REU at Kent State University

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Program Description

During the first few days, our faculty will give lectures that will explain and advertise the projects. By the time the students arrive on campus they will already be familiar with the general description of the projects and may have an idea of what they want to do. These introductory lectures will go beyond providing a deeper explanation of the projects and the related background. They will also give an opportunity for the students to meet our faculty and will ensure the best match possible between the students and their prospective advisors. As a result of these lectures, the participants will be aware of the projects their fellow students will be working on which will help them communicate about their progress in the future weeks. We expect that by Wednesday of the first week the students will make their decisions regarding the projects they want to be involved with. Some of the students may decide to work together on the same project, while others may end up working with more than one advisor.

During the first week we will also provide some training in mathematical software such as GAP, Maple, and MATLAB. The students will also be introduced to LaTeX that they will later use for writing up their project reports. Graduate students will help to run these sessions.

For the rest of the program the students will be working on their research projects with their advisors. This will typically include meeting with the advisors on the daily basis for an hour, although some advisors may want to meet twice a day or for a longer period of time. The advisors will split the projects into small progressive steps and will closely monitor their students' success. Whenever possible, we will try to involve those of our graduate students who are experts in the mathematics related to the given project.

Starting the second week, every Friday all the REU students and advisors will meet for a seminar where the students will make presentations about their progress. They may talk about something they learned or discovered or about the difficulties they encountered during that week. These presentation will be short and informal. Some of the students will have something to say every Friday while others may give such a presentation only every other week.

We will also organize weekly lectures given by our faculty or visitors of the department. The idea of these lectures is to expose our REU students to some beautiful results and constructions in mathematics. Some of the talks will not be directly related to linear algebra but whenever possible the speakers will emphasize connections to our main theme. One of the lectures will be given by Richard Varga, a renowned linear algebraist who is a Professor Emeritus in our department. Per Enflo will talk about the invariant subspace problem. Victor Lomonosov will present a simple proof of Burnside's Theorem. Richard Aron will talk about non-linear analysis and its connections to the linear algebra.

By the end of the fourth week all the students will present oral and written reports on their projects. These reports will reflect on the background they learned and their first steps in their projects. During the eighth week each of the students will make a detailed oral presentation about their project. These talks will be longer and more formal than usual weekly reports, and the students will first practice them with their advisors. They will also submit their final written reports during that week. The expectation is that for some of the students this will be a starting point for a journal article. They will continue working on this with their advisors during the weeks to come.

Informal gatherings will be a regular and important part of our program. One of our aims is that the students get to know each other on a personal level, and bond into a cohesive group that stays in touch after the program finishes. We will organize various outings on week days and on Saturdays we will have major recreational activities. Those may include theater and museum trips, hikes and picnics in the Cuyahoga Valley, hot-air balloon ride, and Blossom music festival.