CSUMS: Theory, techniques, and research in computational mathematics

College Of William And Mary, Williamsburg VA

Investigators

Abstract

Li 0703532 This CSUMS project links faculty from the departments of mathematics, computer science, and applied science at William and Mary to create a computational mathematics component in the undergraduate program. Project personnel modify freshman and sophomore courses to place greater emphasis on computational issues, thereby preparing undergraduates for special upper division courses and eventual participation in undergraduate research. Students do research projects on theoretical and practical problems from numerical linear algebra, quantum computing, optimization, dynamical systems, and mathematical biology. Typically, students in the program start doing research in their junior year and the following summer, and continue their work during their senior year through carefully supervised honors theses. In addition, academic year activities include special computational mathematics seminars and visitors, plus an annual workshop in which students present their discoveries. Important scientific findings are submitted for publication in professional journals and presented at scholarly conferences. In addition, students discuss their results and experiences in local high schools, in the Virginia Governor's School for Science and Mathematics, and in regional two-year colleges. Such outreach presentations should attract a larger and more diverse population of younger students into further study of computational mathematics, and give research students in the program additional practice in communicating mathematics to others. To broaden the perspective of the students in the program, and to encourage the interchange of ideas, there are visits to other institutions and research agencies in the U.S. and abroad. A website is set up to facilitate communication with other research groups and computational mathematics programs. At the base of modern computer and information technology is an interdisciplinary field called computational mathematics. This project unites the skills and knowledge of faculty from the departments of mathematics, computer science, and applied science to create a new computational component within the undergraduate curriculum. It prepares students to participate in undergraduate research projects in the theoretical and practical aspects of computation, and it builds linkages between the computational mathematics programs at William and Mary and similar programs nationally and abroad. Successful experiences in this program attract students to further study in computational mathematics and to careers in the field. The diverse research backgrounds of the program's faculty interact to break down the intellectual compartmentalization that stands in the way of progress for both our students and our faculty. The new ideas developed in the program are disseminated through conference talks and scholarly publication by our students and their faculty mentors. Through outreach to high school and community college programs, they attract a larger and more diverse group of pre-college students into computational mathematics programs here and elsewhere. The project is supported by the MPS Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and the EHR Division of Undergraduate Education.