Japanese

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	HA210000	Subject Classification	Specialized Education
Subject Name	数学通論I
Subject Name （Katakana）	スウガクツウロンイチ
Subject Name in English	Fundamental Concepts of Mathematics I
Instructor	FUJIMORI SHOICHI
Instructor (Katakana)	フジモリ　ショウイチ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year,  First Semester,  1Term
Days, Periods, and Classrooms	(1T) Mon3-4,Fri3-4：SCI E104
Lesson Style	Lecture	Lesson Style (More Details)
			Excercises, Presentations
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, metric spaces, open sets, closed sets, continuous maps, compactness, completeness
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 metric spaces
Class Schedule	lesson 1. Sets and maps lesson 2. Open sets in Euclidean spaces lesson 3. Closed sets in Euclidean spaces lesson 4. Properties of open and closed sets in Euclidean spaces lesson 5. Continuous maps between Euclidean spaces lesson 6. Compact subsets of Euclidean spaces lesson 7. Sequences of points in Euclidean spaces lesson 8. The Heine-Borel Theorem lesson 9. The definition and examples of metric spaces lesson 10. Open and closed subsets in metric spaces lesson 11. Continuous maps between metric spaces lesson 12. Compact metric spaces lesson 13. Properties of compact metric spaces lesson 14. Sequences of points in metric spaces lesson 15. Overall summary The midterm and final exams will be held in the normal class time and place.
Text/Reference Books,etc.	Reference books: M. Umehara and S. Ichiki, Naive 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 sets and maps lesson 2.  Review of open sets in Euclidean spaces lesson 3.  Review of closed sets in Euclidean spaces lesson 4.  Review of properties of open and closed sets in Euclidean spaces lesson 5.  Review of continuous maps between Euclidean spaces lesson 6.  Review of compact subsets of Euclidean spaces lesson 7.  Review of sequences of points in Euclidean spaces lesson 8.  Review of the Heine-Borel Theorem lesson 9.  Review of the definition and examples of metric spaces lesson 10.  Review of open and closed subsets in metric spaces lesson 11.  Review of continuous maps between metric spaces lesson 12.  Review of the definition of compact metric spaces lesson 13.  Review of  properties of compact metric spaces lesson 14.  Review of sequences of points in metric spaces lesson 15.  Overall Review
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.