REU Site: Research, Education and Training in Computational Mathematics and Nonlinear Dynamics of Bio-Inspired and Engineering Systems

George Mason University, Fairfax VA

Investigators

Abstract

The Department of Mathematical Sciences at George Mason University will host a two-year multidisciplinary REU program in computational mathematics and nonlinear dynamics of biological, bio-inspired and engineering systems from June 4 - Aug 3, 2012 and June 3 - Aug 2, 2013. This nine-week summer program will expose twelve highly qualified undergraduate students and two K-12 teachers each year, to advanced topics in mathematics, problem-solving, visualization techniques and applications to bio-inspired and engineering systems. This summer research program will provide the participants with a unique experience of how mathematics can be applied to understand the qualitative and quantitative behavior of biological, bio-inspired and engineering systems. The proposed program will involve three subprograms under a common broad theme that will help understand the quantitative behavior of biological, bio-inspired and engineering systems. These include (a) Modeling and analysis of biological, bio-inspired problems (b) Mathematics of materials and (c) Mathematics Education using Technology. All of them will be synergistically linked together under the umbrella of computational mathematics and nonlinear dynamics. Selected problems range from Aneurysm mechanics to Modeling of Micro Air Vehicles, Design of photovoltaic nanodevices, Porous substrates and Phase diagram calculation for materials engineering applications, as well as the design of efficient educational tools. Through these research problems, we hope to encourage students and teachers to learn by discovery and enhance their understanding of the multidisciplinary role of mathematics in engineering, science and medicine. The teachers will be able to use their problem-solving skills and research experience from the program to do open-ended exploration and develop related lesson studies in their high-school mathematics classrooms. Two graduate students will be involved in this program as graduate mentors for the participants. The program will help nurture the intellectual growth and development of graduate students and also provide them with a valuable experience of mentoring. Each nine-week summer program will also include the following activities: lecture series on topics; graduate mentoring club; guest colloquia; student seminars; computational laboratory as well as scientific and social tours. The REU site will involve seven qualified faculty who have excelled in their research and teaching accomplishments, have guided graduate and undergraduate research, and have been involved in K-12 outreach activities. The multi-disciplinary research program will greatly enhance the awareness of the ever-increasing utility of mathematical and computational approaches in understanding biological, bio-inspired and engineering systems. It will contribute to the scientific development of undergraduate students and K-12 teachers and will nurture the intellectual growth and development of graduate students providing them with a valuable experience of mentoring. This program will integrate and complement the existing successful mentoring programs at GMU, partnerships with local K-12 high schools and also establish new collaborations with other institutions. This symbiotic relationship will provide enhanced learning and research opportunities for targeted students to prepare for success in the mathematical and engineering fields that will assist them from college to graduate school. The REU program will provide a unique and invaluable experience to four K-12 teachers in problem-solving and open-ended exploration that they will use in their high-school mathematics classrooms. This program will also greatly encourage women and underrepresented minorities to pursue multidisciplinary careers that bridge mathematical, computational and biological sciences.