Math 213: Advanced Differential Geometry
Fall 2007

Contents of this page

Late breaking news
Lecture time and location
Prerequisite
Office hours
Textbook
Syllabus
Exams
Grading policy
Handouts
Homework
Policy on calculators
Academic integrity
Anonymous feedback

Late breaking news

(12/21) I just posted HW 10 solutions and final exam solutions. I will also post your survey papers as soon as I receive the final version from each of you (if what I already have is final, please let me know). If you would like to find out your grade, please email me.

Happy holidays and have a fun winter break!

(12/11) Homework 9 solutions have been posted.

(12/10) The final exam has been posted and is due on December 17 by 2 PM. You can give it either directly to me or to staff in MH 308 and they wil put it in my mailbox. Good luck!

Also, I will put all the remaining graded homework assignments in an envelope just outside my office.

(12/6) There was a typo in the posting of HW 10: the chapter numbers are VII and VIII, not VIII and IX (there's no chapter IX in Boothby!).

(12/5) My office hours after the last day of class will be:

Wed. 12/12: 10-12, 2-4
Mon., 12/17: 10-12, 1-2
Thu., 12/20: TBA

(12/3) Homework 10 (the last one!) has been posted and is due on Monday, December 10.

(12/1) Solutions to HW 8 have been posted.

I'll assign the take-home final on December 10. It will be due in a week, on December 17 at 2 PM.

(11/28) I finally posted Homework 9. It's due on December 3. Only one more to go.

(11/21) I just posted solutions to Homework 7. Happy Thanksgiving everyone!

(11/18) Sorry for the delay, but Homework 8 has now been posted and is due on November 26.

(11/6) Solutions to Homework 6 have been posted.

(11/2) I just posted homework 7. It's due on November 12. Also posted are solutions to HW 5.

(10/30, part 2) I have a meeting tomorrow from 10:30 until at least 11:30, so I will only have office hours from 10 to 10:30 and after my meeting until noon. Sorry about that.

(10/30) Midterm solutions have been posted. Btw, I am still accepting solutions to homework 6.

(10/27) A few hints for the midterm. Problem 1.(a): show that it is enough to prove the statement when M = R^n. Then consider the equation f(x) = x in a neighborhood of a Lefshetz fixed point p. Problem 3: sinkce the problem is local, ask yourself, what is the simplest possible expression for X in a chart? Then solve the problem in that chart. Problem 4.(a): Fix a k-plane E and consider a coordinate neighborhood of E defined in the hint, and a corresponding coordinate neighborhood of the orthogonal complement E' of E. Then compute the local expression of the given map in these coordinate neighborhoods. Namely, if the graph of a linear map L : E --> E' is a k-plane F near E, find a linear map K : E' --> E whose graph is the orthogonal complement F' of F. Think of simple operations you can apply to L (or its matrix) to get K.

(10/21) I will bring the midterm to class on Wednesday. There will be four problems due in class next Monday, October 29.

(10/19) Homework 6 has been posted and is due on Wednesday, October 24.

(10/16) I just posted solutions to Homework 4.

(10/11) Just posted a handout (the same one I distributed in class) on a coordinate-free view of the derivative.

(10/7, part 2) I just posted Homework 5, which is due on Monday, October 15.

(10/7) Tomorrow morning I have to do a peer evaluation of somebody's teaching, so I will have to cancel my AM office hours. Sorry about that!

(10/1) I would like everyone to choose his topic for a survey article by October 31. So either stop by office or email me, or both.

(9/29) Homework 3 solutions are on the web.

To get some idea about the survey papers we talked about, check out the bottom of Alan Weinstein's web page, where he has links to Survey articles in Riemannian geometry from his Math 240 courses at Berkeley. Basically, each student would choose a topic and survey the literature about it. Here's my survey "Which manifolds admit a geodesic flow of Anosov type?" from 1992.

(9/28) I just posted Homework 4, which is due on Monday, October 8.

(9/24) Solutions to Homework 2 have been posted.

Important announcement: There will be only one midterm, which means that there will be no midterm next Monday, Oct. 1. Instead, each student will be required to make a 15 minute presentation on a topic of his choosing. We'll discuss this in class.

(9/16) I posted Homework 3 (due on September 26) and Solutions to Homework 1.

