2022 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kotaro Yamada
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue
- Class
- -
- Course Code
- MTH.B501
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 1Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The fundamental theorem of surface theory and its applications will be introduced.
Course description and aims
Students will learn the fundamental theorem of surface theory and its peripheral matters, including a theory of surfaces of constant negative curvature.
Keywords
the fundamental theorem of surface theory, integrability conditions
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
A standard lecture course. Homeworks will be assined for each lesson.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Linear ordinary differential equations | Details will be provided during each class session. |
| Class 2 | Integrability conditions | Details will be provided during each class session. |
| Class 3 | Review of surface theory | Details will be provided during each class session. |
| Class 4 | Gauss and Codazzi equations | Details will be provided during each class session. |
| Class 5 | Fundamental theorem for surface theory | Details will be provided during each class session. |
| Class 6 | Asymptotic Chebyshev net and the sine-Gordon equation | Details will be provided during each class session. |
| Class 7 | Bäcklund transformations | 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 T2SCHOLA
Related courses
- MTH.B211 ： Introduction to Geometry I
- MTH.B212 ： Introduction to Geometry II
Prerequisites
At least, knowledge of undergraduate calculus and linear algebra are required.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
kotaro[at]math.titech.ac.jp
Office hours
N/A
Other
Visit http://www.math.titech.ac.jp/~kotaro/class/2022/geom-e for details.