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.

Office hours:

Mondays 10am and Fridays 2pm.

(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 (date to be determined).
There will be a take-home final exam (date to be determined). The relative weightings of these items will be: Homework 50%, Midterm 20%, Final 30%.

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.