Hiroshima University Syllabus

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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
Subject Name in
Exercises in Fundamental Concepts of Mathematics II
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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(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 
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
(More Details) blackboard 
Learning techniques to be incorporated  
Suggestions on
Preparation and
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 
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  
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. 
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