Course title
V02250002
Geometry 2

 kameko masaki Click to show questionnaire result at 2018
Course description
In the first half of this course, we will explain the definitions of manifold and smooth function.
In the second half of this course, we will discuss the homology theory.
Purpose of class
To understand manifolds and homology theory.
Goals and objectives
  1. A successful student will be able to explain the definition of manifolds and to show that a given space is a manifold.
  2. A successful student will be able to compute critical points of a smooth function defined on a manifold.
  3. A successful student will be able to explain the definition and elementary properties of homology theory and to compute the homology theory of a space.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Manifold Handout No.1 200minutes
2. Function Handout No.2 200minutes
3. Tangent space Handout No.3 200minutes
4. Map Handout No.4 200minutes
5. Regular value Handout No.5 200minutes
6. Recitation on manifolds Handout No.6 200minutes
7. Midterm examination and its review Handout No.7 200minutes
8. Homotopy Handout No.8 200minutes
9. Chain complex Handout No.9 200minutes
10. Category Handout No.10 200minutes
11. Homology Handout No.11 200minutes
12. Computations of homology Handout No.12 200minutes
13. Recitation on homology Handout No.13 200minutes
14. Final examination and its review Handout No.14 200minutes
Total. - - 2800minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 MIdterm Final Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 20% 20%
Total. 40% 60% -
Evaluation method and criteria
Midtermexam 40%, final exam 60%
Textbooks and reference materials
Y. Matsumoto, Tayoutainokiso, TokyoDaigakuShuppannkai
A. Hatcher, Algebraic Topology, Cambridge Univ. Press
Prerequisites
Calculus 1, 2, Linear algebra 1, 2, Foundation of Mathematics, Foundation of Analysis
Office hours and How to contact professors for questions
  • Tuesday 15:00--16:40 in the Fall semester in 2020.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic self-management skills
  • Course that cultivates a basic interpersonal skills
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Mar 21 13:03:12 JST 2020