MATH 305 - The Geometry and Topology of Manifolds

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FA, alternate years. An introduction to the study of manifolds, including both the geometric topology and the differential geometry of manifolds. The emphasis is on low-dimensional manifolds, especially curves and surfaces. Topics include the topology of subsets of Euclidean space, curves and surfaces in Euclidean space, the topological classification of compact connected surfaces, smooth curves and surfaces, curvature, geodesics, the Gauss-Bonnet Theorem and the geometry of space. Prerequisites: MATH 270 or MATH 271 and MATH 231, MATH 255 or MATH 355.