MATH 42 Differential Geometry I

This course will cover curves and surfaces in Euclidean 3-dimensional space. Topics include curvature and torsion of curves, the Frenet-Serret equations, Gaussian and mean curvature of surfaces, geodesics and parallel transport, isometries and Gauss's Theorem Egregium, the Riemann Curvature tensor. One or more of the following topics will be studied if time permits: vector fields, tangent bundles, hypersurfaces, connections, and curvature. Offered in alternate years.

Instructor

Tyomkin

Prerequisite

MATH 22 or MATH 24 or permission of the instructor, and MATH 23.

Degree Requirement Attributes

QDS

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