• Final Exam Review will take place on Friday, December 5, 5-7pm in BA6183.
• The Final will take place on Monday, December 8, 10-1 in BA6183. 
• It will cover  everything we've covered in class, lecture notes and on homework. Specifically, it will cover the following material:
  
• Chapter 1: Generalized manifolds (not in the book) + everything in this chapter except for topological manifolds.
• Chapter 2: Everything.
  
• Chapter 3: Everything except functors.
• Chapter 4: Everything except for covering maps.
• Chapter 5: Submanifolds, embeddings.
• Chapter 6: Sard's Theorem, Whitney embedding theorem for compact manifolds.
  
• Chapter 8 : Vector fields, criteria of smoothness, sufficient condition for the triviality of the tangent bundle.
• Chapter 12: Everything except tensor products of vector spaces.
• Chapter 14:  Alternating tensors, cotangent bundle, tensor bundles on manifolds, differential forms, exterior derivatives.
• Chapter 15: Orientations on vector spaces, orientations on manifolds.
• Chapter 16: Integration of forms, Stokes's Formula, applications to De Rham cohomology

• Rules for the Final : No aids allowed. No calculators or notes!
  

• We will have a Review Session on Friday, December 5, 5-7pm. I will post a room number later.
  

• Here are some practice problems on recent material (including Stokes's formula) to help you prepare for the Final.