Overview. The theoretical development is done in an organized and concise series of lectures. In addition to the rigorous treatment of PDE theories, the lectures are designed not to lose the attention of the less-mathematically inclined students or the focus of experiments. Students will be split into groups of three to four led by two faculty mentors, one mathematician and one engineer/biologist. Students will meet daily with their mentors to discuss ideas and receive feedback, working individually afterwards for the rest of the day. Some of the meetings will take place in the laboratories, where experiments will be conducted. At the end of each week, except the first, all groups will gather for an informal progress seminar, where they will present a brief report on their progress. At the end of the program participants will write a final report on their project and present it at a mini-conference at UHD. Final reports will be posted on the program's website. The REU program will provide students with a stipend of $4000 and cover the costs of accommodation, food, and travel to and from Houston, Texas.
Research setting. The research projects are interdisciplinary, involving solid mechanics and water transport in plants for example, and include construction and analysis of mathematical models through analytic and computational techniques. Most of the projects also include a laboratory and/or field work component that gives students a firsthand experience in collecting data underlying the models. These models will be studied through a combination of qualitative analysis and numerical simulation. Effects of parameter variation will be surveyed to interpret the results and to formulate practical conclusions. Each research team consists of four to six students and two faculty members. Students will set up the experiment under the supervision of the faculty mentors, and experimental data/outcome will be collected and analyzed by students. The most unique aspect of our REU program is the integrated use of numerics. That is, students will learn numerical methods for solving PDEs in addition to the analytical methods. Three numerical methods will be learned and used by students: finite difference, finite elements, and boundary elements. By taking the viewpoint that applications of theory need to be observed through calculation and graphical display, numerical implementation is accomplished through the use of MATLAB, one of the most popular applied mathematics software packages.
Environment. Regular social events will be organized to provide an outlet for participants and help them feel more comfortable in Houston. We will organize our field trips on Fridays of the first 6 weeks; the field trips will include visits to the University of Houston, Rice University, Texas A&M University campuses, the NASA facilities, Texas Medical Center and advanced technological companies such as Smith International, to give the students a better idea of graduate school opportunities, practical uses of mathematics and potential careers related to them. We will also organize informal sessions with active researchers from Houston area universities to give participants an opportunity to connect with professional mathematicians and biologists at a human level.