An Undergraduate Research Program in Combinatorics and Number Theory

该计划的目标是为八名本科数学学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行设置，强调发展每个学生的独立性。在杜卢斯，这种方法是对待那些具有极高潜力进行重大研究的本科生，就好像他们正在研究一个博士论文问题，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项目校友协助。参与者研究开放问题和最近文献中的插图。主题包括避免模式的排列，涉及单词的组合问题，以及组合数论中的问题。学生在阅读研究文章中获得经验，找到有见地的例子，提出探索性的问题，认识到微妙的模式，经常写报告，每周一次的演讲，提出问题，并使用计算软件，与同行合作，处理挫折和挫折，并熟悉出版过程。参与者将通过在会议和研讨会上介绍他们的成果而融入数学研究界。该奖项反映了NSF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而被认为值得支持。

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.