Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2022Year Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program WSA31000 Specialized Education 多様幾何基礎講義Ａ タヨウキカキソコウギエー Geometry A FUJIMORI SHOICHI,KODA YUYA,OKUDA TAKAYUKI フジモリ　ショウイチ,コウダ　ユウヤ,オクダ　タカユキ Higashi-Hiroshima 1st-Year,  First Semester,  1Term (1T) Mon3-4,Weds7-8：SCI B501 Lecture Lecture using blackboard 2.0 J : Japanese 7 : Graduate Special Studies 25 : Science and Technology 01 : Mathematics/Statistics Topology, Simplicial complex, Homology Studying fundamentals of homology groups. Lesson 1. IntroductionLesson 2. The structure theorem for finitely generated abelian groupsLesson 3. Chain complexesLesson 4. Simplicial complexesLesson 5. Simplicial mapsLesson 6. Homology groups of simplicial complexesLesson 7. ExamplesLesson 8. Geometric meaning of homology groupsLesson 9. Induced homomorphisms of homology groupsLesson 10. The Euler-Poincaré FormulaLesson 11. Exact homology sequencesLesson 12. Mayer-Vietoris sequences Lesson 13. The homology groups of closed surfacesLesson 14. Degree of mapsLesson 15. Overall summary No textbook. Reference book: Allen Hatcher, Algebraic Topology, Cambridge University Press.Sergey V. Matveev, Lectures on Algebraic Topology, European Mathematical Society. Blackboard Lesson 1. Review of basic point-set topologyLesson 2. Review of  the structure theorem for finitely generated abelian groupsLesson 3. Review of chain complexesLesson 4. Review of simplicial complexesLesson 5. Review of  simplicial mapsLesson 6. Review of the homology groups of simplicial complexesLesson 7. Review of examplesLesson 8. Review of geometric meaning of homology groupsLesson 9. Review of the induced homomorphisms of homology groupsLesson 10. Review of the Euler-Poincaré FormulaLesson 11. Review of the exact homology sequencesLesson 12. Review of the Mayer-Vietoris sequencesLesson 13. Review of the homology groups of closed surfaces Lesson 14. Review of the degree of mapsLesson 15. Overall review Evaluation will be based on homework assignments and class activities. 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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