Applied Mathematics and Scientific Computation

Mathematical modeling and numerical analysis are increasingly important in many areas of science and technology. The dramatic improvement in algorithms and hardware in recent decades has facilitated the treatment of applied mathematical models which were considered intractable only a few years ago. This has led to the emergence of Scientific Computing as a "third scientific methodology", as distinct from theory and experimentation. Exploiting this new approach requires (a) sound mathematical training, (b) expertise in the practical aspects of computing and algorithm development, and (c) an interdisciplinary, scientific viewpoint which transcends traditional disciplinary boundaries.

The graduate program in Scientific Computing at BGSU is built upon Analysis. At its core are optimization and the numerical simulation of models involving partial differential equations. Through the coursework, the student will acquire rigorous training in real, complex and functional analysis, as well as a breadth of understanding of applied models. He or she will also gain significant practical computational experience which will be of great value in further research or in an industrial setting.

The student will also find opportunities for the interdisciplinary application of mathematics in a number of diverse areas. These include Geophysics, Materials Science, Mathematical Biology, Physics, and Chemistry.

Areas of Active Research

Highlights of research projects being conducted at BGSU by members for the Applied Mathematics faculty in collaboration with researchers from other departments include:

* Numerical Partial Differential Equations

Computational methodology combined with convergence theory, including: the method of characteristics, "mixed finite element methods", and multigrid methodology;

* Inverse Problems

Parameter estimation for partial differential equations; theory and methodology for large-scale ill-posed optimization, iterative spectral decomposition methods, and regularization techniques.

* Multiphase Porus Media Fluid Flow

Theoretical and numerical treatment of mathematical models with applications in petroleum extraction and groundwater contamination remediation.

* Nonlinear Diffusion-Reaction Models

A collaborative effort surface science, with researchers from the interdisciplinary "Center for Materials Science" in chemistry and electron microscopy, to model thin-film deposition and chemical kinetics at gas/metal interfaces such as occur in semi-conductor manufacture.

* Relativistic Gas Dynamics

A collaborative effort with the Department of Physics, extending state of the art techniques for Computational Fluid Dynamics from the Newtonian regime to the relativistic regime for the simulation of galactic jets.

Degree Programs

The Master of Arts degree with concentration in Scientific Computation is offered by the Department of Mathematics and Statistics. Through proper selection of coursework the student can prepare for entry as an applied mathematician into industry or government. Alternatively, the student can use the degree to prepare for a doctorate in applied mathematics or related fields.

The Doctor of Philosophy degree is also offered by the Department. A key goal in this program is the preparation of the student for the pursuit of focused research and, at the same time, a breadth of training in the mathematical sciences.

Requirements for the M.A.

• A total of at least 30 hours of graduate level course work, including cognate courses.
• Applied Mathematics courses (part of the requisite 30 hours), including Boundary Value Problems, Matrix Computations, Numerical Solution of Partial Differential Equations, Optimization, and Approximation Theory.
• Successful completion of a Master's thesis or of comprehensive examinations.

Requirement for the Ph.D.

Students must: earn at least six credits in a single cognate area; complete sixty hours of coursework; pass a set of written preliminary exams, and write and defend an original dissertation.

The Department

The Department of Mathematics and Statistics has thirty-two permanent faculty members. Research interests are varied, and include analysis, applied mathematics, probability and statistics, algebra, number theory, topology, and mathematics education. The Department enjoys active and collegial relationships with the other science departments on campus. The student will find a liberal arts atmosphere in a University setting, which is conducive to interdisciplinary education and basic research.

Weekly seminars are held in various areas of mathematics, including an interdisciplinary seminar on scientific computation in which students and faculty from this and other department make presentations on topics of mutual interest.