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
-
C. L. Cox » finite
element methods, viscoelastic flow modeling, parallel processing, numerical
linear algebra, groundwater modeling
-
V. J. Ervin
» numerical analysis, computational mathematics, partial differential
equations
-
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
-
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
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
Recent M.S. Graduates (master's project title)
- Donald Adongo ("A MATLAB User Interface for CXTFIT")
- Dan Brauss ("Modeling of the Wet-Spinning Process")
- Kirsten Bernasconi ("Education Reform: Algebra in Elementary School")
- Eric Blum ("An Introduction to Numerical Modeling of Stock Options")
- John Chrispell ("Exploration of Solvers for Partial Differential Equations Using
the PETSc Framework")
- Scott Crosbie ("Implementation of the Parallel Algebraic Splitting Method")
- Robert Draper ("A PVM Based Implementation of Johnsson's Algorithm for
the Parallel Solution of Tridiagonal Linear Systems")
- Alan Guest ("A Trail Inventory of the Clemson Experimental Forest")
- Cheridy Hammond ("Mapping of the South Carolina Botanical Garden")
- Stephanie Kennedy ("Clemson Experimental Forest Trail Inventory")
- Jason Martin ("ADI Methods in Two and Three Dimensions")
- Miranda Massoud ("Mathematics Reform: A Report on the Connected Mathematics Project")
- Kristen Miller ("Mathematics Curriculum: Case Study of a First Grade Class")
- Gonul Okcu ("Developing Internet Interaction with MATLAB for Biological
Modelling")
- Tamra Payne ("Mathematical Modeling of Unsaturated Porous Media Flow and
Transport")
- Hongwen Sun ("Java Applets for Calculus")
- Patti Sylvia ("On Viscoelastic Flow Modeling Using Newton's Method")
- Melissa Twarek ("A Feasibility Study of ArcView Internet Map Server
Extension for the South Carolina Botanical Garden")
- Amy Ward ("A 2-D Flow and Transport Viewer")
- Ruth Wassermann ("Simulation of 2-D Contaminant Transport in Groundwater")
- Kristen Woodward ("A Graceful Approach: A Look at the Graceful Labeling Conjecture")
Recent Ph.D. Graduates (dissertation title)
- Russell D. Albright ("Independence Properties and Learning
in Graph-Theoretic Probability Representations")
- Mark E. Cawood ("Numerical Analysis of Algorithms which Solve the Multi-Input
State Feedback Robust Pole Assignment Problem")
- Walter F. Jones ("A Numerical Analysis of Richards's Equation for Unsaturated
Porous Media Flow")
- William W. Miles ("Modeling Time-Dependent, Multicomponent, Viscoelastic Fluid Flow")
- Louis Ntasin ("A Posteriori Error Estimation and Adaptive Computation of Viscoelastic
Fluid Flows")
- Tamra H. Payne ("Quantifying Error in the Analysis of Partitioning Interwell
Tracer Tests")
- John Paul Roop ("Variational Solution of the Fractional Advection Dispersion Equation")
- David Szurley ("Optimal Control for Polymer Process Modeling")
- Kelly Waters ("A Parallel Implementation of the Glowinski-Pironneau Algorithm for the Modified
Stokes Problem")
Current Ph.D. Students (dissertation advisor)
Additional Computational Math Links
Last Updated: June 30, 2005
Send comments to:shierd@clemson.edu