Japanese

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HA240000	Subject Classification	Specialized Education
Subject Name	数学通論II演習
Subject Name （Katakana）	スウガクツウロンニエンシュウ
Subject Name in English	Exercises in Fundamental Concepts of Mathematics II
Instructor	SUKENAGA MASAYUKI,ISHIHARA KAI
Instructor (Katakana)	スケナガ　マサユキ,イシハラ　カイ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year,  Second Semester,  3Term
Days, Periods, and Classrooms	(3T) Thur7-8,Fri7-8：SCI E210
Lesson Style	Seminar	Lesson Style (More Details)
			Excercises, presentations
Credits	1.0	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	Exercises in fundamentals of point-set topology
Class Schedule	lesson 1. exercises in the definition and examples of topological space lesson 2. exercises in open sets and closed sets lesson 3. exercises in continuous maps lesson 4. exercises in relative topology lesson 5. exercises in product topology lesson 6. exercises in quotient topology lesson 7. exercises in compactness lesson 8. exercises in the properties of compact space lesson 9. Review of the midterm exam questions and answers lesson 10. exercises in connectivity lesson 11. exercises in path-connectivity lesson 12. exercises in separation axioms lesson 13. exercises in Hausdorff space lesson 14. exercises in the axiom of countability lesson 15. Review of the final exam questions and answers
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 topological spaces (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 final exam questions and answers
Requirements
Grading Method	Evaluation will be based on examinations, 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.