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 English	Fundamental 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 Outline	Studying 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 Review	lesson 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 theorem
Requirements
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.