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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。数学系在得克萨斯州州立大学在圣马科斯将主办一个为期八周的REU网站在2022年，2023年和2024年的夏天，涉及每年9名学生在一个教师导师的监督下，在三人一组的工作。被选中的参与者将来自不同的申请人，教师导师将监督研究项目的参与者。除了成功的研究成果，该计划的目标是向学生介绍数学研究和更广泛的数学界的各个方面。与此同时，学生将与教师建立指导关系，因为他们考虑攻读研究生学位和数学职业。学生将成为主办机构活跃社区的一部分。除了REU，参与者将有各种活动，参加几个暑期项目，并与访问校园的知名数学家互动。一个多元化的参与者是强烈希望，并将优先考虑来自数学界代表性不足的群体的申请人。这包括少数民族学生、妇女以及来自资源有限的机构的学生，以支持本科生的独立研究项目。研究项目包括基于教师导师的研究兴趣的各种主题。具体的项目包括交换代数产生的图和拟阵，shellability的单纯复形，代数和组合方面的高维平铺，图论问题产生的群论，总理图的特殊类别的群体，算术性质的群体不变量，线性和置换表示的群体，统计分析的DNA测序数据和生存分析数据科学。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知识。学生将被要求在口头报告中提出他们的研究结果，并将在总结他们的工作在数学研究论文的指导。在该计划的过程中，学生将接受各种技能的培训，包括文献综述，使用GAP，Macaulay 2，Sage和R等软件制作和检查示例，口头演示技能以及使用LaTeX进行书面数学交流。项目结束后，将继续与参与者进行交流，并鼓励学生在下一学年的地方，地区和国家会议上展示他们的工作。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。