Course title
330072001
Set Theory and Topology

 SUZUKI Tatsuo
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
The object of this course is to understand fundamental concepts of set theory and topology, and to be able to prove some theorems in it.
Course description
This is a course on set theory and topology. Students will learn about properties of open sets in a Euclid space, definition of a metric space and topological space, and some topological properties.
Goals and objectives
  1. To understand fundamental concepts of set theory.
  2. To be able to prove some theorems in set theory.
  3. To understand fundamental concepts of topology.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Assignment 1 Midterm exam Final assignment Total.
1. 10% 10% 10% 30%
2. 10% 20% 10% 40%
3. 10% 20% 30%
Total. 20% 40% 40% -
Evaluation method and criteria
Assignment 1 (20%), Midterm exam (40%), Final assignment (40%)
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Sets and mappings Review of fundamental mathematics 150minutes
2. Binary relation, order relation and equivalence relation Review of sets and mappings 200minutes
3. Euclid space Review of binary relation, order relation and equivalence relation 200minutes
4. Open sets in a Euclid space, Assignment 1 Review of Euclid space 200minutes
5. Properties of open sets Review of open sets in a Euclid space 200minutes
6. Metric space Review of properties of open sets 200minutes
7. Open sets in a metric space Review of metric space 200minutes
8. Midterm examination and comments Review of the above 200minutes
9. Continuous mapping over metric spaces Review of open sets in a metric space 200minutes
10. Topological space Review of continuous mapping over metric spaces 200minutes
11. Continuous mapping over topological spaces Review of topological space 200minutes
12. Compactness Review of continuous mapping over topological spaces 200minutes
13. Hausdorff space, Connectedness Review of compactness 200minutes
14. Final assignment and comments Review of the above 200minutes
Total. - - 2750minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Will be announced in the first class.
Prerequisites
Fundamental mathematics
Office hours and How to contact professors for questions
  • Tuesday 12:40-13:10
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
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 applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Mar 14 14:20:03 JST 2026