REU Site: Algebra, Combinatorics, and Statistics

REU 网站：代数、组合学和统计学

• 批准号: 2150205
• 负责人: Yong Yang
• 金额: $ 30.54万
• 依托单位: Texas State University - San Marcos
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-03-01 至 2025-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2150205&HistoricalAwards=false
• 关键词: REU; Site; Algebra; Combinatorics; Statistics

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The Department of Mathematics at the Texas State University at San Marcos will host an eight-week REU Site in the summers of 2022, 2023, and 2024, involving nine students per year working in teams of three under the supervision of a faculty mentor. The selected participants will come from a diverse pool of applicants, and the faculty mentors will supervise the participants in research projects. Beyond successful research outcomes, the objectives of the program are to introduce students to aspects of mathematical research and the broader mathematical community. At the same time, the students will build mentoring relationships with faculty as they consider pursuing graduate degrees and a career in mathematics. Students will be part of an active community at the hosting institution. In addition to the REU, the participants will have various activities, participating in several summer programs and interacting with established mathematicians who visit the campus. A diverse body of participants is strongly desired, and priority will be given to applicants from groups that are underrepresented in the mathematical community. This includes minority students, women, as well as those students coming from institutions with limited resources to support independent research projects for their undergraduates. The research projects include a diverse collection of topics based on the research interests of the faculty mentors. Specific projects include commutative algebra arising from graphs and matroids, shellability of simplicial complexes, algebraic and combinatorial aspects of higher dimensional tiling, graph theoretic problems arising from group theory, prime graphs of special classes of groups, arithmetical properties of group invariants, linear and permutational representations of groups, statistical analysis on DNA sequencing data, and survival analysis in data science. Participants will regularly meet with their research team and their mentors and spend some of the time learning the necessary background before and while pursuing original research. Students will be asked to present their findings in oral presentations and will be guided in summarizing their work in a mathematical research paper. In the course of the program, students will be trained in various skills, including literature review, using software such as GAP, Macaulay2, Sage, and R to make and check examples, oral presentation skills, and written mathematical communication using LaTeX. Communication with the participants will continue after the program ends, and students will be encouraged to present their work at local, regional, and national conferences in the subsequent academic year.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.

该奖项的全部或部分资金根据《2021 年美国救援计划法案》（公法 117-2）提供。德克萨斯州立大学圣马科斯分校数学系将在 2022 年、2023 年和 2024 年夏季举办为期八周的 REU Site，每年有 9 名学生在教师导师的监督下以三人一组的形式进行工作。选定的参与者将来自不同的申请者，教师导师将监督研究项目的参与者。除了成功的研究成果之外，该项目的目标是向学生介绍数学研究的各个方面和更广泛的数学社区。与此同时，学生在考虑攻读研究生学位和从事数学职业时，将与教师建立指导关系。学生将成为主办机构活跃社区的一部分。除了 REU 之外，参与者还将参加各种活动，参加多个暑期项目并与参观校园的知名数学家进行互动。强烈希望有多元化的参与者，并且将优先考虑来自数学界代表性不足的群体的申请人。这包括少数族裔学生、女性，以及来自资源有限、无法支持本科生独立研究项目的院校的学生。研究项目包括基于教师导师的研究兴趣的各种主题。具体项目包括由图和拟阵产生的交换代数、单纯复形的可壳性、高维平铺的代数和组合方面、群论中产生的图论问题、特殊类群的素图、群不变量的算术性质、群的线性和置换表示、DNA测序数据的统计分析以及数据科学中的生存分析。参与者将定期与他们的研究团队和导师会面，并在进行原创研究之前和期间花一些时间学习必要的背景。学生将被要求以口头报告的形式展示他们的发现，并指导他们在数学研究论文中总结他们的工作。在课程中，学生将接受各种技能的训练，包括文献综述、使用GAP、Macaulay2、Sage和R等软件制作和检查示例、口头表达技巧以及使用LaTeX进行书面数学交流。项目结束后，与参与者的沟通将继续进行，并鼓励学生在随后的学年在地方、地区和国家会议上展示他们的作品。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。