Differentiable Manifolds I, MATH 549, Spring 2020

Instructor: Daniel Groves, 727 SEO e.mail

Course webpage: http://www.math.uic.edu/~groves/teaching/2019-20/549/

Course hours:

MWF, 11:00-11:50AM, Room 304, Taft Hall. Starting Monday, March 30, all classes will be held online through webex. See Blackboard for instructions.

REMINDER: No classes (in person or online) the week of March 16 (extra week of Spring Break), or March 23 (ordinary Spring Break).

Office hours:

Mondays 10am and Fridays 2pm. Online through Webex.

(Or, you can make an apointment by e.mail or try stopping past my office.)

Text: "Introduction to smooth manifolds" by J.M. Lee, 2nd edition, Springer GTM, 2012.
Free eBook access through UIC library here.

Syllabus: Download here.

Course description:
This is a first year graduate course on smooth manifolds. We will introduce and study (smooth) manifolds, smooth maps, tangent spaces, vector fields and differential forms.

The plan is to cover most of the book in varying amounts of detail.

For this class, you will need to know some basic topology, and also linear algebra and calculus. Lee's book has Appendices on these topics which cover the necessary material.

Assessment: Homework sets will be due approximately every 1-2 weeks.
There will be a take-home midterm exam, due Monday, March 2, 2020.
There will be a take-home final exam (See below). Due on Friday May 8, by email.. The relative weightings of these items will be: Homework 50%, Midterm 20%, Final 30%.

Take-home Final: (Due Friday, May 8, 2020, by midnight Chicago time.) Download here.

Homework:

  • Due, Wednesday January 22, at the beginning of class. Do this homework.

  • Due, Monday, February 3, at the beginning of class. Do this homework. Note: updated due date.

  • Due, Wednesday, February 12, at the beginning of class. Do this homework.

  • Due, Wednesday, February 19, at the beginning of class. Do this homework.

  • Due, Monday, March 2, at the beginning of class. Do this midterm. (See the instructions on the exam.)

  • Due, Wednesday, March 11, at the beginning of class. Do this homework.

  • Due, Wednesday, April 1, at the beginning of class. Do this homework. NOTE: Updated due date.

  • Due, Wednesday, April 8, at the beginning of class. (Please submit via email, scanned handwritten pages are fine). Do this homework.

  • Due, Wednesday, April 15, at the beginning of class. (via email). Do this homework.

  • Due, Wednesday, April 22, at the beginning of class. (via email). Do this homework.