REU Site: Research Experience for Undergraduates in Algebra and Discrete Mathematics at Auburn University

这项NSF奖项将在2020-2022年的每个夏天支持8名本科生在奥本大学进行8周的代数和离散数学研究。该项目是美国国家科学基金会资助的REU项目的延续，该项目由建议者在1999年、2000年、2005-2008年和2010-2019年在奥本大学实施。我们几乎所有不再是本科生的校友都上了研究生，略多于一半的人读的是数学，其他的是数学教育、计算机科学、统计学和统计科学，包括生物学的数学分支。由此可见，我们的项目对本科生和各个数学学科都有积极的影响。我们的目标是让一半的参与者是女性，我们在招收少数族裔学生方面的努力，以及我们对美国东南部地区的关注，支持了NSF发展多元化劳动力的愿景。在2013年至2017年，我们的一些最近和最近的校友参加了马萨姆计划，国家科学基金会奖1343651号，前往南部非洲参加南部非洲数学科学协会的年度会议、研讨会和马萨姆高级研究所，目的是促进美非与撒哈拉以南非洲数学家的合作研究；这种参与将继续下去。这个项目是由数学科学中的劳动力计划和已建立的激励竞争研究计划(EPSCoR)共同资助的。我们的REU专注于代数(计算代数、Groebner基)和离散数学(图论、图形和超图、数论、信息和编码理论)中的一些当前研究问题。活动的模式将一如既往：在头2-3周集中介绍问题和问题领域，在第3周由每个参与者进行强制性的“破冰”报告，然后在剩下的5周进行“研究”阶段，最后由每个参与者进行最后的报告。在研究所阶段，将有教职员工和研究生、客座数学家以及参与者本人的频繁演讲，但该阶段的主要特点将是参与者与教师、研究生和他们自己进行的各种组合的研究。该计划的目的是为参与者提供真实的数学研究体验，目标是激发学生进入研究生院并追求学术研究事业的热情。与过去几年一样，研究成果将发表在书籍或参考期刊上，并在研究会议上展示。这一奖项反映了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。

This NSF award will support 8 undergraduate students for 8 weeks at Auburn University in each of the summers 2020-2022 to conduct research in algebra and discrete mathematics. The program is a continuation of successful NSF funded REU programs conducted by the proposers at Auburn in 1999, 2000, 2005-2008, and 2010-2019. Almost all of our alumni who are no longer undergraduates went to graduate school, slightly more than half in mathematics and the others in mathematics education, computer science, statistics and statistical sciences, including mathematical branches of biology. This shows that our program has positive impact on undergraduates and various mathematical disciplines. Our goal of having half of the participants to be women, our effort in recruiting minority students, and our focus on the American Southeast support NSF's vision of developing a diverse workforce. In 2013-2017, a number of our recent and not-so-recent alumni participated in the Masamu Program, NSF Award No. 1343651, by going to Southern Africa for the annual Southern Africa Mathematical Sciences Association conference, workshop, and Masamu Advanced Study Institute for the purpose of fostering US-Africa collaborative research with Sub-Saharan African mathematicians; this participation will continue. This project is jointly funded by the Workforce Program in the Mathematical Sciences and the Established Program to Stimulate Competitive Research (EPSCoR).Our REU focuses on some of the current research problems in algebra (computational algebra, Groebner bases) and discrete mathematics (graph theory, graphs and hypergraphs, number theory, information and coding theory). The pattern of activities will be as before: intensive introduction to problems and problem areas in the first 2-3 weeks, capped by an obligatory "ice-breaker" presentation by each participant in the 3rd week, followed by a "research institute" phase in the remaining 5 weeks, capped by a final presentation by each participant. During the research institute phase there will be frequent talks given by faculty and graduate students of the department, visiting mathematicians, and the participants themselves, but the main feature of that phase will be research carried on by the participants, in various combinations with faculty, graduate students, and by themselves. The purpose of the program is to give the participants an authentic experience of mathematical research with the goal of exciting students about going to graduate school and pursuing academic research careers. As in past years, research results will be published in books or refereed journals and presented at 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.