Two years ago I wrote a little handout on the Implicit Function Theorem, which I would like to revise for this class, but before I have time to do that, you can take a look at the old version.

(9/10) I'm sorry for having to cancel my morning office hours today (it was due to factors beyond my control). To make up for that, I'll have additional office hours from 3 to 4 both this Wednesday and next Wednesday (9/19). Also, I'm moving the deadline for submitting Homework 1 to this Wednesday (9/12).

(9/8) On Monday, September 10, I will be about half an hour late to my morning office hours, which will therefore be from 10:30 to noon. But I'll have afternoon office hours on Wednesday (9/12), from 2:45 to 3:45.

(9/4) Homework 2 has been posted and is due on Monday, September 17.

(8/29) Homework 1 has been posted and is due on Monday, September 10.

(8/28) Good news: Math 213 has survived! I'll update this page and post the first homework soon.

(8/7) The good news is that we have 4 students in the class, the bad news is that we need two more... I'll keep you posted.

(7/24) As of today, there are still only 3 registered students. Hope we can get at least 3 more soon! If you know someone who may be interested, please spread the word!

(7/13) IMPORTANT: only 3 students have so far registered for this class, and we need at least 6 for it to run. If we don't have enogh people by the beginning of August, the class may get cancelled. So if you are thinking of taking the class or just want to check it out, it would be helpful to register as soon as possible.

(6/14) Welcome to the home page of Math 213 for Fall 2007! If you are planning to take this class, please register as soon as possible. If you need a permission number, please email me to get one. We need at least six people in order for the class to run. Math 213 is offered very infrequently, so it would be a shame if it gets cancelled.

If you are still not sure if you want to take the class, feel free to email me for more information.


Lecture time and location

MW 13:30-14:45 in SH 414

Prerequisite

Math 113 (with a grade of "C-" or better) or instructor consent.

We actually won't be relying much on Math 113, so if you're not sure if are sufficiently prepared to take this class, please come talk to me or just email me.


Office hours

MW 10-12, M 3-4 and by appointment


Textbook

William M. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry, second revised edition, 2002


Syllabus

(Tentative and approximate)

Chapters I-IV, V.1-3, VI.2-5, parts of Ch. VII and VIII from Boothby.

Greensheet


Exams

There will be one take-home midterm, and a final exam. Each student will also write a short literature review paper on topic of his choice and present it to the whole class. The exam schedule:
Midterm: October 24 (Solutions)
Final exam: December 17
There will be no make-up exams.


Grading policy

Homework 20%, Midterm 20%, Paper and presentation 20%, Final 40%


Handouts

A coordinate-free view of the derivative of a map between Euclidean spaces


Homework

Late homework policy. One class meeting late: 50% penalty; two class meetings late: no credit.

# Due date Assignment Solutions
1 9/12 Ch. I, ex. 3.4, 5.1, 5.4 HW 1
2 9/17 Ch. II, ex. 4.5, 5.2, 5.5, 7.3 HW 2
3 9/26 Ch. III, ex. 1.2, 1.3, 2.3, 2.6, 3.1, 3.7 HW 3
4 10/8 Ch. III, ex. 4.3, 4.7, 5.1, 5.7, 6.3 HW 4
5 10/15 Ch. III, ex. 7.4, 7.5, 7.8, 8.6 HW 5
6 10/24 Ch. IV, ex. 2.5, 2.6, 3.5, 3.7 HW 6
7 11/12 Ch. IV, ex. 7.10, 7.11. Ch. V, ex. 3.1, 4.3, 4.4, 4.8 HW 7
8 11/26 Ch. V, ex. 7.2. Ch. VII, ex. 2.4, 2.5, 3.3, 3.5 HW 8
9 12/3 Ch. VII, ex. 5.1, 6.3, 6.5, 7.4, 7.5 HW 9
10 12/10 Ch. VII, ex. 8.3, 9.4, 9.5. Ch. VIII, ex. 3.2, 3.3, 3.4 HW 10


Policy on calculators

Not permitted.


Academic integrity

By default, I regard my students as honest individuals and expect them to abide by the University policy on academic integrity.


Anonymous feedback

If you have any comments or suggestions, please fill out this anonymous feedback form.
Slobodan N. Simić

Last modified: Fri Dec 21 20:58:50 PST 2007