Math 622, Spring 2008:
Differential geometry I
Meeting: MWF 1:50-2:40pm CE 223

Instructor: Joseph (JM) Landsberg

Office: Milner 329

Phone: (979)-458- 0625
E-mail: jml@math.tamu.edu
office hours: Mon. 10-11am, Tues 1-2pm,   or by appointment.

Syllabus:  Surfaces in 3-space and generalizations to submanifolds of Euclidean space;
Smooth manifolds and mappings; tensors; differential forms; 
Lie groups and algebras; Stokes' theorem; deRham cohomology;
Frobenius theorem;  Riemannian manifolds.

Click here for a class by class schedule of topics

Pre-requisites: Math 304 or approval of instructor

Texts: 

1. M. Spivak, A comprehensive introduction to differential geometry I
(third edition, 1999) Publish or Perish Inc. (primary text)

2. T. Ivey and J. Landsberg, Cartan for beginners: differential
geometry via moving frames and exterior differential systems
(2003) AMS. (secondary text)

3,4. M. Spivak, A comprehensive introduction to differential geometry II, III
(third edition, 1999) Publish or Perish Inc. (recommended supplement)

All texts will be on reserve at the library and I have extra copies of
all the texts that I can loan out for short periods.


 
 

Homework:  There will be a weekly homework assignment. I will one day each week  going over
assigned homework problems.  Assignments will be posted at least one
week in advance of their due date.

Homework 1, due 1/23/8
Homework 2, due 1/30/8
Homework 3, due 2/6/8
Homework 4, due 2/13/8
Homework 5, due 2/20/8
Homework 6, due 2/27/8
Homework 7, due 3/17/8 (double credit assignment)
Homework 8, due 4/2/8
Homework 9, due 4/9/8
Homework 10, due 4/16/8
Homework 11, due 4/23/8

  By request, the final exam will be handed out on Wed.,  4/23/8 in class and due in
my office 4/30/8 by 12noon. You may use your class notes, Spivak and CFB when working
on the test, but you may not use any other sources. You also may ask me questions.

  There will be a take home exam handed out in class Friday, 2/29
and due in class on Monday, 3/3.

  Friday, April 4: Second exam: in class - multiple choice (but must provide short justification
of answers). Closed book and notebook, but you may bring 3 pages of handwritten notes to the exam-
these notes must be written by you (not a photocopy).
Exams: There will be at least one take home midterm exam plus a final exam.

Grading policy: homework 50%, midterm exams 30%, final exam 20%.

 
Policy regarding absences related to injury or illness: All such absences will be excused
if sufficient documentation is provided as per University policy and
the instructor will help the student make up any missed material.
 

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