Hiroshima University Syllabus |

Japanese

Academic Year 2024Year School/Graduate School School of Science Lecture Code HA220000 Subject Classification Specialized Education Subject Name 数学通論I演習 Subject Name

（Katakana）スウガクツウロンイチエンシュウ Subject Name in

EnglishExercises in Fundamental Concepts of Mathematics I Instructor FUJIMORI SHOICHI,CASTELLANOS LUIS PEDRO Instructor

(Katakana)フジモリ ショウイチ,カステヤノス モスコソ ルイス ペドロ Campus Higashi-Hiroshima Semester/Term 2nd-Year, First Semester, 1Term Days, Periods, and Classrooms (1T) Thur7-8,Fri7-8：SCI E209 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, 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 OutlineExercises in fundamentals of metric spaces Class Schedule lesson 1. Exercises in sets and maps

lesson 2. Exercises in open sets in Euclidean spaces

lesson 3. Exercises in closed sets in Euclidean spaces

lesson 4. Exercises in properties of open and closed sets in Euclidean spaces

lesson 5. Exercises in continuous maps between Euclidean spaces

lesson 6. Exercises in compact subsets of Euclidean spaces

lesson 7. Exercises in sequences of points in Euclidean spaces

lesson 8. Exercises in the Heine-Borel Theorem

lesson 9. Exercises in the definition and examples of metric spaces

lesson 10. Exercises in open and closed subsets in metric spaces

lesson 11. Exercises in continuous maps between metric spaces

lesson 12. Exercises in compact metric spaces

lesson 13. Exercises in properties of compact metric spaces

lesson 14. Exercises in 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

Reviewlesson 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 ReviewRequirements 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.