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 R^{n}
Manifolds as subspaces of R^{n} 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 R^{n}
Another Definition of T_{a}(R^{n}) Vector Fields on Open Subsets of R^{n} 
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 MidSemester Break. No Class. 
Week #9:
Oct. 22  26 Homework 
Lie Groups
Vector Fields Administrative Note: Monday, October 22 is the MidSemester 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 R^{n} 
Week #13:
Nov. 19  23 
Differentiation of Vector Fields along Submanifolds in R^{n}
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. 