An Overview of the Computational and Applied Mathematics (CAM) Graduate Program

The Computational and Applied Mathematics (CAM) Graduate Program was instituted for the education and training of graduate students in an interdisciplinary environment. We seek to impart to students a broad and deep understanding of the computational, mathematical, and application specific issues that arise in the analysis, modeling, and simulation of natural, engineered, and other systems.

This program is unique in its interdisciplinary emphasis. In order to make significant progress in many of the most challenging problems facing society today, teams with expertise in multiple disciplines are required. Professionals trained in an interdisciplinary environment are critical members of such teams, as they can effectively communicate with each team member, and contribute in novel ways to the solution of the problems faced because they understand at some level all facets of the problem.

Such an interdisciplinary emphasis is possible only because the CAM program does not reside within a single academic department, nor even within a single academic college, but rather it resides within a research institute, the Institute for Computational Engineering and Sciences ( ICES ). CAM draws its faculty from 13 distinct departments within the 3 colleges Engineering, Natural Science, and Business. Exposure to ICES researchers and visitors, and access to ICES facilities and research centers provides a stimulating intellectual environment for our students, and places them at the forefront of computational and applied mathematics.

CAM doctoral dissertations have made new and significant discoveries in a number of important areas. Included are improved modeling of the acoustical properties of the human ear, the electromagnetics of wave-guiding structures, transient wave propagation in unbounded domains, highly heterogeneous elastic structures, viscous incompressible flow problems, miscible displacement of one fluid by another in porous media, transport of contaminants in the ground, and assessing uncertainty in the characterization of the earth's subsurface as it relates to fluid flow. Many novel and important computational techniques have been developed or improved by CAM students in their work. These tools have application in many related areas, and so have broad impact on analysis, modeling, and simulation. Included are improvements in the approximation of hyperbolic conservation laws, discontinuous Galerkin methods, subdivision tree based multiresolution representation of arbitrary triangle meshes, hp-adaptive finite element methods, and a parallel infrastructure for scalable adaptive finite element methods. (See the list of CAM dissertations and the list of ICES technical reports for more details.)

The CAM program is intellectually stimulating and rewarding, but it is also extremely demanding. We keep it relatively small so that we can foster quality and depth. Our approximately 40 graduate students take classes and learn first-hand from mathematicians and computer scientists, and from scientific, engineering, and business professors in their related applications areas. The CAM program requires each student to develop graduate level proficiency in three main concentration areas. These are (A) Applicable Mathematics, (B) Scientific Computation and Numerical Analysis, and (C) Mathematical Modeling and Applications to an important area of academic research within the physical or life sciences, engineering, or financial modeling. The program, and especially area C, is designed to be very flexible, so that each student can develop his or her own course of study appropriately, yet without neglecting to be exposed to the broad range of ideas and techniques within the three CAM concentration areas. Each dissertation must demonstrate an interdisciplinary theme and draw on knowledge from each of these three areas.

We have two paths or options in our program. Both options lead to the same CAM Ph.D. degree, with the same emphasis on interdisciplinary research and the same demanding standards of achievement. However, not all students begin the program with equal preparation in, especially, Areas A and C. Thus we provide complementary paths that differ only in their requirements during the early years of graduate study.

The Computational and Applied Mathematics (CAM) option stresses to some degree the mathematical (Area A) side of the program, and it is suited more to students with a solid undergraduate background in mathematics. This option also allows the student more time to explore and develop interests regarding an application topic for Area C, and more time to select a graduate advisor.

The Computational Engineering and Sciences (CES) option stresses the application area (Area C) and allows more time to develop graduate level proficiency in applicable mathematics (Area A). This option is suited to undergraduate engineering, science, and business students who know generally the application area of their interest, but who desire a slower-paced introduction to the intellectual demands of graduate level mathematics.

We are very proud of our graduates , who have gone on to pursue careers in a wide variety of disciplines and environments. They generally work in industrial settings, government laboratories, or in academics. Of those in academics, they have chosen to join departments of mathematics, civil engineering, mechanical engineering, and solid mechanics. We take this as confirmation that our CAM degree is a truly interdisciplinary and valuable degree.

THE INSTITUTE FOR COMPUTATIONAL ENGINEERING AND SCIENCES | ICES

An Overview of the Computational and Applied Mathematics (CAM) Graduate Program