University Mathematics
Differential Geometry
The geometry of curves and surfaces in space, studied with the tools of calculus and linear algebra.
Curriculum / Syllabus
- Curves in the Plane and in Space
- Curvature, Torsion and the Frenet-Serret Frame
- Regular Surfaces and Tangent Planes
- The First Fundamental Form
- The Gauss Map and the Second Fundamental Form
- Gaussian and Mean Curvature
- Geodesics and the Gauss-Bonnet Theorem
Exam & Course Strategy
Exams combine heavy computation, such as the curvatures of given curves and surfaces, with short proofs. Organising the computation carefully matters as much as knowing the theory.