MAT 295-01 - Special Topic: Differential Geometry

4 credits (Fall)

Einstein showed that gravity may be viewed as curvature of space-time. Curvature makes sense when we view a surface from outside, but how can we understand or study curvature from within a space? This course will introduce the tools mathematicians use for such study, and will thus serve as the mathematical background needed for understanding General Relativity. Topics will include tangent spaces and vector fields, differential forms, tensors, Lie derivatives, geodesics, and the Riemannian connection.

Prerequisite: MAT 133 and MAT 215.
Instructor: French

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