Note about diffeological submanifolds.
Note about smooth functions on embedded submanifolds.
Vitaly Kuznetsov's note on the notion of smooth embeddings.
(These notes were posted after the course ended, for possible future usage.)

Comment on Question (1)(a) from the exam.

Description of the marks distribution

Here are the homework problems that were not from the book:

• From homework 6;
• From week 8 (homework 7?) ;
• From week 10 (homework 9?) .

Instructor:   Professor Yael Karshon
Email:   karshon@math.toronto.edu
Office hours:   after class, or by appointment.
Office:   BA 6119,   (416) 978-7895

TA:   David Li-Bland

Lectures: Wednesdays and Fridays, BA6183, 9:30 - 11:00 am,
except that from Sept.21 through Oct.7 we'll meet 9:10 - 11:00 am.
Professor Karshon will be away on the week of Nov.28th.

Rough outline: Manifolds, smooth maps, tangent bundles;
immersions, submersions, transversality, smooth approximations;
differential forms, integration, de Rham cohomology;
flows, Lie derivatives.

Textbook: John M. Lee, Introduction to Smooth Manifolds (also see the corrections linked from here).

• Raoul Bott and Loring Tu, Differential Forms in Algebraic Topology.
• Theodor Brocker and Klaus Janich, Introduction to Differential Topology.
• Glen E. Bredon, Topology and Geometry
• Victor Guillemin and Alan Pollack, Differential Topology
• John M. Lee, Introduction to Topological Manifolds
• John Milnor, Topology from the Differentiable Viewpoint
• George De Rham, Differentiable Manifolds
• Michael Spivak, A Comprehensive Introduction to Differential Geometry
• Frank W. Warner, Foundations of Differentable Manifolds and Lie Groups

Prerequisites: Linear algebra; vector calculus; point set topology.

Requirements for credit: participation 5%, assignments 50%, final exam 45%.

• You are encouraged to discuss the problem sets with friends. But you must write
  the solution later, on your own. You may not read each other's written solutions
  before their submission.
• Late problem sets will not be accepted. Please hand in whatever you have
  at the deadline, even if you feel that you could do much better.