SCUDEM (SIMIODE Challenge Using Differential Equations Modeling)
A team-based mathematical modeling competition in which groups of three students use differential equations to model a real-world problem in physics/engineering, chemistry/life sciences, or social sciences, culminating in a 10-minute video presentation reviewed by judges.
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International Mathematical Modeling Challenge (IM2C)
An international team competition in which high school students spend five consecutive days applying mathematics to analyze and solve an open-ended real-world problem and submit a written solution report; in the USA, participation is by invitation based on performance in COMAP's HiMCM/MidMCM contests.
MIT PRIMES-USA
A free, year-long remote mentored research program from MIT's math department in which high school juniors and sophomores from outside the Boston area work on original, unsolved math problems with guidance from MIT researchers.
International Invitational Math Optimization Challenge (IIMOC)
A free, virtual international team competition in which high school and college students tackle algorithmic optimization problems over a multi-week window, submitting solutions to a leaderboard for ranking — introducing techniques used in operations research and computer science.
Bay Area BioGENEius Challenge (Applied Math Track)
A high-level research competition. Winning projects often use bioinformatics (statistical analysis of genetic data).
Bay Area Mathematical Olympiad (BAMO)
A proof-based math competition (4-hour, 5-question exam) for students in two divisions, proctored in person at schools and math circles, run by MSRI/Berkeley Math Circle.
Data Science Institute Summer Lab (University of Chicago)
A paid eight-week summer research program in which Chicago-area high school students are paired with a UChicago Data Science Institute mentor to conduct applied data-science research across domains such as public policy, climate, and biomedicine.