Hiroshima University Syllabus |

Japanese

Academic Year 2024Year School/Graduate School School of Science Lecture Code HA230000 Subject Classification Specialized Education Subject Name 数学通論II Subject Name

（Katakana）スウガクツウロンニ Subject Name in

EnglishFundamental Concepts of Mathematics II Instructor ISHIHARA KAI Instructor

(Katakana)イシハラ カイ Campus Higashi-Hiroshima Semester/Term 2nd-Year, Second Semester, 3Term Days, Periods, and Classrooms (3T) Weds1-2,Fri3-4：SCI E104 Lesson Style Lecture Lesson Style

(More Details)Lecture using blackboard Credits 2.0 Class Hours/Week Language of Instruction J : Japanese Course Level 2 : Undergraduate Low-Intermediate Course Area（Area） 25 : Science and Technology Course Area（Discipline） 01 : Mathematics/Statistics Eligible Students Keywords Topological spaces, continuous maps, product topology, quotient topology, connectivity, Separation axioms, compactness, bases for topological spaces, metrization 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 classical basic theory which is a base of modern mathematics. Being able to find and explain issues from specific events.

（Abilities and Skills）

・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).Class Objectives

/Class OutlineStudying fundamentals of topological spaces Class Schedule lesson 1. Definition of topological space

lesson 2. Open and closed sets

lesson 3. Continuous maps

lesson 4. Relative topology

lesson 5. Product topology

Bases for topological spaces amd the Second Axiom of Countability

lesson 6. Quotient topology

lesson 7. Compactness

lesson 8. Compact space

lesson 9. Midterm exam

lesson 10. Connectivity

lesson 11. Path-connectivity

lesson 12. Separation Axioms

lesson 13. Hausdorff space

lesson 14. Axiom of countability

lesson 15. Metrization theorem

The midterm and final exams will be held in the normal class time and place.Text/Reference

Books,etc.Textbook:

N/A

Reference books:

M. Umehara and S. Ichiki, Naive set theory and general topology (Shokabo),

F. Uchida, Set theory and general topology (Shokabo),

S. Morita, Sets and topological spaces (Asakura-shoten),

K. Matsuzaka, Introduction to sets and topology (Iwanami-shoten)PC or AV used in

Class,etc.(More Details) Blackboard Learning techniques to be incorporated Suggestions on

Preparation and

Reviewlesson 1. Review of the definition and examples of topological spaces

lesson 2. Review of the definitions of open and closed sets

lesson 3. Review of the definitions of continuous maps

lesson 4. Review of the definition of relative topology

lesson 5. Review of the definition of product topology

lesson 6. Review of the definition of quotient topology

lesson 7. Review of the definition of compact spaces

lesson 8. Review of the properties of compact spaces

lesson 9. Review of the midterm exam questions and answers

lesson 10. Review of the definition of connective spaces

lesson 11. Review of the definition of path-connective spaces

lesson 12. Review of the definition of Separation Axioms

lesson 13. Review of the definition of Hausdorff space

lesson 14. Review of the definition of Axiom of Countability

lesson 15. Review of the metrization theoremRequirements 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.