Math 5193 - Smooth Manifolds

http://math.okstate.edu/people/lebl/osu5193-f15/

Lectures: M 2:30 - 3:45, Th 2:30-3:45, MSCS 509
Problem session: F 2:30-3:20, MSCS 509

Lecturer:

Jiří Lebl
Web: http://math.okstate.edu/people/lebl/
Office: MSCS 505
Office hours: Monday 4-5pm, Wednesday 11:30-12:30pm, Thursday 4-5pm, and by appointment at other times.
Office phone: (405) 744-7750
Email: lebl at okstate dot edu

Text/Schedule:

John M. Lee, Introduction to Smooth Manifolds, Second edition, 2013, Springer.

The link above is a link to Springer, and we have electronic access to the book at OSU, so you can read it online if you wish (as PDFs).

Grading/Homework:

We will have weekly homework and we will have a problem session to go over the homework problems in (you should try to solve them before hand). Your grade will be based on participation in the problem session.

Homework:

Homework 1, for problem session on Friday Aug. 21:
page 30: 1-3, 1-4, 1-5

Homework 2, for problem session on Friday Aug. 28:
page 30: 1-6, 1-7, 1-8, 1-9, 1-10 (feel free to "pick and choose" of course, these should all be fairly straight forward though).

Homework 3, for problem session on Friday Sep. 4:
page 30: 1-11, 1-12
page 48: 2-1, 2-3, 2-5, 2-6, 2-7, 2-9, 2-10 (you should definitely try this one)

Homework 4, for problem session on Friday Sep. 11:
We can go through more of hw 3. And also
page 75: 3-1, 3-5

Homework 5, for problem session on Friday Sep. 18:
We can go through more of hw 3. And also
page 75: 3-2, 3-3, 3-4, 3-6, 3-8

Homework 6, there is no problem session on Friday, though you guys can still meet if you want to, I can't be there:
page 95: 4-1, 4-5, 4-6, 4-8, 4-13

Homework 7, for the problem session on Friday Oct. 2:
page 123: 5-1, 5-4, 5-5, 5-6, 5-7, 5-11, 5-15

Homework 8, unfortunately no class on Friday, but look at these problems:
page 123: 5-16, 5-18, 5-19, 5-21, 5-22

Homework 9, for the problem session on Friday Oct. 16:
We can also look at the previous problems.
page 147: 6-1, 6-2

Homework 10, for the problem session on Friday Oct. 23:
page 147: 6-5, 6-8, 6-9, 6-11, 6-14, (and maybe 6-16, 6-17)

Homework 11, for the problem session on Friday Oct. 30:
page 171: 7-1, 7-2, 7-3, 7-4, 7-6, 7-7

Homework 12, for the problem session on Friday Nov. 13:
page 199: 8-2, 8-3, 8-6, 8-9, 8-10, 8-13

Homework 13, for the problem session on Friday Nov. 20:
page 245: 9-1, 9-2, 9-3, 9-4, 9-5, 9-6, 9-7

Homework 14, for the problem session on Friday Dec. 4:
page 299: 11-1, 11-2, 11-4, 11-7, 11-13, 11-15, 11-17

Useful books for reference:

Boothby, Introduction to Differentiable Manifolds and Riemannian Geometry - Another book about at our level

R. Narasimhan, Analysis on Real and Complex Manifolds - Very good book, though maybe somewhat advanced.

Spivak, Calculus on Manifolds - Very nice and short intro, but only does submanifolds of euclidean space, so more basic than what we are doing. Might be nice to look at for a different point of view.