Hiroshima University Syllabus |

Japanese

Academic Year 2024Year School/Graduate School School of Science Lecture Code HB260000 Subject Classification Specialized Education Subject Name 幾何学Ｃ Subject Name

（Katakana）キカガクC Subject Name in

EnglishGeometry C Instructor ISHIHARA KAI Instructor

(Katakana)イシハラ カイ Campus Higashi-Hiroshima Semester/Term 4th-Year, First Semester, 1Term Days, Periods, and Classrooms (1T) Mon3-4,Weds7-8：SCI E210 Lesson Style Lecture Lesson Style

(More Details)Lecture using blackboard Credits 2.0 Class Hours/Week Language of Instruction J : Japanese Course Level 4 : Undergraduate Advanced 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)Mathematics

（Knowledge and Understanding）

・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics.Class Objectives

/Class OutlineStudying 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 summaryText/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

ReviewLesson 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 reviewRequirements 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.