HB090000 Exercises in Geometry B

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HB090000 Subject Classification Specialized Education

Subject Name 幾何学Ｂ演習

Subject Name
（Katakana）キカガクBエンシュウ

Subject Name in
English Exercises in Geometry B

Instructor OKUDA TAKAYUKI

Instructor
(Katakana) オクダ　タカユキ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Tues3-4,Fri9-10：SCI E211

Lesson Style Seminar Lesson Style
(More Details) Face-to-face

Excercises, Presentations

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Topology, Homotopies, Fundamental groups, Covering spaces

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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions.

Class Objectives
/Class Outline Exercises in fundamentals of fundamental groups and covering spaces.

Class Schedule Lecture 1: Course overview and review of point-set topology
Lecture 2: Homotopies of continuous maps
Lecture 3: Homotopy equivalence of topological spaces
Lecture 4: Basic techniques for studying homotopy classes
Lecture 5: Triples of topological spaces
Lecture 6: Fundamental groupoid and fundamental group
Lecture 7: The fundamental group of the circle
Lecture 8: The fundamental group as a homotopy invariant
Lecture 9: Fundamental groups of product spaces, group presentations
Lecture 10: Free products of groups, the Van Kampen theorem
Lecture 11: Covering maps
Lecture 12: Lifting of paths
Lecture 13: Universal covering spaces
Lecture 14: Discontinuous groups
Lecture 15: Summary

Text/Reference
Books,etc. No textbook.
Reference book:
James Munkres, Topology (2nd Edition), Pearson;
Allen Hatcher, Algebraic Topology, Cambridge University Press.

PC or AV used in
Class,etc.

(More Details) Paper materials, Blackboard

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Lesson 1-5. Review of lecture notes and basic point-set topology
Lesson 6-10. Review of lecture notes and group theory
Lesson 11-15. Review of lecture notes

Requirements

Grading Method Evaluation will be based on homework assignments, class activities and oral presentations.

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	2026Year	School/Graduate School	School of Science
Lecture Code	HB090000	Subject Classification	Specialized Education
Subject Name	幾何学Ｂ演習
Subject Name （Katakana）	キカガクBエンシュウ
Subject Name in English	Exercises in Geometry B
Instructor	OKUDA TAKAYUKI
Instructor (Katakana)	オクダ　タカユキ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues3-4,Fri9-10：SCI E211
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face
Excercises, Presentations
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Topology, Homotopies, Fundamental groups, Covering spaces
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 （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). ・To acquire skills to formulate and solve mathematical questions.
Class Objectives /Class Outline	Exercises in fundamentals of fundamental groups and covering spaces.
Class Schedule	Lecture 1: Course overview and review of point-set topology Lecture 2: Homotopies of continuous maps Lecture 3: Homotopy equivalence of topological spaces Lecture 4: Basic techniques for studying homotopy classes Lecture 5: Triples of topological spaces Lecture 6: Fundamental groupoid and fundamental group Lecture 7: The fundamental group of the circle Lecture 8: The fundamental group as a homotopy invariant Lecture 9: Fundamental groups of product spaces, group presentations Lecture 10: Free products of groups, the Van Kampen theorem Lecture 11: Covering maps Lecture 12: Lifting of paths Lecture 13: Universal covering spaces Lecture 14: Discontinuous groups Lecture 15: Summary
Text/Reference Books,etc.	No textbook. Reference book: James Munkres, Topology (2nd Edition), Pearson; Allen Hatcher, Algebraic Topology, Cambridge University Press.
PC or AV used in Class,etc.
(More Details)	Paper materials, Blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson 1-5. Review of lecture notes and basic point-set topology Lesson 6-10. Review of lecture notes and group theory Lesson 11-15. Review of lecture notes
Requirements
Grading Method	Evaluation will be based on homework assignments, class activities and oral presentations.
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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