Manifolds

Manifolds are a basic concept that unite ideas from linear algebra, multivariable calculus, geometry, and topology. Math and physics research require a familiarity with manifolds. Topics covered include the definition of a smooth manifold either as a smooth subset of R^n or as an abstract manifold, coordinating charts, and transition functions. The course will cover concrete examples: e.g. surfaces and 3-manifolds.Other topics include tangent vectors, vector fields, tensors, exterior algebra, differential forms, change of coordinates, Stokes’ Theorem and the basics of De Rham cohomology.