• You are encouraged to discuss ideas with other students. Nonetheless, every piece of work you turn in must be your own. 
• Introduction to differential geometry. Topics
  include differentiable manifolds, vector fields, tensor
  bundles, the Frobenius theorem, Stokes’ theorem, Lie
  groups. Prerequisite: MATH 6410
  

This syllabus is meant to be a tentative schedule for the semester.

Week	Topic(s)/Sections Covered	Homework	DueDate /Solution
Aug. 21	Ch 1. Smooth manifolds:	hw1(pdf) hw1(tex)
Aug. 28	Ch 1. Smooth manifolds:
Sep. 4	Ch 2 Smooth Maps
Sep. 11	Ch 2 Smooth Maps
Sep. 18	Ch3  Tangent Vectors	hw2(pdf) hw2(tex)
Sep  25	Ch4 Vector fields
Oct. 2	Ch6 The Cotangent Bundle
Oct. 9	Ch 7 Submersions, Immersions and Embedding Ch 8 Submanifolds
Oct. 16	Fall break Ch 11 Tensors
Oct. 23	Ch 7 Submersions, Immersions and Embedding
Oct. 30	Ch 8 Submanifolds   curves and Flows
Nov. 6	Ch 8 Submanifolds Lie Derivatives
Nov.13	Embedding Theorem   Manifolds and Foliations
Nov. 20	Thanksgiving   Embedding Theorem
Nov. 27	Lie groups & Lie algebra p37-p30, p93-p100	Take home Final (pdf) Take home Final(tex)
Dec. 4	Lie subgroup 194-199 on Manifolds Last day of class (Dec. 8)