PRIMES, MathROOTS, and CrowdMath: Expanding Opportunities for High School Students

PRIMES是马萨诸塞州理工学院为高中生开设的一个免费的、为期一年的课后研究和充实项目。它包括三个主要部分：麻省理工学院PRIMES为来自大波士顿的学生提供数学和计算机科学的研究项目; PRIMES-USA是一个针对高中三年级学生的国家数学研究计划; PRIMES Circle是波士顿地区城市公立高中学生的数学丰富部分。在与麻省理工学院招生合作，PRIMES还运行MathROOTS，一个免费的为期两周的数学丰富的住宅夏季计划，为来自代表性不足的背景或服务不足的社区的高潜力高中学生。PRIMES开发了一种基于学习和研究相结合的创新方法，允许高中生学习数学和科学的高级领域，并在一年的时间内参与尖端研究。项目由大学教师制定，并由研究生和博士后学者指导。每年有90多名学生参加PRIMES。他们在麻省理工学院的年度会议上展示他们的项目，向公众开放;他们撰写研究和临时论文，在线发布供免费访问;他们提交原创研究以在学术期刊上发表。PRIMES为有才华的高中生提供了一个独特的机会来体验数学研究的乐趣和美丽，激励他们追求数学科学的职业生涯，并通过为有前途的年轻女性和代表性不足的群体提供额外的机会来帮助数学界实现多样化。在这个项目中，PRIMES的学生将从事各种纯数学和应用数学主题的研究项目，其中包括有理函数的分支类型;曲面上曲线的统计和组合学;有限图的雅可比矩阵;拟不变量;正特征的有理Cherednik代数的表示;折叠随机行走;节点的多交叉数;交通建模，多相流和自动汽车;特征为2的超代数;跳谷不变的置换集;置换的模式置换等价。阅读小组将学习抽象代数，概率方法，阿贝尔定理，表示论，解析数论和密码学的文本。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

PRIMES is a free, year-long after-school research and enrichment program for high school students, based at the Massachusetts Institute of Technology. It includes three main sections: MIT PRIMES offers research projects in math and computer science to students from Greater Boston; PRIMES-USA is a national math research program for high school juniors; and PRIMES Circle is a math enrichment section for urban public high school students from the Boston area. In collaboration with MIT Admissions, PRIMES also runs MathROOTS, a free two-week math enrichment residential summer program for high-potential high school students from underrepresented backgrounds or underserved communities. PRIMES has developed an innovative approach, based on the combination of learning and research, which allows high school students to learn advanced areas of math and science and to participate in cutting-edge research within a year-long timeframe. Projects are formulated by university faculty and mentored by graduate students and postdoctoral scholars. Every year, more than 90 students participate in PRIMES. They present their projects at an annual conference at MIT, open to the public; they write research and expository papers, posted online for free access; and they submit original research for publication in academic journals. PRIMES gives talented high school students a unique opportunity to experience the joy and beauty of mathematical research, inspires them to pursue careers in the mathematical sciences, and helps diversify the mathematical community by providing additional opportunities for promising young women and underrepresented groups. In this project, PRIMES students will work on research projects on a variety of pure and applied mathematical topics, which include Branching types of rational functions; Statistics and combinatorics of curves on surfaces; Jacobians of finite graphs; Quasiinvariants; Representations of rational Cherednik algebras in positive characteristic; Folding random walks; Multi-crossing number for knots; Traffic modeling, multi-phase flow, and autonomous cars; Superalgebra in characteristic 2; Sets of permutations invariant under valley-hopping; and Pattern replacement equivalences of permutations. Reading groups will study texts on abstract algebra, the probabilistic method, Abel's Theorem, representation theory, analytic number theory, and cryptography. Enrichment topics will include knot theory, probability, game theory, graph theory, and combinatorics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.