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May 11, 2024
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MA 5531 - Introduction to Manifolds This course introduces the concept of a manifold, and uses it to explain how the traditional Euclidean and non-Euclidean geometries are simply special cases of this more general type of space. Specific topics will include the curvature of curves and surfaces, geodesics, topology of surfaces, the Gauss-Bonnet theorem, introduction to 3-manifolds, and visualizing the curvature of space.
Prerequisites & Notes Upper-level undergraduate course in geometry.
Credits: 3 SH
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