2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry B1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kotaro Yamada
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Fri
- Class
- -
- Course Code
- MTH.B406
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Mar 19, 2025
- Language
- English
Syllabus
Course overview and goals
As an application of the fundamental theorem for surface theory, construction of pseudospherical surfaces, which are local models of Lobachevsky's non-euclidean geometry, will be introduced.
Course description and aims
Students will learn a way to apply the fundamental theorem for surface theory, and observe various mathematical phenomena in the way of construction.
Keywords
Fundamental theorem of surface theory, pseudospherical surfaces, sine Gordon equations
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Non-euclidean geometry | Details will be provided during each class session |
| Class 2 | Surfaces of constant Gaussian curvature | Details will be provided during each class session |
| Class 3 | Pseudospherical surfaces and asymptotic Chebyshev net | Details will be provided during each class session |
| Class 4 | A construction of pseudospherical surfaces | Details will be provided during each class session |
| Class 5 | Hilbert's theorem | Details will be provided during each class session |
| Class 6 | Surfaces in Lorentz-Minkowski space | Details will be provided during each class session |
| Class 7 | Realization of the hyperbolic plane | Details will be provided during each class session |
Study advice (preparation and review)
Official Message: To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
No textbook is set. Lecture note will be provided.
Reference books, course materials, etc.
Masaaki Umehara and Kotaro Yamada, Differential Geometry of Curves and Surfaces, Transl. by Wayne Rossman, World Scientific Publ.,
2017, ISBN 978-9814740234 (hardcover); 978-9814740241 (softcover)
Evaluation methods and criteria
Graded by homeworks. Details will be announced through LMS (formerly T2SCHOLA)
Related courses
- MTH.B211 ： Introduction to Geometry I
- MTH.B212 ： Introduction to Geometry II
Prerequisites
At least, undergraduate level knowledge of linear algebra, calculus and elementary complex analysis are required.
Other
Visit http://www.kotaroy.com/official/class/2025-geom-b1 for details