Math 208 = Manifolds I = Intro to Mfds. Fall 2017

  • Standard text: Introduction to Smooth Manifolds by John M. Lee. Any edition.
  • Other texts: There are probably over one hundred texts covering an Introduction to manifolds and calculus on them besides Lee. One significantly more concise than Lee I can recomment is Bishop and Goldberg . I first learned from Warner which also covers the de Rham theory, and from `Gravitation' by Misner, Thorne and Wheeler. A text even more leisurely than Lee is volume one of Spivak's five volume set `` A comprehensive introduction to differential geometry''. I urge you to take a look at some other texts.
  • Very highly recommended additional text: Milnor: Topology from the differentiable viewpoint.

  • Preparation requirements: point-set topology, active knowledge of basic analysis and linear algebra.

  • Office Hours: (tentative!) M: 8-9AM. F: 11:40 to 1:15.

  • Material: The definition of a smooth manifold. Examples: spheres, orthogonal groups, projective spaces, spaces of lines, Grassmannians, ... The IFTs. Regular and critical points and values for maps. Sard. The tangent bundle. Vector fields, their flows and Lie brackets. Partitions of Unity. Whitney embedding thm. We will cover Chapters 1-5, 8, 9 of the textbook and some parts of Chapters 6, 7 and 10.

    Syllabus.
    Problems.
    tentative lecture schedule

    More Homework; .
    Homework Solutions; .
    lecture notes


    `Self-contained intro to Lie Derivatives ; nice notes. thx for the find Nigel

  • Coursework: There will be weekly homework sets OR in-class problems, an in-class midterm, and a take-home final.