HB060000 Geometry A

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB060000 Subject Classification Specialized Education

Subject Name 幾何学Ａ

Subject Name
（Katakana）キカガクA

Subject Name in
English Geometry A

Instructor FUJIMORI SHOICHI

Instructor
(Katakana) フジモリ　ショウイチ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, First Semester, 2Term

Days, Periods, and Classrooms (2T) Weds1-2,Fri7-8：SCI E209

Lesson Style Lecture Lesson Style
(More Details) 　

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords curve, surface, curvature, Gauss-Bonnet theorem

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Mathematics
（Knowledge and Understanding）
・Understanding on primary theory of modern mathematics established on classical theory.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline The purpose is to understand various notions of curvature using differential calculus.

Class Schedule lesson1 Introduction and matrix valued functions
lesson2 Plane curves and their length
lesson3 Curvature of plane curves
lesson4 The fundamental theorem of plane curves
lesson5 The rotation index of a closed curve
lesson6 Space curves
lesson7 The first and second fundamental forms of a surface
lesson8 Gaussian curvature, mean curvature
lesson9 The Gauss-Codazzi equations
lesson10 Integrability conditions and the fundamental theorem of surfaces
lesson11 Covariant derivative and geodesics
lesson12 Shortest paths and geodesics
lesson13 Vector analysis
lesson14 The Gauss-Bonnet theorem
lesson15 Proof of the Gauss-Bonnet theorem

The final exam will be held in the normal class time and place.

Text/Reference
Books,etc. No textbook.
Reference books:
M. Umehara and K. Yamada, Differential Geometry of Curves and Surfaces (World Scientific Pub Co Inc) 2017

PC or AV used in
Class,etc. 　

(More Details) Blackboard

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review In each lecture, some easy computations and proofs will be omitted.
It is needed to check them by your hand.
Asking questions to the lecturer is always welcome.

Requirements

Grading Method Evaluation will be based on exams and class activities.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HB060000	Subject Classification	Specialized Education
Subject Name	幾何学Ａ
Subject Name （Katakana）	キカガクA
Subject Name in English	Geometry A
Instructor	FUJIMORI SHOICHI
Instructor (Katakana)	フジモリ　ショウイチ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Weds1-2,Fri7-8：SCI E209
Lesson Style	Lecture	Lesson Style (More Details)

Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	curve, surface, curvature, Gauss-Bonnet theorem
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Mathematics （Knowledge and Understanding）・Understanding on primary theory of modern mathematics established on classical theory. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	The purpose is to understand various notions of curvature using differential calculus.
Class Schedule	lesson1 Introduction and matrix valued functions lesson2 Plane curves and their length lesson3 Curvature of plane curves lesson4 The fundamental theorem of plane curves lesson5 The rotation index of a closed curve lesson6 Space curves lesson7 The first and second fundamental forms of a surface lesson8 Gaussian curvature, mean curvature lesson9 The Gauss-Codazzi equations lesson10 Integrability conditions and the fundamental theorem of surfaces lesson11 Covariant derivative and geodesics lesson12 Shortest paths and geodesics lesson13 Vector analysis lesson14 The Gauss-Bonnet theorem lesson15 Proof of the Gauss-Bonnet theorem The final exam will be held in the normal class time and place.
Text/Reference Books,etc.	No textbook. Reference books: M. Umehara and K. Yamada, Differential Geometry of Curves and Surfaces (World Scientific Pub Co Inc) 2017
PC or AV used in Class,etc.
(More Details)	Blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	In each lecture, some easy computations and proofs will be omitted. It is needed to check them by your hand. Asking questions to the lecturer is always welcome.
Requirements
Grading Method	Evaluation will be based on exams and class activities.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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