Arick Shao 邵崇哲


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.

Current Teaching

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:

  1. Introduction (basic ideas in geometry and topology), parametric curves
  2. What is a curve (independence of parametrization), orientation, tangent lines
  3. Arc length, path/line integrals
  4. Curvature, plane curves (signed curvature, winding number)
  5. Space curves (torsion), knots
  6. Reidemeister theorem, knot invariants
  7. (Reading week, no classes)
  8. Jones polynomial, parametric surfaces
  9. What is a surface, tangent planes
  10. Unit normals, orientation, first fundamental form
  11. Surface area, surface integrals, second fundamental form
  12. Principal, mean, and Gauss curvatures; Theorema egregium; Gauss-Bonnet theorem

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