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Differential geometry studies local and global properties of curved spaces.

Topics of the lecture will be:

• Curves and surfaces in Euclidean space
• Metrics and (Riemannian) manifolds
• Surface tension and notions of curvature
• Vector fields, tensors, covariant derivative
• Geodesic curves, exponential map
• Gauß-Bonnet theorem, curvature and topology
• Connection to discrete differential geometry

Prerequisits: Analysis I, II and Linear Algebra I, II