Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HA240000 Specialized Education 数学通論II演習 スウガクツウロンニエンシュウ Exercises in Fundamental Concepts of Mathematics II SUKENAGA MASAYUKI,ISHIHARA KAI スケナガ　マサユキ,イシハラ　カイ Higashi-Hiroshima 2nd-Year,  Second Semester,  3Term (3T) Thur7-8,Fri7-8：SCI E210 Seminar Excercises, presentations 1.0 J : Japanese 2 : Undergraduate Low-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics Topological spaces, continuous maps, product topology, quotient topology, connectivity, Separation axioms, compactness, bases for topological spaces, metrization 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). Exercises in fundamentals of point-set topology lesson 1. exercises in the definition and examples of topological spacelesson 2. exercises in open sets and closed setslesson 3. exercises in continuous mapslesson 4. exercises in relative topologylesson 5. exercises in product topologylesson 6. exercises in quotient topologylesson 7. exercises in compactnesslesson 8. exercises in the properties of compact spacelesson 9. Review of the midterm exam questions and answerslesson 10. exercises in connectivitylesson 11. exercises in path-connectivitylesson 12. exercises in separation axiomslesson 13. exercises in Hausdorff spacelesson 14. exercises in the axiom of countabilitylesson 15. Review of the final exam questions and answers Textbook: N/AReference 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) blackboard lesson 1.  Review of  the definition and examples of topological spaceslesson 2.  Review of  the definitions of open and closed setslesson 3.  Review of the definitions of continuous mapslesson 4.  Review of the definition of relative topologylesson 5.  Review of the definition of product topologylesson 6.  Review of the definition of quotient topologylesson 7.  Review of the definition of compact spaceslesson 8.  Review of the properties of compact spaceslesson 9.  Review of the midterm exam questions and answerslesson 10.  Review of the definition of connective spaceslesson 11.  Review of the definition of  path-connective spaceslesson 12.  Review of the definition of Separation Axiomslesson 13.  Review of the definition of Hausdorff spacelesson 14.  Review of the definition of Axiom of Countabilitylesson 15.  Review of the final exam questions and answers Evaluation will be based on examinations, class activities and oral presentations. 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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