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.

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