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Differentiable Manifolds


Multilinear algebra of finite dimensional vector spaces over fields; differentiable structures and tangent and tensor bundles; differentiable mappings and differentials; exterior differential forms; curves and surfaces as differentiable manifolds; affine connections and covariant differentiation; Riemannian manifolds.


"Lectures on Differential Geometry", Chern, Chen and Lam, World Scientific, 1980.


MATH 765 and 790 or 792.

Credit Hours: 

Syllabus: This course is an introduction to the theory of differential geometry, covering the basic topics like differentiable manifolds, submanifolds, smooth maps, (co)tangent bundles, vector fields, Lie bracket, differential forms, exterior derivative, deRham cohomology, connections, curvatures, Riemannian metrics, etc. More advanced special topics like Riemannian, symplectic, or Poisson geometry may be included if time permits.

(Lerner 2011 )


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Nicole Johnson found a way to express her baton twirling using math.  See video.