Math 622, Spring 12:
Differential Geometry I
Meeting: MWF 10:20-11:10 Blocker 161
Office: Milner 329
E-mail: jml@math.tamu.edu
please include "622" in the subject line when emailing me
office hours: Mon. 1-2pm, Thurs. 10:30-11:30 and by appointment
my cv
E-mail. I will be contacting the class though the TAMU e-mail system. Be sure
to check your neo.tamu.edu account regularly, or have those e-mails forwarded to your
preferred account.
Prerequisites. We will use some basic concepts from Linear Algebra and Topology.
See, for example, the appendices of Lee's text.
If you are short on the prerequisites, or would prefer to study
classical surface theory, then you might consider Math 439.
Course texts.
Introduction to Smooth Manifolds, John M. Lee, Springer; click here for errata to the bookand Cartan for Beginners, Ivey and Landsberg, AMS some errata here
Course description: This is the first semester of a year-long graduate course in differential geometry.
Material. We will cover material from the following chapters of Lee's text: 1 -
8, 10 - 14, 17, 19. We will also go over the classical surface theory from a modern
perspective, chapters 1,2 of CFB. If time allows we will work though Chapters 9,
18, 20 of Lee. See the syllabus for more detail.
Grade complaints: If you think a homework or exam was graded incorrectly you
have one week from the time the graded assignment was returned to you to bring the
issue to the instructor's attention. No complaints after that time will be considered.
Grading policy: Weekly homework assignments (50%), two midterms (15%) and a final
exam (20%).
Schedule (tenative - assignments may change up to a week before they are due)
Week 1: read L (=Lee) chaps 1,2, due Wed. 1/25 p28-9 Problems from Chapter 1: #4,5,6,7
Week 2: read L ch 3, and CFB (=Cartan for Beginners) sections 1.1 and
1.4. Due Wed. 2/1 L ch2: 1c,6,8,10 and CFB exercises 1.4.2:1-5.
Week 3: read L ch 4, and CFB appendix B. Due Wed. 2/8 L-Chap 3: 1,4,5,7,8, CFB-Ex. A.2.3: 1,2,3 (omit the symplectic group for
exercise 1).
Week 4: read L chs 5,6 and CFBappendix A and the rest of chap 1.
Due Wed. 2/15 L: Ch 4: 5,9,11,16,19 and CFB: A.1.8.3, A.1.10 A.4.8: 2,3,4
Week 5: read L ch 11 due Wed. 2/22 L-Ch 5: 3,7 CFB A.1.8: 4.5, A.1.12, A.1.13
Week 6: Exam 2/29, closed book, but you may bring 2 pages of handwritten notes to the exam.
Here are some practice questions
Homework Friday 3/2 (by request): CFB1.6.14.1, 1.8.4:1,2,5, 2.2.2:1,2,3, 4a,4b,5
Week 7: due 3/7: CFB: 2.3.1.4, 2.3.3, 2.4.2, 2.5.5(1), 2.5.5(2).
Week 8: Spring break
Week 9: due 3/21: CFB: 2.5.4(3) (here assume the fibers are positive dimensional), 2.8.1:1,2,4.
Note this is a light assignment so you can enjoy spring break!
Week 10: due 3/28: these 3 problems
Exam Friday 3/30 - here are some practice questions
Week 12: due Monday 4/9: CFB 2.6.13.3, 2.6.13.4, Lee 17-2a,b, 18.5, 18.11
Week 13: due Wed. 4/18: Lee 14-8,9,10 (note - you may, in fact should, use the definition of
the Laplacian (d*d* + *d*d) and notice that on functions it simplifies to *d*d)
Week 14: due Wed. 4/25: CFB 2.9.1, 2.9.4.1, 2.9.4.2, 2.10.2, 2.10.3, 2.10.4
Answers to homework (provided by grader)
hw 1
hw 2
hw3
hw4
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.
Americans with Disabilities Act (ADA) Policy Statement
The following ADA Policy Statement (part of the Policy on Individual
Disabling Conditions) was submitted to the University Curriculum
Committee by the Department of Student Life. The policy statement was
forwarded to the Faculty Senate for information.
The Americans with Disabilities Act (ADA) is a federal
anti-discrimination statute that provides comprehensive civil rights
protection for persons with disabilities. Among other things, this
legislation requires that all students with disabilities be guaranteed
a learning environment that provides for reasonable accommodation of
their disabilities. If you believe you have a disability requiring an
accommodation, please contact the Department of Student Life,
Disability Services Office, in Room B116 of Cain Hall or call 862-4570.
Academic Integrity Statement
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
All syllabi shall contain a section that states the Aggie Honor Code
and refers the student to the Honor Council Rules and Procedures on the
web http://www.tamu.edu/aggiehonor