This term of the 225 sequence will cover vector fields, differential forms, and associated topics (integral curves, the Frobenius Theorem, Lie derivative) together with an introduction to cohomology from the differential forms viewpoint (deRham cohomology).The text is Spivak, A Comprehensive Introduction to Differential Geometry, volume 1.

This material is interesting in its own right, and it is crucial to modern differential geometry, geometric analysis, mathematical physics, and topology. Please note that the contents of the course are distinctly different from the contents of Math 225B in previous years. The 225 sequence has been revised. The 225B term used to consist of an introduction to algebraic topology in the standard terms of fundamental group and singular homology and cohomology theory, and the material now to be in 225B was formerly covered in 225A. The algebraic topology material is now deferred to 225C, and 225A is now devoted to differential topology. This change is official and permanent but has not been noted in all the descriptions, on line and otherwise. More details of the organization of the present course and its contents will be presented on the first day of class.