(he/him/his)

Computational mathematician, focused on large-scale scientific computation.

Graduate and Upper-level Undergraduate Courses in Computational Mathematics

Current courses

Southern Methodist University, Department of Mathematics, Fall 2024

Fall 2024: None (on sabbatical)

Math 6317 – Numerical Methods II

Graduate, Southern Methodist University, Department of Mathematics

Covers interpolation and approximation of functions, numerical differentiation and integration, basic methods for initial value problems in ordinary differential equations, and basic approximation methods for one-dimensional initial-boundary value problems. Topics focus on algorithm development and the theory underlying each method.

Math 6316 – Numerical Methods I

Graduate, Southern Methodist University, Department of Mathematics

The efficient solution of dense and sparse linear systems, least squares problems and eigenvalue problems. Elementary and orthogonal matrix transformations provide a unified treatment. In addition to algorithm development, the course emphasizes the theory underlying the methods.

Math 5316 – Introduction to Matrix Computation

Undergraduate, Southern Methodist University, Department of Mathematics

The efficient solution of dense and sparse linear systems, least squares problems, and eigenvalue problems. Elementary and orthogonal matrix transformations provide a unified treatment. Programming is in MATLAB, with a focus on algorithms.

Math 5315 – Introduction to Numerical Analysis

Undergraduate, Southern Methodist University, Department of Mathematics

Numerical solution of linear and nonlinear equations, interpolation and approximation of functions, numerical integration, floating-point arithmetic, and the numerical solution of initial value problems in ordinary differential equations. Student use of the computer is emphasized.

Math 4315 – Advanced Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

Advanced algorithms central to scientific and engineering computing. Topics include solution of linear systems of equations, functional approximation, initial-value problems, and boundary-value problems. Special attention is given to algorithm derivation and implementation.

Math 3316 – Introduction to High-Performance Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

An elementary survey course that includes techniques for root-finding, interpolation, functional approximation, linear equations, and numerical integration. Computational work focuses on the Python and C++ programming languages using Linux.

Math 3315 – Introduction to Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

An elementary survey course that includes techniques for root-finding, interpolation, functional approximation, numerical differentiation and numerical integration. Special attention is given to MATLAB programming, algorithm implementations, and library codes. Students registering for this course must also register for an associated computer laboratory.

Math 3304 – Introduction to Linear Algebra

Undergraduate, Southern Methodist University, Department of Mathematics

Matrices and linear equations, Gaussian elimination, determinants, rank, geometrical notions, eigenvalue problems, and coordinate transformations, norms, inner products, orthogonal projections, Gram-Schmidt and least squares.

Math 3302 – Calculus 3 / Multivariable Calculus

Undergraduate, Southern Methodist University, Department of Mathematics

A continuation of Calculus 2. Topics include arametric equations, polar coordinates, partial differentiation, multiple integrals, and vector analysis.

SMU HPC Workshops

Graduate, Southern Methodist University, Department of Mathematics

Inaugural SMU HPC workshops, sponsored by the SMU Center for Scientific Computation. These focused on general high-performance computing computing, with specific instruction on using the new SMU ManeFrame cluster.

Math 174 – Numerical Methods in Science and Engineering

Undergraduate, University of California, San Diego

Floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations.

Math 20D – Introduction to Differential Equations

Undergraduate, University of California, San Diego

Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Systems. Series solutions. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using MATLAB.

CAAM 335 – Matrix Analysis (Teaching Assistant)

Undergraduate, Rice University, Department of Computational and Applied Mathematics

Equilibria and the solution of linear systems and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration. Optional 1-credit laboratory motivates concepts from the course via physical experiments involving circuits, spring networks, and vibrating mechanical systems.