The Computational and Applied Mathematics (CAM) Group consists of Donna Calhoun, Michal Kopera, Jodi Mead, Michael Perlmutter, Grady Wright and Barbara Zubik-Kowal.
In addition to their work in the Math Department, members of the CAM group also participate inthe Computing Ph.D. Program, with focus on emphases in Computational Math Science & Engineering (CMSE), Data Science, and Artificial Intelligence.
CAM faculty also supervise students in the Math MS program, and serve as committee members in various graduate programs across campus. As an undergraduate, you can work with members of CAM group in the Computational and Applied Math emphasis.
Mathematical Sciences Major – Computational and Applied Math emphasis
Computational and Applied Mathematics (CAM) is an emphasis path within the Mathematical Sciences Major. CAM combines deep mathematical knowledge with computational tools to solve real-world problems in science, engineering, technology, economics and beyond. It combines mathematical modeling, numerical analysis, and computation to understand complex systems, simulate physical processes, and analyze data. Students learn advanced mathematical and numerical techniques for solving challenging problems.
As a student in this emphasis, you will learn computational thinking and problem solving, and complete a selection of courses in linear algebra, differential equations, numerical analysis and scientific computing. After completing this emphasis, you can be a data scientist, scientific software engineer, quantitative analyst, research scientist, or pursue an advanced degree in computational and applied mathematics, data science and engineering.
Industries which rely on CAM experts are software, aerospace, finance, actuarial science, artificial intelligence, pharmaceutical, semiconductor, biomedical engineering and many more!
Faculty interests
Donna Calhoun works on solving partial differential equations using finite volume methods on logically Cartesian meshes. Two areas are of particular importance when using Cartesian meshes are handling problems that are posed in non-rectangular domains, and efficiently distributing computational resources only in regions of the Cartesian mesh where the solution of interest. To handle geometry, Donna has developed immersed interface methods, embedded boundary methods and mapped grid methods. Immersed or embedded boundary methods simply cut complex geometry out of the background Cartesian mesh, and treat the irregular cells near the embedded boundary as special cases. In mapped grid approaches, the Cartesian mesh is mapped, via a smooth or piecewise smooth transformation to a non-rectangular domain such as a disk or surface mesh. For all of these methods, special finite volume solvers must be developed for the hyperbolic, elliptic or parabolic terms the equations of interest. To improve computational efficiency, Donna has also worked extensively with adaptively refined meshes (AMR).
Michal Kopera is interested in computational and applied mathematics, high-performance scientific computing, computational fluid dynamics, adaptive mesh refinement, and scientific software development. Michal is working on developing ocean models using modern numerical methods (spectral elements, discontinuous Galerkin). An important aspect of his work is the ability of a model to represent complex geometries, and dynamically adapt the mesh to an evolving solution.
Jodi Mead‘s research centers on advancing the mathematical foundations and computational methodologies for data assimilation, inverse methods, and uncertainty quantification. She develops algorithms that bridge theory and real-world application, particularly for systems where data and models must be integrated to improve predictive capability. Her work has produced new techniques for regularization parameter estimation, model-error covariance characterization, and joint inversion of multiple data types. These advances have been applied to diverse environmental and geophysical challenges, including wildfire smoke transport and subsurface imaging.
Michael Perlmutter’s primary area of research is Geometric Deep Learning, i.e., deep learning for graph- and manifold-structured data. This includes both (a) work on the geometric scattering transform, a predesigned, wavelet-based model of neural networks, and (b) work constructing high-performing networks for signed and/or directed graphs. Recently, he has become increasingly interested in using these methods in biomedical applications such as AI-aided drug discovery, analyzing metabolic networks, and predicting patient outcomes from single-cell data.
Grady Wright‘s research interests are in high-order methods for partial differential equations, approximation theory, low rank methods, scientific computing, and numerical software development. He works on problems in biology (biofluids and biomechanics), geophysics (geophysical fluid flows), and astronomy (cosmic microwave background). He develops methods based on radial basis functions, (compact) finite-differences, and spectral methods for these problems. A common theme of his work is complex geometries, such as spheres and more general surfaces.
Barbara Zubik-Kowal is working on a variety of problems: cancer models, immune system dynamics, threshold models, dendritic and brain models, models in fluid mechanics, chaos, electromagnetics, space-time dependent NLS with memory, and others. The model problems are described by delay differential equations (DDEs) – a general class including both delay and classical ordinary and partial DEs, which depend additionally on their solutions at some past stage(s). DDEs are popular as they arise from various applications, like biology, medicine, physics, control theory, and others. Her research activities focus on predictive modeling, parallel scientific computing (delay, integro-differential and classical DEs), numerical stability, construction and implementation of novel numerical methods, and development of numerical software.
Emeritus faculty
Stephen Brill‘s research is in the area of numerical solution of ordinary and partial differential equations, particularly those which model single- and multi-phase flow and contaminant transport in porous media. He is presently working on obtaining analytical formulas for collocation discretizations of convection-diffusion equations and studying these formulas to choose the value of free parameters so as to obtain highly accurate numerical solutions.