Department of Mathematical Sciences

Computational Mathematics

Advanced work in all areas of science and technology relies critically on computation. Computational mathematics involves the design and analysis of mathematical models for various problems and the construction of algorithms which efficiently and accurately compute solutions. A concentration area in Computational Mathematics includes courses in digital modeling, continuous and discrete simulation, and numerical analysis. The goal of the program is to offer depth in the area of concentration and breadth in the other mathematical sciences, with special emphasis on courses that will provide tools for innovative approaches to computer applications in industry. The first course in digital models is an introductory, but fundamental, course concerned with the construction of models for various problem types and the study of the structure of problem solving. The course in scientific computing, also a basic course, includes the study of some of the most frequently used mathematical algorithms in scientific problems. Students can specialize in computational problems which primarily lend themselves to discrete or to continuous mathematical models. Advanced courses in discrete and continuous simulation are available.

Faculty

  • M. E. Cawood : Numerical linear algebra, optimization, numerical methods for differential equations
  • Q. Chen : Partial differential equations, finite volume and finite difference methods, geophysical fluid dynamics, ocean modeling, turbulence
  • C. L. Cox : Finite element methods, viscoelastic flow modeling, parallel processing, numerical linear algebra, groundwater modeling
  • V. J. Ervin : Coordinator » numerical analysis, computational mathematics, partial differential equations
  • T. Heister : Numerical methods for PDEs, Finite Elements, massively parallel computing, preconditioning
  • E. W. Jenkins : Newton-Krylov-Schwarz methods, mixed finite element methods for acoustic waves, air-water models
  • H. K. Lee : Numerical methods for PDEs, parallel algorithms, computational optimal control, finite element methods
  • W. F. Moss : Mathematical modeling, computational mathematics, inquiry based K-12 science education, technology based curriculum development, effective teaching with technology
  • L. Rebholz : Numerical PDE, Turbulence, Large scale scientific computing   
  • D. D. Warner : Numerical analysis, computational science, parallel computing, distributed scientific simulations

Curriculum

Data Structures, Graph Algorithms, Computational Problems in Discrete Structures, Numerical Linear Algebra, Numerical Approximation Theory, Numerical Solution of Ordinary and Partial Differential Equations, Digital Models, Introduction to Scientific Computing. Some of the courses in computer science at the graduate level offered by the Department of Computer Science which may be chosen as electives are: Theory of Computation, Introduction to Artificial Intelligence, Design and Analysis of Algorithms, and Software Development Methodology. Students often take a graduate course in engineering or science which supports their graduate research.

Courses (Course Descriptions)

  • Introduction to Scientific Computing (860)
  • Advanced Numerical Analysis (861)
  • Digital Models I (863)
  • Data Structures (865)
  • Finite Element Method (866)
  • Scientific Simulations in Java (983)
  • Fiber and Film Systems: Modeling and Simulation (983)

Course Substitution Policy  

Sample Curricula

  • Sample Program for M.S. Concentration in Computational Mathematics
    • Fall:  805, 810, 865
    • Spring:  860, 821, 853
    • Summer:  803
    • Fall:  822, 825, 861
    • Spring:  927, 983, modeling course in another department, 892

Additional Computational Math Links