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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。得克萨斯州立大学圣马科斯的数学系将在2022年，2023年和2024年的夏季举办一个为期八周的REU站点，涉及每年在教师导师的监督下在三人组中工作的9名学生。选定的参与者将来自各种各样的申请人，教师导师将监督研究项目的参与者。除了成功的研究成果外，该计划的目标是向学生介绍数学研究和更广泛的数学社区的各个方面。同时，学生将在考虑攻读研究生学位和数学职业时与教师建立指导关系。学生将成为托管机构活跃社区的一部分。除了REU外，参与者还将进行各种活动，参加几个夏季计划，并与访问校园的成熟数学家进行互动。强烈希望有各种各样的参与者，并将优先考虑数学社区中代表性不足的团体的申请人优先。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，以支持其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集合。特定的项目包括由图和成绩单引起的交换代数，简单络合物的可撒性，较高维平地的代数和组合方面，图形理论问题是由小组特种类别组的主要图，组的主要图形图，小组的算术属性，小组不可知病的算术性能，线性和线性分析的数据分析和数据分析，统计分析和数据分析。参与者将定期与他们的研究团队和导师会面，并花一些时间在追求原始研究之前和在进行原始研究之前学习必要的背景。将要求学生在口头演讲中介绍他们的发现，并将在数学研究论文中汇总他们的工作。在计划的过程中，学生将接受各种技能的培训，包括文献审查，使用差距，Macaulay2，Sage和R等软件来制作和检查示例，口头演示技巧以及使用乳胶的书面数学交流。该计划结束后，与参与者的沟通将继续进行，并鼓励学生在随后的学年在本地，地区和民族会议上介绍他们的作品。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的审查标准通过评估来进行评估。