2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry A1
- 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.B405
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 1Q
- Syllabus updated
- Mar 19, 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.
Keywords
the fundamental theorem of surface theory, integrability conditions, differential geometry
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 | Overview | Details will be provided during each class session |
| Class 2 | Fundamental theorem for linear ordinary differential equations | Details will be provided during each class session |
| Class 3 | Integrability conditions | Details will be provided during each class session |
| Class 4 | Surfaces in Euclidean 3-space | Details will be provided during each class session |
| Class 5 | Gauss and Codazzi equations | Details will be provided during each class session |
| Class 6 | Fundamental theorem for surface theory | Details will be provided during each class session |
| Class 7 | Applications of the fundamental theorem | 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.,
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 https://www.kotaroy.com/official/class/2025/geom-a1.html for details