Teaching

CU Boulder

APPM 4600: Numerical Analysis and Scientific Computing

This upper-division undergraduate course covers the classic numerical analysis techniques including root finding for functions and nonlinear systems of equations, interpolation, approximation, quadrature, some numerical linear algebra and an introduction to numerical differential equation. The course includes a weekly lab where students work on developing scientific computing skills in Phython including writing low level code in a portable manner and some introduction to parallel computing. Additionally, students maintain a GitHub repository. The semester culminates with a project where students work on their technical writing while pushing beyond the course material applying to problems of interests to them.

APPM 4610: Numerical Differential Equations

This upper-division undergraduate course introduces students to techniques for approximating solutions to differential equations. Topics include time stepping techniques for initial value problems such as finite differences and Runge-Kutta methods, techniques for one dimensional boundary value problems including finite difference, finite element, spectral collocation and integral equation methods. Then the time stepping techniques are put together to tackle approximating solutions to the heat equation. Convergence analysis for these partial differential techniques are investigated. Like APPM 4600, the semester culminates with a project where students tasked to push beyond the course material and apply techniques to problems of interest to them.

APPM 5600: Graduate Numerical Analysis

This first year graduate student course prepares graduate students for the preliminary examination. Topics covered include root finding, nonlinear system, interpolation, approximation, and some numerical linear algebra. This course involves more analysis than the corresponding undergraduate course.

APPM 4650: Numerical Analysis

This is the old version of the numerical analysis course. In Fall 2021, this course began transitioning to the APPM 4600 format.

Rice University

CAAM 551: Numerical Linear Algebra

This graduate course covers stability of classic linear algebra techniques including QR and LU factorizations. Direct solvers of sparse linear systems are also covered. As are state of the art linear techniques including rank revealing QR, randomized linear algebra and fast direct solvers.

The goal of this course is to give graduate students the background so they are knowledgeable users of linear algebra software and have the ability to integrate state of the art linear algebra techniques into their research.

Semester: Fall 2018

CAAM 536: Numerical Methods for PDEs

This graduate course covers Finite Difference, Finite Element methods and one other discretization technique of the professors choice. When Dr. Gillman teaches this course the recently developed HPS (Hierarchical Poincaré-Steklov) method.

The goal of this course is to introduce engineering graduate students to discretization techniques they will come across in their research. Students finish the term being able to read papers on numerical PDEs, write their own codes and be knowledge users of commercial PDE software.

Semesters: Spring 2018, Spring 2017, Spring 2016

CAAM 336: Differential Equations in Science and Engineering

This undergraduate course covers Finite Difference, Finite Element and Fourier Spectral methods for solving two point boundary value problems and PDEs that are first order in time. Each method is derived from calculus and linear algebra.

The goal of this course is to introduce engineering undergraduate students to numerical methods.

Semesters: Fall 2017, Fall 2016

CAAM 553: Numerical Analysis

This graduate course provides first year graduate students the numerical analysis tools that are the foundations of applied mathematics. Topics include interpolation, quadrature, root finding, and methods for finding eigenvalues.

The goal of this course is to prepare graduate students for research and the qualifying exam.

Semesters: Fall 2015, Fall 2014

CAAM 652: Topics in numerical differential equations

This special topics course introduces graduate students to boundary integral equations and fast direct solvers for dense linear systems.

Semesters: Spring 2015

Dartmouth College

Spring 2014 Math 13: Multivariable Calculus

Math 46: Introduction to applied mathematics

Fall 2013 Math 53: Chaos!

Spring 2013 Math 46: Introduction to applied mathematics

Winter 2013 Math 8: Caluculus of one and several variables

Math 126: Partial Differential Equations

Spring 2012 Math 23: Differential Equations

Winter 2012 Math 23: Differential Equations

Fall 2011 Math 8: Caluculus of one and several variables