Math 396: Honors Analysis II

Professor: David E Speyer

Winter 2018

Overview: This course has a bit of a scattered collection of topics, but is ultimately heading towards the construction of abstract manifolds and the proof of Stokes theorem.

In January, I will cover a collection of linear algebra topics which usually do not make it into a first course, such as tensors and Jordan normal form. We'll then discuss the formalism of differential k-forms. Our main topic after this will be the study of manifolds.

Course meets: Monday, Wednesday, Friday 2:30-4:00; 1518 CC Little

Office Hours: I will hold office hours 2844 East Hall, Wednesday 9:30-12:00 and Thursday 1:00-3:30. Noah and Jin will hold office hours Thursday 5:30-6:30 in the Nesbitt room. The discussion section will meet Wednesdays 4:00-5:00, in a location to be determined. I am also glad to make appointments to meet at other times.


Teaching Assistants: Wenyu Jin (wyjin AT umich) and Noah Luntzlara (nluntzla AT umich).

IBL Fridays: I will continue to use most Fridays for IBL problems. This term, I think I will more often use them for short topics that tie to the rest of the material, rather than take on a major theme such as Lie groups, although I do have some Lie group problems I want to tackle in the second half of the course. I will assign students in pairs to write up the solutions to the problems for particular days. Here is the schedule of recorders, and the notes to date.

Student work expected: I will assign weekly problem sets, due on Fridays in class. I will drop the lowest two homework grades.

There will be an in class exam near the end of February, most likely Wednesday the 21st. The final exam will be Monday, April 23, from 1:30 pm to 3:30 pm.

Grading: I will combine your grades into a numerical score, which will then be turned into letter grades by a curve which I expect will be quite generous. The numerical score will be computed as follows: 60% homeworks, 10% for the midterm, 20% for the final, 10% for participation in the Friday discussions and in recording the results of them.

Homework Policy: You are welcome to consult each other provided (1) you list all people and sources who aided you, or whom you aided and (2) you write-up the solutions independently, in your own language. If you seek help from mathematicians/math students outside the course, you should be seeking general advice, not specific solutions, and must disclose this help. I am, of course, glad to provide help, as are your TA's Noah Luntzlara and Wenyu Jin.

I don't intend for you to need to consult books and papers outside your notes. If you do consult such, you should be looking for better/other understanding of the definitions and concepts, not solutions to the problems.

You MAY NOT post homework problems to internet fora seeking solutions. Although I participate in some such fora, I feel that they have a major tendency to be too explicit in their help; you can read further thoughts of mine here. You may post questions asking for clarifications and alternate perspectives on concepts and results we have covered.

Seeking problem solutions from people and sources outside this course, or directly copying solutions from your fellow students, is plagiarism and will meet severe consequences.

Problem Sets

Problem Set 1 (TeX) due Friday January 12.

Problem Set 2 (TeX) due Friday January 19.

Problem Set 3 (TeX) due Friday January 26.

Problem Set 4 (TeX) due Friday February 2.

Problem Set 5 (TeX) due Friday February 9.

Problem Set 6 (TeX) due Friday March 9.

Problem Set 7 (TeX) due Friday March 16.

Problem Set 8 (TeX) due Friday March 23.

Problem Set 9 (TeX) due Friday March 30.

Problem Set 10 (TeX) due Friday April 6.

Problem Set 11 (TeX) due Friday April 13.

Useful links

Brian Conrad's notes on paracompactness. Actually, while I'm at it, all of Brian Conrad's notes are quite impressive.