REU Site: Algebra, Combinatorics, and Statistics

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。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年夏季举办一个为期八周的REU网站，每年有九名学生在一名教师导师的监督下三人一组工作。被选中的参与者将来自不同的申请者池，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，学生们将在考虑攻读研究生学位和从事数学职业时，与教职员工建立指导关系。学生将成为主办机构活跃社区的一部分。除了REU，参与者还将有各种活动，参加几个暑期项目，并与参观校园的知名数学家互动。参与者的多样性是非常必要的，数学界代表性不足的群体的申请者将被优先考虑。这包括少数族裔学生、女性，以及那些来自资源有限的机构的学生，他们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不同主题集合。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、由群论引起的图论问题、特殊群类的素图、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他们的导师会面，并在从事原创研究之前和同时花一些时间学习必要的背景知识。学生将被要求以口头报告的形式陈述他们的发现，并将被引导在一篇数学研究论文中总结他们的工作。在课程过程中，学生将接受各种技能的培训，包括文献回顾，使用GAP、Macaulay2、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。与参与者的交流将在项目结束后继续进行，学生将被鼓励在下一学年的地方、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优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.