Hiroshima University Syllabus

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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
Subject Name in
Fundamental Concepts of Mathematics II
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
(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
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. 
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
(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 metrization theorem 
Grading Method Evaluation will be based on exams and class activities. 
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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