Co-Supervisor of Spencer Frei with Gantumur Tsogtgerel, McGill University, Summer 2012
Together with Gantumur Tsogtgerel, I helped oversee Spencer's summer research project involving weak convergence methods in PDE.
- Math 262: Intermediate Calculus
- Math 666: Seminar Math and Stats 1 Differential Geometry and Continuum Mechanics
Math 666 is a course I designed myself in which the students—both from mathematics and mechanical engineering—took turns presenting topics that I had selected in advance. The goal was to learn differential geometry and, at the same time, demonstrate how the tools of differential geometry can be used in continuum mechanics. The topics covered in this course were
Math 666 Class Dinner
- A Brief Introduction to Continuum Mechanics
- The Definition of a Manifold
- Tangent and Cotangent Spaces
- Applications of Tangent and Cotangent Spaces
- Multilinear Algebra
- Groups and Manifolds
- Lie Bracket and Lie Derivative
- Fiber Bundles
- Different Constructions of Space-Time
- The Material Groupoid
- Connections, Curvature, and Torsion
- Riemannian Geometry
- The Principle of Material Frame-Indifference
- Basic Inhomogeneity Theory
Carnegie Mellon University
- 21-105: Pre-Calculus
- 21-260: Differential Equations
- 21-127: Concepts of Mathematics
Seminars And Reading Groups
Organizer, Mathematical Biology Working Group, Spring 2014
This group meets weekly and allows graduate students and postdocs the opportunity to present their current work to other people in the mathematical biology group at the University of Dundee.
Co-Organizer, Geometric Measure Theory Reading Group, Spring 2012
and I organized a reading group for graduate students and postdocs based on the first few chapters of Geometric Measure Theory by Frank Morgan. We covered some basic properties the space of currents and some of its useful subspaces. We concluded the seminar with a compactness theorem and its application to Plateau's problem.
Co-Organizer, Operator Theory Reading Group, McGill University, Fall 2011
and I organized a reading group for graduate students and postdocs based on the first few chapters of Principles of Functional Analysis by Martin Scheshter. The two main topics that were covered were Riesz theory for compact operators and Fredholm operators.
Co-Organizer, Graduate Student Seminar, Carnegie Mellon University, 2009-2010
and I started a weekly seminar for graduate students to present whatever they are working on.