REU Site: Matrix Analysis, its Applications and Related Combinatorics

我们的目的有两个：(1)通过为期8周的强化辅导暑期计划，向有前途的数学学生介绍当前感兴趣的问题的真正研究；(2)为各种多少相关的、未解决的问题做出实质性的研究贡献。对于数学研究生学习以及该领域的大多数最终职业来说，研究是必要的，与传统的本科课程工作有很大的不同。经验表明，在一群能力相似的学生中诚实地接触真实的研究，对于学生未来的决策以及为可能的研究生学习做准备和激励是非常有效的。这个REU项目的平台是矩阵分析和应用，广义的，包括组合学。这是一个极好的可访问的、有价值的和开放式问题的来源，也是一个最有价值的领域，作为未来数学工作的知识库的一部分。私家侦探通过他自己的研究计划和广泛的国际联系，产生了许多问题，这些问题的进展将引起社会的兴趣。此外，在前几个夏天已经取得进展的多个部分的几个大问题上的工作可能会继续进行。这在过去和将来可能会在受人尊敬的传统期刊上产生许多学生撰写的出版物，这将对该领域做出持久的贡献。

Our purpose is two-fold: (1) to introduce promising mathematics students to real research in problems of current interest, through intensive, 8-week, mentored, summer programs; and (2) to make substantial research contributions to a variety of somewhat related, unsolved problems. The research that is necessary for graduate study in mathematics, and most eventual careers in the field, is quite different from traditional undergraduate course work. Experience has shown that an honest exposure to real research, within a group of like-ability students, is very efficient for future decision making by the students and as preparation and inspiration for likely graduate study.The platform for this REU program is matrix analysis and applications, broadly defined, including combinatorics. This is an excellent source of accessible, worthwhile, and open-ended problems and a most valuable area as part of the knowledge base for future work in mathematics. The PI, through his own research program and wide variety of international contacts, generates many problems, progress on which will be of interest to the community. In addition, work is likely to continue on several large problems, with many parts, on which progress has been made in prior summers. This has in the past, and likely will in the future, generate many student-authored publications, in respected, traditional journals, that will be a lasting contribution to the field.