Hiroshima University Syllabus

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Japanese
Academic Year 2022Year 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 FUJIMORI SHOICHI,KODA YUYA,OKUDA TAKAYUKI
Instructor
(Katakana)
フジモリ ショウイチ,コウダ ユウヤ,オクダ タカユキ
Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  1Term
Days, Periods, and Classrooms (1T) Mon3-4,Weds7-8:SCI B501
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
 
Criterion referenced
Evaluation
 
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. 
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