2025 Fall:
2025 Fall:
Curves and Surfaces
Curves and Surfaces
Lectures: On Mondays, 11:00-12:45, in Gorlaeus Building - BW.0.07
Classes: Sept 1, 8, 15, 22, 29, Oct 6, 13, 27, Nov 3, 10, 17, 24, Dec 1, 8
There will be videos (from Covid times) available about the material. Link here .
In addition to the Lectures, there are discussion sessions run by the TA on Thursdays, 15:15-17:00 in Gorlaeus Building - BW.0.07.
The TA is Daphne Strubbe, the email address is d.s.strubbe@umail.leidenuniv.nl.
If you have any questions, do not hesitate to contact us. My email address is hablicsekhm@math.leidenuniv.nl.
There will be two exams during the course.
Midterm exam: In room: Oct 13, Monday 11:00-12:30 in BW.0.07. If you cannot make it, there will be another opportunity: Oct 16, 15:15-16:45 in BW.0.07.
Final Exam: Jan 7, 13:15-16:15, in Gorlaeus Building - EM.1.09
Retake exam for the final exam: Jan 28, 13:15-16:15 in Gorlaeus Building - DM.1.09
Mock exam: MockExam
By appointment. Feel free to email me ANYTIME. My email address is hablicsekhm@math.leidenuniv.nl. I reply to any email in one business day.
Manfredo P. Do Carmo: Differential Geometry of Curves and Surfaces
Notes about the material: Lecture Book
1. Multivariate differentiation: implicit function theorem, inverse function theorem
2. Curves: Parametrized curves, curvature, canonical form, and global properties of plane curves
3. Surfaces: Regular surfaces, tangent planes, fundamental forms, orientation, Gauss-map, geodesics, Gauss-Bonnet theorem
4. Introduction to Topological Manifolds: Classification of surfaces, Whitney's embedding theorem
The final grade is the weighted average of two written exam (30%+60%) and attendance grade (10%).
Because of ChatGPT and other AI softwares the homeworks will not be graded. However, I will assign exercises weekly. It is completely voluntary to do them or not. They can be found here: Exercises.
To get the 10% in attendance, you need to be present at least 50% of the lectures and the tutorials together.
Cheating and other academic misconduct will not be tolerated.
The course also has a Brightspace page. Please, register there as well. (as well as in USIS)
If you have any questions/comments/concerns, feel free to write an anonymous comment (see below) or send an email to mhablicsek at gmail dot com.