Time: Monday, Wednesday 2:30-4:45, Exam Time: Wednesday 1:00-3:45
Lecture room: 2412
Instructor: Suhyoung Choi 4403(office)
Office Hours: TBA
email: schoi at math dot kaist dot ac dot kr Phone: 2732
% Send me e-mails if there are any questions.
We will study the differentiable manifolds, differential forms on
manifolds, integration of forms, some differential geometry, the
Gauss-Bonnet theorem, and so on. More details will be given in the last
week of February at the course homepage.
Course book: Main: Differential forms and applications, M.P. do Carmo (Springer, downloadable from the main library)
Supplementary: Calculus on Manifolds, by Spivak, Benjamin/Cummings, Chapter 6 of Vector calculus 4th edition, Hubbard and Hubbard,
Matrix Editions, Elementary differential geometry 2nd Edition, Pressley, (Springer, downloadable)
Topics: Differentlal forms, line integrals, differentiable manifolds, Stoke's theorem, geometry of surfaces
Grading: Assignment (30pts.) Presentation-Report (60pts.) Attendance (10pts.) Total 100pts.
(There will be no midterm or final. We will have presentations
instead. For Presentations, I will assign problems or other things to be
presented during the exam time. The report will be the write-up of the
presentation.
The presentation will take place during the exam period or some
other scheduled time. There might be some changes. See KLMS for any announcements. )
Schedule:
- 1st Week : Chapter 1 Differential forms (For the first two weeks, we will have video lectures only. Use KLMS to see these.)
- 2nd Week : Chapter 1
- 3rd Week : Chapter 2. Line integrals
- 4th Week : Chapter 2
- 5th Week: Chapter 3. Differentiable manifold (April 15th Election day)
- 6th Week: Chapter 3.
- 7th week: Chapter 4: Integration on manifolds
- 8th week: Midterm exam time presentations
- 9th week: Chapter 4
- 10th week: Chapter 5: Differential geometry of surfaces
-11th week: Chapter 5
-12th week: Chapter 5
-13th week: Chapter 6: The Gauss-Bonnet theorem and the Morse theoerem
-14th week: Chapter 6
-15th week: Chapter 6
-16th week: Final exam time presentations
Reports:
These will be submitted to the KLMS.
The scores of the late homework will be taken off by a formula.
Important Reminder: You need to solve problems in the order given in
the book. You have to mark the problems you did not solve.