CIS 610, Spring 2011

Brief description:

This course covers some basic material on manifolds, Riemannian Geometry, and Harmonic Analysis, keeping in mind applications of these theories to medical imaging, computer vision, computer graphics and machine learning. The treatment will be rigorous but I will try very hard to convey intuitions and to give many examples illustrating all these concepts.


  1. Manifolds, Tangent Spaces, Cotangent Space
  2. Riemannian Manifolds and Connections
  3. Geodesics on Riemannian Manifolds
  4. Curvature in Riemanian Manifolds
  5. Spherical Harmonics

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Jean Gallier