
EPGY — The Education Program for Gifted Youth (EPGY) at Stanford University is a continuing project dedicated to developing and offering multimedia computer-based distance-learning courses.
Idea Math — The IDEA MATH program has been created to help talented students who want to advance their problem solving skills, both to expand their mathematical horizons, and to maximize their performance in math competitions.
Math Zoom — Summer Program for Bright and Motivated Youth.
PROMYS — PROMYS is a six-week summer program at Boston University designed to encourage motivated high school students to explore the creative world of mathematics in a supportive community of peers, counselors, research mathematicians, and visiting scientists.
San Jose Math Circle — The San Jose Math Circle (SJMC) is a weekly math meeting for middle school and high school students. Over 30 students come each week and are presented with difficult, original and always fun mathematical puzzles.
Stanford Math Circle — See description for San Jose Math Circle.