APPLIED MATHEMATICS

AND MODELING

The College of William & Mary in Virginia

Applied mathematics concerns the application of mathematical tools and processes to the solution of problems of practical interest to society. Consequently, the applied mathematician frequently has one foot in an area of mathematics and the other in physics, chemistry, biology, engineering, or some other branch of applied science. The solution of scientific problems typically involves a four-fold process:

  • Research to develop a depth of understanding of the physical problem.
  • Restatement of the physical problem in terms of a mathematical model. Math models most often take the form of ordinary or partial differential equations or of matrix systems. Inevitably mathematical models contain various levels of approximation, in which certain (hopefully) insignificant factors have been neglected.
  • Solution of the mathematical model, usually by numerical methods.
  • Interpretation of the mathematical solution in terms of the original physical problem and assessment of the validity of the solution in light of any approximations that have been.

 

 

Thus the applied-math toolbox contains, among many other mathematical tools, modeling techniques, approximation theory, linear algebra, numerical analysis, probability and statistics, and optimization. The successful student whose major is applied mathematics should be well equipped for a variety of interesting career possibilities including university positions, industrial applied mathematics, and research in national laboratories.

 

Faculty research interests in Applied Mathematics & Modeling include:

·  Prof. Christopher A. Del Negro (Neurophysiology, Motor Pattern Generation)

·  Prof. Mark Hinders (Nondestructive Evaluation, Medical Imaging, Robotics)

·  Prof. Charles R. Johnson (Matrix analysis and its applications)

·  Prof. Rex Kincaid (Network location theory, sensor/actuator placement)

·  Prof. Henry Krakauer (Theoretical methods for piezo- and ferro- electric materials)

·  Prof. Lawrence Leemis (Reliability, simulation, probability, statistics)

·  Prof. Chi-Kwong Li (Matrix analysis, operator theory, combinatorial theory)

·  Prof. Leah Shaw (Computational Biology, Nonlinear Dynamics, Epidemic Modeling)

·  Prof. Greg Smith (Computational Neuroscience, Cellular Biophysics)

·  Prof. Eugene R. Tracy (Plasma theory and nonlinear dynamics)

·  Prof. Robert Vold (Solid State FTNMR & Spectroscopy)

 

Also, William and Mary's Institute for Integrative Bird Behavior Studies (iibbs) is a newly formed initiative bringing together researchers from Biology, Mathematics, School of Marine Sciences, and our Center for Conservation to study the behavioral ecology and conservation of populations and communities. Formed by several Applied Science affiliates, Professors Dan Cristol, John Swaddle and Sebastian Schreiber, the goals of iibbs/BioMath are to:

 

Formalize and strengthen William and Mary's expertise in behavior and ecology, particularly in relation to mathematical applications and modeling of populations and behaviors;

Provide strong, personalized mentorship for undergraduate and graduate students at the interface of biology and mathematics;

Provide inspiring educational and research opportunities for students, including Applied Science PhD students;

Support active collaboration among faculty and students from different disciplines and departments, particularly in BioMath areas which are of interest to Applied Science graduate students.

 

Recognizing the important overlap between computer science and operations research, the College offers an M.S. with a specialization in Computational Operations Research (COR) administered by the Computer Science Department in cooperation with the Department of Mathematics. Qualified students may elect to continue graduate work in operations research leading to a Ph.D. in either the Computer Science Department (with a computational emphasis) or the Applied Science Department (with an applied mathematics and modeling emphasis). These opportunities are facilitated by the participation of the departments of Mathematics, Computer Science, and Applied Science in the Computational Science Cluster, a federation of departments and schools at William & Mary committed to fostering research and education in computational science.

 

Computational Science Training for Undergraduates in the Mathematical Sciences (CSUMS) is a new collaborative program between the Departments of Mathematics, Applied Science, and Computer Science at the College of William & Mary. We are actively recruiting William & Mary undergraduate students interested in participating in a CSUMS research project. The benefit of participation in CSUMS include the possibility of support to work on a research project with a group of CSUMS faculty members during the Spring semester of your junior year. If you wish to continue your research, competitive stipends are available to provide support during the summer between your junior and senior years, along with the possibility of on-campus housing. In addition, travel support is available to attend conferences or visit research groups at other institutions either in the U.S. or abroad.