# 21-450: Differential Geometry Schedule and Homework

For each week there will be a link to a page with a reading assignment and a homework assignment.

This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.

 Week #1:  Aug. 27 - 31 Homework Structures on Rn Manifolds as subspaces of Rn Abstract Manifolds Week #2:  Sept. 3 - 7 Homework Differentiability of functions of Several Variables Administrative Note: Monday, September 3 is Labor Day. No Class. Week #3:  Sept. 10 - 14 Homework The space of Tangent Vectors at a Point of Rn Another Definition of Ta(Rn) Vector Fields on Open Subsets of Rn Week #4:  Sept. 17 - 19 Homework The Definition of a Differentiable Manifold Further Examples Differentiable Functions and Mappings Week #5:  Sept. 24 - 28 Homework The Tangent Space at a Point of a Manifold The Inverse Function Theorem The Rank of a Mapping Week #6:  Oct. 1 - 5 Homework Rank of a Mapping: Immersions Submanifolds Week #7:  Oct. 8 - 12 Homework Submanifolds Exam #1 will be given in class on Friday, October 12. Here is some more information about the exam Week #8:  Oct. 15 - 19 Lie Groups Administrative note: Friday, October 19 is the Mid-Semester Break. No Class. Week #9:  Oct. 22 - 26 Homework Lie Groups Vector Fields Administrative Note: Monday, October 22 is the Mid-Semester Break. No Class. Week #10:  Oct. 29 - Nov. 2 Homework Vector Fields(The Tangent Bundle) One Parameter Groups and Local One Parameter Groups Acting on Manifolds The Existence Theorem for Ordinary Differential Equations Week #11:  Nov. 5 - 9 Homework The Lie Algebra of Vector Fields on a Manifold Tangent Covectors Bilinear Forms: The Riemannian Metric Week #12:  Nov. 12 - 16 Homework Riemannian Manifolds as Metric Spaces Differentiation of Vector Fields along Curves in Rn Week #13:  Nov. 19 - 23 Differentiation of Vector Fields along Submanifolds in Rn Administrative note: Wednesday, November 21 through Friday, November 23 is the Thanksgiving Break. No Class. Week #14:  Nov. 26 - 30 Week #15:  Dec. 3 - 7 Final Exam:  Dec. 10 - 14 Administrative Note: Monday, Dec. 10 is the last day of Classes.