Current course offerings

Please Note: Course profiles marked as not available may still be in development.

Course description

Curves: Parameterised curves, regular curves, arc length. Local theory, Frenet frame. Global properties of plane curves. Regular surfaces: Change of parameterisation, differential functions on surfaces. The tangent plane, the differential of a map. First fundamental form, area functional. Geometry of the Gauss map: fundamental properties, local coordinates. Vector fields. Minimal surfaces and other applications. Intrinsic and extrinsic geometry of surfaces: isometries, conformal maps. Selected topics from: Theorema egregium. Parallel transport, geodesics. Gauss-Bonnet Theorem and applications. Exponential map. Geodesic polar coordinates. Introduction to smooth manifolds.

Archived offerings