American Mathematical Society Summer Math Camps & Programs:
www.ams.org/programs/high-school
Summer programs that help students explore the world of mathematics research (most are residential programs accepting applications nationwide).
Cornell University CATALYST Academy https://sites.coecis.cornell.edu/catalystacademy/
A one-week summer residential engineering program for rising high school sophomores, juniors, and seniors.
Cornell University CURIE Academy (girls only) https://sites.coecis.cornell.edu/curieacademy/
A one-week summer residential program for high school girls who excel in math and science. The focus is on juniors and seniors who may not have had prior opportunities to explore engineering, but want to learn more about the many opportunities in engineering in an interactive atmosphere.
Hampshire College - Summer studies in mathematics www.hcssim.org An intensive six-week encounter with college-level mathematics for talented and highly motivated high school students.. Located at Hampshire College, Amherst, MA
Math Camp at Puget Sound www.mathcamp.org
Canada/USA Mathcamp is an intensive 5-week-long summer program for mathematically talented high school students, designed to expose these students to the beauty of advanced mathematical ideas and to new ways of thinking.
Program in Mathematics for Young Scientists (PROMYS) at Boston University www.promys.org
PROMYS is a six-week summer program at Boston University designed to encourage strongly motivated high school students to explore in depth the creative world of mathematics in a supportive community of peers, counselors, research mathematicians, and visiting scientists.
Admission is rolling. Cost is ar0und $2,700 and need-based aid is available.
Rose Mathematics Program at Ohio State www.math.osu.edu/ross
Students to explore math, a six week summer program at the Ohio State University in Columbus, OH.
Cost is around $2,200, with some scholarship money available.
Stanford University Mathematics Camp https://spcs.stanford.edu/programs/stanford-university-mathematics-camp-sumac
Four weeks of serious mathematical pursuits.
Financial aid is available.
Young Scholars Program in Discrete Mathematics at Rutgers www.dimacs.rutgers.edu/ysp Selected students participate in an intensive four-week residential academic program that provides a challenging introduction to discrete mathematics