Time: Monday, Wednesday 10:30-11:45
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.
This is an EDU4.0 course. Each week, you will study the material and watch the videos for that week before the classes. We will meet in class for discussions on the problems assigned for each week. This will begin from the second week. Lecture videos will be on KLMS. We will divide the class intro groups of three to four students. Groups will be assigned discussion problems on Monday, and groups will give presentations on Wednesday.
Course book: Main: Differential forms and applications, M.P. do Carmo (Springer, downloadable from the main library)
Grading:
Final and Midterm Exams (50%.)
Presentation-Report (40%) Attendance and class contribution (10%)
Schedule:
- 1st Week : Introduction and a review of Analysis
- 2nd Week : Chapter 1. Differential forms
- 3rd Week : Chapter 1. Differential forms (March 3rd holiday)
- 4th Week : Chapter 2, Line integrals
- 5th Week: Chapter 2.
- 6th Week: Chapter 3. Differentiable manifold
- 7th week: Chapter 3,
- 8th week: Midterm exam
- 9th week: Chapter 4, Integration on manifolds
- 10th week: Chapter 4:
- 11th week: Chapter 5. Differential geometry of surfaces (May 5,6 holiday)
-12th week: Chapter 5.
-13th week: Chapter 5.
-14th week: Chapter 6. The Gauss-Bonnet theorem and the Morse theoerem
-15th week: Chapter 6.
-16th week: Final exam