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

PRIMES是一个免费的、为期一年的高中生课后研究和充实项目，总部设在麻省理工学院。它包括三个主要部分：MIT PRIMES为来自大波士顿地区的学生提供数学和计算机科学的研究项目；prime - usa是一项面向初中生的国家级数学研究项目；prime Circle则是为波士顿地区的城市公立高中学生开设的数学充实课程。PRIMES还与麻省理工学院招生局（MIT Admissions）合作，为来自代表性不足的背景或服务欠缺的社区的高潜力高中生提供为期两周的免费数学丰富住宿暑期项目MathROOTS。PRIMES开发了一种基于学习和研究相结合的创新方法，使高中生能够在一年的时间内学习先进的数学和科学领域，并参与前沿研究。项目由大学教师制定，研究生和博士后学者指导。每年有超过90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；他们撰写研究和说明性论文，在网上免费发布；他们提交原创研究成果在学术期刊上发表。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，帮助数学界多元化。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，包括有理函数的分支类型；曲面上曲线的统计学与组合学；有限图的雅可比矩阵；Quasiinvariants;有理Cherednik代数的正特征表示折叠随机漫步；结的多次交叉数；交通建模、多相流和自动驾驶汽车；特征2中的超代数；跳谷条件下的排列不变量集和排列的模式替换等价。阅读小组将学习有关抽象代数、概率方法、阿贝尔定理、表示理论、解析数论和密码学的文本。丰富的主题将包括结理论、概率论、博弈论、图论和组合学。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.