Basic Information

• Instructor: Eugene Lerman
• e-mail: lerman at illinois edu
• Homepage: lerman.web.illinois.edu/
• Course page: lerman.web.illinois.edu/518/f23/518f23.html
• Office: 37 CAB
• Office Hours: see my calendar and/or by appointment
• Phone: 244-9510
• Class meets: MWF 12:00-12:50 pm    in Davenport Hall 136
• Hand-written lecture notes will posted  here
• I plan to collect homework on Moodle (Moodle login help is here )

Prerequisites

Point set topology (``abstract'' topological spaces and continuous maps, product and disjoint union topologies, the notion of being Hausdorff, second countability, connectedness, path connectedness, compactness and local compactness... and probably a few more things), linear algebra and some analysis (e.g., multivariable inverse function theorem).
If you have any questions or concerns, please talk to me or contact me by e-mail.

Course outline

1. Manifolds: Definitions and examples including projective spaces and Lie groups; smooth functions and mappings; submanifolds; Inverse Function Theorem and its applications including transversality; tangent and cotangent vectors, tangent and cotangent bundles, vector bundles in general; manifolds with boundary; orientations.


2. Calculus on Manifolds: Vector fields, flows, and Lie derivative, Lie bracket; differential forms and the exterior algebra of forms; orientations again; exterior derivative, contraction, and Lie derivative of forms; integration and Stokes Theorem, DeRham cohomology.
    

Recommended Texts

• Introduction to Smooth Manifolds by John M. Lee, Springer, ISBN: 978-1-4419-9981-8 (Print) 978-1-4419-9982-5  [free online access from a campus computer]
• Foundations of Differentiable Manifolds and Lie Groups  by Frank W. Warner [free online access from a campus computer]
   

• Homework: Homework problems are to be assigned once a week. They are due the following week usually before midnight on Wednesdays. Late homework will be penalized. There are several reasons why I want the homework to be turned in on time. First of all, if you are not keeping up with the homework, you are not keeping up with the class, and then you may well get lost in the lectures. Secondly, it is hard to grade fairly the homework that is turned in late. The grader would have to keep careful track of the grading rubrics and so on. In short: late homework is bad for you and means more work for the grader.

  If you have questions about your homework score please take it up with the grader first. If you and the grader can't resolve the issue I will step in.

  If you have questions about the homework itself, please use the forum on Moodle and/or see me in the office hours.  If you email me with a question about homework I will likely post your question on Moodle and reply there.

• Grades: The course grade will be based on weekly homework (35%), a midterm (25%) and a final (40%). The formula is here to give you a sense of how you are doing in class. The formula is not set in stone and I may deviate by a point or two in either direction. This said, I strongly recommend studying for the final no matter how well you are doing on the midterm and the homework. Failing the final is a bad idea and could make it hard to impossible for me to give you a passing grade.

• Exams: The midterm will take place on  October 11 in the regular classroom (Davenport Hall 136)  

         The final, according to the non-combined final examination schedule is to take place on Friday, December 15 1:30pm-4:30pm in the regular classroom (Davenport Hall 136)

         Requests for a make-up exam require a serious documentation and are almost never granted.

Attendance is expected

Academic Integrity

Campus police safety information. Plus a one page handout

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Last modified: Tuesday, Aug 15, 2023