Computational mathematics plays a critical role in the infrastructure of modern science. To foster the development of computational and mathematical science skills, in this CSUMS project the investigator and his colleagues establish an ongoing program of undergraduate research at George Mason University. The program involves selected talented undergraduates in several overlapping research opportunities that share a reliance on computational mathematics. Undergraduate mathematics majors work with established professors on timely problems of computational mathematics with immediate applications in materials science, astronomy, space weather, dynamical systems modeling, biophysics, neuroscience, financial mathematics, statistics, and fluid dynamics. The five co-investigators on the project, from the Department of Mathematical Sciences and the Department of Computational and Data Sciences, are joined by 20 other professors with experience in mentoring high-school and undergraduate students. Each CSUMS cohort works together in a central knowledge core class, to rotate from year to year, and shortly thereafter specializes to one of several particular research projects related to the core. Students are supervised by tenured/tenure track faculty and produce a poster and a written thesis describing their research by the end of the year.
This project addresses the important need to inspire and educate the next generation of computational scientists. Due to the heavy reliance of contemporary science on computational modeling, experts in computational mathematics will be necessary for the advancement of science in the U.S. This project assists in the creation of well-trained computational mathematicians by involving today's mathematics majors in significant applied research at the undergraduate level. Research experiences make them more likely to succeed at the graduate level, in the completion of advanced degrees in computational areas. The CSUMS program at George Mason University exposes the student to interesting, computationally accessible research problems in critical competitiveness areas, including materials science, computational fluid dynamics, financial mathematics, and several other areas in the biological and physical sciences. Additionally, the program educates students about the value of computational skills while they are still formulating their career directions. The project is supported by the MPS Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and the EHR Division of Undergraduate Education.
The focus of the GMU CSUMS project is to transition undergraduate students who have learned the fundamentals of computational mathematics into a position where they can contribute to research projects in the computational sciences. Our goal is to enhance the research infrastructure and competitiveness of the nation by providing the students with the skills and opportunities needed to participate in cutting-edge research as undergraduates, and by encouraging them to pursue research in graduate school or other professional venues. Each annual cohort of students began training at the beginning of the summer with a demanding course in applied partial differential equations, followed by an intensive research period directed by a senior professor or team of professors. Students worked in groups during the remainder of the summer, being introduced to a research area and gradually becoming more independent at the tasks. By early fall, they were traveling to a regional undergraduate mathematics conference to report orally on their research projects. During the ensuing academic year, the students continued their research with their assigned mentors, and in addition attended a weekly seminar class on how to give oral presentations, how to construct posters, and learning to write papers. During Fall semester, the emphasis is on learning to give an effective talk on the research they have started during the summer. This has in the past been a significant cohort-building activity, where the students further their research skills by learning scientific modes of communication. During Spring semester, the emphasis is on writing skills. Our main goal was to give the students skills roughly equivalent to first-year graduate students, so as to ease their transition to graduate school, and perhaps to give them the confidence that they can succeed in such an environment. During the academic year, all student participants traveled to at least one national conference to present their research to national and international experts. Over the duration of the CSUMS grant, 51 undergraduate mathematics majors at George Mason University were full participants in the program, including 10 female students, and 3 African-American and 3 Hispanic students. Of the 51 participants, 15 have not yet graduated from college. Of the remaining 36, all successfully graduated with a BS in Mathematics (including many double majors) and 24 went on to graduate school in Mathematics or a mathematics-related area. Beyond the CSUMS participants who were directly affected, the program has had a wider impact than expected on the mathematics department and university. The Applied Partial Differential Equations course that was developed just for the CSUMS participants will become a regular course at GMU, and the lecture notes have been contracted by a major publisher to become a textbook. The existence of the CSUMS program has made the Mathematics major significantly more popular at the university, and the Assoc. Dean of the Honors College has informed us that she and others find it a significant boon to recruiting talented students to the university. Many of the participants have switched to the Mathematics major from competing disciplines, or declared a double major, to take part in the CSUMS program. It has greatly increased our visibility in the university as students show their research results at campus functions, receive prizes at national conferences from CSUMS-sponsored research and gather publicity for their presentations and publications. One of the least quantifiable elements of these projects was the excitement that our students felt about being able to participate and carry out significant, independent research projects under the direction of a real mathematician mentor. Having the students participate in regional and national conferences also opened up the world of mathematical and computational research to them, and let them understand the research process from conception to presentation.
