日本語

Course Code etc
Academic Year 2024
College College of Science
Course Code CA407
Theme・Subtitle
Class Format Face to face (all classes are face-to-face)
Class Format (Supplementary Items) 対面
Campus Lecture
Campus Ikebukuro
Semester Fall semester
DayPeriod・Room Mon.3・4406
Credit 2
Course Number MAT3210
Language Japanese
Class Registration Method Course Code Registration
Grade (Year) Required 配当年次は開講学部のR Guideに掲載している科目表で確認してください。
prerequisite regulations
Acceptance of Other Colleges 履修登録システムの『他学部・他研究科履修不許可科目一覧』で確認してください。
course cancellation 〇(履修中止可/ Eligible for cancellation)
Online Classes Subject to 60-Credit Upper Limit
Relationship with Degree Policy 各授業科目は、学部・研究科の定める学位授与方針(DP)や教育課程編成の方針(CP)に基づき、カリキュラム上に配置されています。詳細はカリキュラム・マップで確認することができます。
Notes
Text Code CA407

【Course Objectives】

Study cellular decomposition and homology groups of topological spaces as a means of perceiving the overall image of figures such as surfaces. Learn the Gauss–Bonnet theorem, which combines curvature, which is a local quantity with the Euler characteristic, which is a global quantity.

【Course Contents】

Geometry 1 used calculus to deal with the local theory of curves and surfaces, and studied curvature in detail. In Geometry 2, geodesic lines on surfaces are defined as a generalization of straight lines on a plane, and their properties are examined. Next we introduce the space form, which is characterized by the constant Gaussian curvature, and look at how Euclidean geometry is generalized. Then, after explaining the necessary facts about topological spaces, homology groups are defined and it is explained how they reflect a global aspect of shapes. After defining the Betti number and Euler’s characteristic using homology groups, the Gauss–Bonnet theorem is proven, which gives a relation between the curvature, a local quantity, with the Euler characteristic, a quantity defined from a global information.

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