Math 549: Differentiable Manifolds I

David Dumas

University of Illinois at Chicago
Fall 2017

[Boy's Surface]
Boy's surface: An immersion of the projective plane into R3.
Main Text J. M. Lee, Introduction to smooth manifolds, 2ed, Springer GTM, 2012.
(Free ebook access through UIC library)
Other Texts W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2ed, Academic Press, 1986.
F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer GTM, 1983.
Lectures MWF 9:00am in Taft 305
Optional make-up lecture: Dec 11, 9:00am, in Taft 305
Office SEO 503
Office hours Monday 2-3 in SEO 503
Wednesday 11-12 in MSLC (SEO 430)
or by appointment
CRN 38306

About the final exam

The final exam will be held on Tuesday December 12, 10:30am-12:30pm in Taft Hall 305 (our usual classroom).

The exam will have a total of six problems, of which you will be required to complete any four.

The exam is cumulative. There will be a slight emphasis on material covered after the midterm.

The exam problems will be shorter than most of the homework problems, but similar in overall difficulty.


Calendar & Grading

This is a condensed summary of some important dates and the weights used to compute your course grade. The course syllabus is the definitive reference for course policies.
Date/time Course grade fraction
Homework Most Mondays (See list below.) 40%
Take-home midterm Due Mon Oct 16 at 9:00am in class 20%
Final Exam Tue Dec 12, 10:30am-12:30pm 40%


Homework should be submitted directly to the mailbox of the grader, Victor Jatoba, in the third floor mailroom of SEO by 1:00pm on the date indicated.

Note that the submission procedure for the midterm exam is different; it will be collected by the instructor at the beginning of lecture on October 16.

Typeset solutions are encouraged but not required. If writing solutions by hand, please make sure they are legible. Staple homework if it spans several sheets of paper.

Many of the homework problems are assigned directly from the primary textbook. Some other problems are modified versions of exercises in the primary or secondary textbooks (as indicated by a tag with the author's name) or are adapted from the following sources:

Extra problems


Some pathologies and counterexamples


Students who are learning TeX / LaTeX and who want to typeset their homework may find this template helpful:
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