Spring 2025 Analysis on manifolds (MAS420)


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)
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: Final and Midterm Exams (50%.) Presentation-Report (40%) Attendance and class contribution (10%)


Schedule:
- 1st Week : Chapter 1 Differential forms
- 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
- 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