講義名 幾何学特論A1（Advanced topics in Geometry A1） 科目コード：MTH.B405
開講学期 １Q 単位数 1--0--0
担当 山田 光太郎 教授：本館２階２３１号室（内線３３８９）
【講義の概要とねらい】
The fundamental theorem of surface theory and its applications will be introduced.
【到達目標】
Students will learn the fundamental theorem of surface theory and its peripheral matters.
【キーワード】
the fundamental theorem of surface theory, integrability conditions, differential geometry
【学生が身につける力】
Specialist skills
【授業の進め方】
A standard lecture course. Homeworks will be assined for each lesson.
【授業計画・課題】
| Class 1 | Overview |
| Class 2 | Fundamental theorem for linear ordinary differential equations |
| Class 3 | Integrability conditions |
| Class 4 | Surfaces in Euclidean 3-space |
| Class 5 | Gauss and Codazzi equations |
| Class 6 | Fundamental theorem for surface theory |
| Class 7 | Applications of the fundamental theorem |
Details will be provided during each class session
【授業時間外学修（予習・復習等）】
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.
【教科書】
No textbook is set. Lecture note will be provided.
【参考書、講義資料等】
Masaaki Umehara and Kotaro Yamada, Differential Geometry of Curves and Surfaces, Transl. by Wayne Rossman, World Scientific Publ.,
【成績評価の基準及び方法】
Graded by homeworks. Details will be announced through LMS (formerly T2SCHOLA)
【関連する科目】
MTH.B211 ： Introduction to Geometry I
MTH.B212 ： Introduction to Geometry II
【履修の条件（知識・技能・履修科目等）】
At least, undergraduate level knowledge of linear algebra, calculus and elementary complex analysis are required.