The Williams College SMALL REU Program

威廉姆斯学院小型 REU 项目

• 批准号: 1947438
• 负责人: Steven Miller
• 金额: $ 41.61万
• 依托单位: Williams College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1947438&HistoricalAwards=false
• 关键词: Williams; College; SMALL; REU; Program

In the Williams College SMALL REU program, for ten weeks each summer (nine in residence at Williams and one at home), 25 to 40 undergraduates work on research projects under the direction of a faculty member in mathematics or statistics. There are usually between 4 and 7 groups each summer of various sizes. The summer culminates with presentations (at Williams and often at conferences), and most groups write up their work for submission to a research journal. There are weekly talks by faculty and students, both in mathematics and in related fields. Students are part of a vibrant scientific community; over 100 students do original research in mathematics and the sciences at Williams each summer, and there are a variety of academic and social activities bringing all the summer students and faculty together. Now in its fourth decade, participants are connected with alumni of the program who are able to provide excellent perspective, advice, and mentorship. The goal of this REU is to introduce undergraduates to the excitement and challenge of doing original research in mathematics. Topics will be drawn from a variety of fields. Possible areas include algebraic geometry, Bayesian statistics, combinatorics, commutative algebra, computational geometry, CR structures, discrete geometry, dynamics and ergodic theory, graph theory, hyperbolic manifolds, knot theory, mathematical biology, mathematical physics, measure theory, minimal surfaces, number theory, probability, random matrix theory, representation theory, Riemannian geometry, symmetry groups, and tropical geometry. In the process, students learn lots of background material. They typically work in groups, meeting with advisors as needed, and are encouraged to present as well as publish their work, all valuable skills for graduate school as well as non-academic pursuits. A variety of mathematical activities and topics provides a rich intellectual environment; students live together and are constantly discussing their work, and attend weekly talks by the faculty so they learn the basics of all the different areas being investigated that summer. Our nation needs a wider appreciation and understanding of mathematics, and cannot afford to leave anyone out. We have increased the numbers of students from traditionally under-represented groups participating in the program over the last five years, as well as from community college backgrounds, and we are continuing to look for new and better ways to encourage applications from women, minorities, first generation college students, and other underrepresented groups. Students, faculty and the broader mathematics community will benefit from the presentation and publication of original research. Students will develop a lifetime network of peers and mentors, and many of them will pursue graduate studies, partially because of their REU experience. Almost all students publish papers in research journals and many present their results at national and international research conferences.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.

在威廉姆斯学院小REU计划，每年夏天十周（九个在威廉姆斯居住，一个在家里），25至40名本科生在数学或统计学教员的指导下从事研究项目。每年夏天通常有4到7个不同大小的团体。夏天的高潮是演讲（在威廉姆斯和经常在会议上），大多数小组都把他们的工作写下来提交给研究期刊。教师和学生每周都有数学和相关领域的讲座。学生是一个充满活力的科学社区的一部分;超过100名学生做数学和科学的原创研究在威廉姆斯每年夏天，有各种各样的学术和社会活动，使所有的暑期学生和教师在一起。现在在其第四个十年，参与者与该计划的校友谁能够提供优秀的观点，建议和指导连接。这个REU的目标是向本科生介绍数学原创研究的兴奋和挑战。主题将来自各个领域。可能的领域包括代数几何、贝叶斯统计、组合数学、交换代数、计算几何、CR结构、离散几何、动力学和遍历理论、图论、双曲流形、纽结理论、数学生物学、数学物理、测度论、极小曲面、数论、概率、随机矩阵理论、表示论、黎曼几何、对称群和热带几何。在这个过程中，学生们学习了大量的背景材料。他们通常以小组形式工作，根据需要与顾问会面，并鼓励他们展示和发表自己的作品，这些都是研究生院和非学术追求的宝贵技能。各种数学活动和主题提供了丰富的智力环境;学生住在一起，并不断讨论他们的工作，并参加教师的每周谈话，使他们学习的所有不同领域的基础知识正在调查的那个夏天。 我们的国家需要更广泛地欣赏和理解数学，不能遗漏任何人。 在过去的五年里，我们增加了来自传统上代表性不足的群体以及社区大学背景的学生人数，我们正在继续寻找新的更好的方法来鼓励女性，少数民族，第一代大学生和其他代表性不足的群体申请。 学生，教师和更广泛的数学界将受益于原创研究的介绍和出版。学生将发展一个终身网络的同龄人和导师，他们中的许多人将继续研究生学习，部分原因是他们的REU经验。几乎所有的学生都在研究期刊上发表论文，许多学生在国家和国际研究会议上展示他们的成果。该奖项反映了NSF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。

项目成果

Constructions of generalized MSTD sets in higher dimensions

高维广义 MSTD 集的构造

• DOI: 10.1016/j.jnt.2021.03.029
• 发表时间: 2022
• 期刊: Journal of Number Theory
• 影响因子: 0.7
• 作者: Kim, Elena;Miller, Steven J.
• 通讯作者: Miller, Steven J.

Completeness of Positive Linear Recurrence Sequences

正线性递归序列的完备性

• 发表时间: 2023
• 期刊: Combinatorial and Additive Number Theory V
• 作者: Ela Boldyriew, John Haviland

Limiting Spectral Distributions of Families of Block Matrix Ensembles

块矩阵系综族的极限谱分布

• 发表时间: 2023
• 期刊: PUMP journal of undergraduate research
• 作者: Teresa Dunn, Henry Fleischmann

Characterization of completions of noncatenary local domains and noncatenary local UFDs

非接触网本地域和非接触网本地 UFD 的完井特征

• DOI: 10.1016/j.jalgebra.2018.12.016
• 发表时间: 2019
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Avery, Chloe I.;Booms, Caitlyn;Kostolansky, Timothy M.;Loepp, S.;Semendinger, Alex
• 通讯作者: Semendinger, Alex

Distinct Angle Problems and Variants

不同角度问题及其变体

• DOI: 10.1007/s00454-022-00466-w
• 发表时间: 2023
• 期刊: Discrete & Computational Geometry
• 影响因子: 0.8
• 作者: Fleischmann, Henry L.;Hu, Hongyi B.;Jackson, Faye;Miller, Steven J.;Palsson, Eyvindur A.;Pesikoff, Ethan;Wolf, Charles
• 通讯作者: Wolf, Charles