Japanese

Academic Year	2024Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code	WSA31000	Subject Classification	Specialized Education
Subject Name	多様幾何基礎講義Ａ
Subject Name （Katakana）	タヨウキカキソコウギエー
Subject Name in English	Geometry A
Instructor	ISHIHARA KAI
Instructor (Katakana)	イシハラ　カイ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year,  First Semester,  1Term
Days, Periods, and Classrooms	(1T) Mon3-4,Weds7-8
Lesson Style	Lecture	Lesson Style (More Details)
			Lecture using blackboard
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	7 : Graduate Special Studies
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Topology, Simplicial complex, Homology
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)
Class Objectives /Class Outline	Studying fundamentals of homology groups.
Class Schedule	Lesson 1. Introduction Lesson 2. The structure theorem for finitely generated abelian groups Lesson 3. Chain complexes Lesson 4. Simplicial complexes Lesson 5. Simplicial maps Lesson 6. Homology groups of simplicial complexes Lesson 7. Examples Lesson 8. Geometric meaning of homology groups Lesson 9. Induced homomorphisms of homology groups Lesson 10. The Euler-Poincaré Formula Lesson 11. Exact homology sequences Lesson 12. Mayer-Vietoris sequences Lesson 13. The homology groups of closed surfaces Lesson 14. Degree of maps Lesson 15. Overall summary
Text/Reference Books,etc.	No textbook. Reference book: Allen Hatcher, Algebraic Topology, Cambridge University Press. Sergey V. Matveev, Lectures on Algebraic Topology, European Mathematical Society.
PC or AV used in Class,etc.
	(More Details)	Blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson 1. Review of basic point-set topology Lesson 2. Review of  the structure theorem for finitely generated abelian groups Lesson 3. Review of chain complexes Lesson 4. Review of simplicial complexes Lesson 5. Review of  simplicial maps Lesson 6. Review of the homology groups of simplicial complexes Lesson 7. Review of examples Lesson 8. Review of geometric meaning of homology groups Lesson 9. Review of the induced homomorphisms of homology groups Lesson 10. Review of the Euler-Poincaré Formula Lesson 11. Review of the exact homology sequences Lesson 12. Review of the Mayer-Vietoris sequences Lesson 13. Review of the homology groups of closed surfaces Lesson 14. Review of the degree of maps Lesson 15. Overall review
Requirements
Grading Method	Evaluation will be based on homework assignments 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.