The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of surfaces in Euclidean space. For this, you'll need a solid background in multivariable calculus and linear algebra. The plan is to get as far as the proof of the Gauss-Bonnet Theorem,
and at the same time to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.
Prerequisites. MAT 205 (Calc III) and MAT 210 (Linear Algebra).
Meetings: Tuesdays and Thursdays 1-2:20PM in Library W4535
Text
Do Carmo, Differential Geometry of Curves and Surfaces
Homework
will be due at the first meeting each week.
Grading
Final grade will be determined by Midterm scores
(25% each), homework (15%) and final exam (35%). A grade will also
be computed on the final exam alone; student gets the better of the 2.
