In addition to research, I also teach university-level mathematics courses.
This mainly involves preparing and delivering lectures and, in most cases, planning at least some of the course material itself.
I also do some grading of examinations, with the specific amounts depending on the situation.
MTH5109: Geometry II: Knots and Surfaces
- Position: Instructor
- Location: Queen Mary University of London
- Term: Fall 2017
- Course webpage (On QMPlus)
This is a second-year undergraduate course on the differential geometry of curves and surfaces, along with a brief excursion to knot theory.
Approximate list of topics covered, by week:
- Introduction (basic ideas in geometry and topology), parametric curves
- What is a curve (independence of parametrization), orientation, tangent lines
- Arc length, path/line integrals
- Curvature, plane curves (signed curvature, winding number)
- Space curves (torsion), knots
- Reidemeister theorem, knot invariants
- (Reading week, no classes)
- Jones polynomial, parametric surfaces
- What is a surface, tangent planes
- Unit normals, orientation, first fundamental form
- Surface area, surface integrals, second fundamental form
- Principal, mean, and Gauss curvatures; Theorema egregium; Gauss-Bonnet theorem