An Undergraduate Research Program in Combinatorics and Number Theory

该计划的目标是为8名数学本科生提供专业水平的研究经验。该计划提供了一个独特的研究社区的同龄人设置，强调发展每个学生的独立性。德卢斯大学的做法是，对待具有极高研究潜力的本科生，就像对待他们正在研究博士论文问题一样，导师提供问题和指导，但避免直接参与解决问题。PI由三名研究生和许多是项目校友的访客协助。参与者从最近的文献中研究开放的问题和猜想。主题包括避免模式排列，涉及单词的组合问题，以及组合数论中的问题。学生们在阅读研究文章、寻找有洞察力的例子、提出探索性问题、识别微妙的模式、频繁撰写报告、每周发表演讲、提出问题和做出猜测、使用计算软件、与同行合作、处理挫折和挫折以及熟悉出版过程等方面获得经验。参与者将通过在会议和会议上展示他们的成果来融入数学研究界。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The objective of the program is to provide a professional level research experience for eight undergraduate mathematics students. The program provides a unique research community-of-peers setting that emphasizes developing the independence of each student. At Duluth the approach is to treat undergraduate students with extraordinarily high potential for doing significant research as though they are working on a PhD thesis problem where the adviser provides the problem and mentoring but avoids direct involvement in solving the problem. The PI is assisted by three graduate students and many visitors who are program alumni.Participants work on open problems and conjectures from the recent literature. Topics include pattern-avoiding permutations, combinatorial problems involving words, and problems in combinatorial number theory. Students gain experience in reading research articles, finding insightful examples, asking probing questions, recognizing subtle patterns, writing frequent reports, giving weekly presentations, posing problems and making conjectures, using computational software, working with peers, dealing with setbacks and frustration, and becoming familiar with the publication process. Participants will be integrated in the mathematical research community by giving presentations of their results at meetings and 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.