MAT1300, Fall 2014


MAT1300 (Topology I) - Fall 2014
Faculty: Vitali Kapovitch Office: HU 1023 Telephone: (416)-978-6786 email: vtk@math.toronto.edu Office Hours : Tue 2-4 pm and by appointment "He who asks is a fool for five minutes, but he who does not ask remains a fool forever". -- Chinese Proverb	Grader : James Mracek Office: HU 1027 Telephone: 416-946-4008 email: jmracek@math.toronto.edu Homework marking questions: Th 1-2 pm

The Text for this course: "Introduction to Smooth Manifolds" by John M. Lee, 2nd edition.

"Introduction to Smooth Manifolds" by John M. Lee: Chapters 1-6, 8, 9, 11, 12, 14-16. If time allows also Chapters 17-18.
Supplemental material from lectures.

Homework- 25%
Term Test - 30%
Final Exam - 45%

Homework assignments will be posted every Thursday. It will be due the following Thursday at the lecture.
Please staple your homeworks. Unstapled homeworks will be penalized 2 points.
NO late homework will be accepted. If you have questions or complaints about marking of homework please first contact the grader, James Mracek (his contact info is at the top of the page). If you are still unsatisfied after talking to him you can talk to me.
Important: There will be no make up midterms! If you have a valid reason to miss the term test, the corresponding portion of the Final exam will count as your term test grade.

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 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.
Here are the notes on exterior derivatives, de Rham cohomology and orientation from November 18.
Here are the notes on differential forms.
Here are the notes on the lectures on tensor algebra.
Here are the solutions to problem 14-2 from homework 8.
Here are the solutions to the term test. Please go over them carefully and make sure you understand how to do all the problems.

Here are the solution to problem 2-14 from homework 3.
Here are the notes for lecture 5 on September 23.
If you have questions or complaints about marking of homework please first contact the grader, James Mracek (his contact info is at the top of the page). If you are still unsatisfied after talking to him you can talk to me.
Short notes on Lecture 3.
Short notes on Lecture 2.
Short notes on Lecture 1.

Term Test

Final Exam