2024 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science
Exercises in Set and Topology I
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Takeshi Gotoda / Toshiaki Murofushi / Zin Arai / Sakie Suzuki / Masaaki Umehara / Shunsuke Tsuchioka / Jin Takahashi / Shunsuke Ichiki / Shinya Nishibata
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Wed
- Class
- -
- Course Code
- MCS.T202
- Number of credits
- 010
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 17, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course is offered simultaneously with the lecture "MCS.T201: Set and Topology I" and provides exercises on set theory and metric space.
The aim of this course is to understand the fundamentals of set theory and metric space well and apply them to practical problems.
Course description and aims
The students are expected to understand important examples of set theory and metric space, to learn the fundamentals to handle mathematical subjects rigorously and also to be able to apply them to practical problems.
Keywords
Set, Map, Family of Sets, Axiom of Choice, Equivalence Relation, Quotient Set, Cardinality, Order Relation, Well-ordered set, Metric Space
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lectures provide exercises on topics of "MCS.T201 : Set and Topology I". The students are strongly encouraged to register for "MCS.T201 : Set and Topology I".
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Logic, Sets | report1 |
| Class 2 | Operations of sets, Mappings | report2 |
| Class 3 | Properties of mappings, Indexed families of sets | report3 |
| Class 4 | Equivalence relations and quotient sets, Axiom of Choice | report4 |
| Class 5 | Cardinality, Countable sets/Uncountable sets, Cardinality of the continuum | report5 |
| Class 6 | Order relations, Well-ordered sets, Zorn's lemma | report6 |
| Class 7 | Euclidean spaces, Metric spaces | report7 |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
"Naive Set Theory and General Topology - the Empty Set as a Companion - (in Japanese)" by Masaaki Umehara and Shunsuke Ichiki published by Shokabo.
Reference books, course materials, etc.
The person in charge will hand out materials accordingly.
Evaluation methods and criteria
By scores of reports and class performance. Details will be announced in the first lecture.
Related courses
- MCS.T201 ： Set and Topology I
Prerequisites
The students who register for this course are strongly encouraged to do for "MCS.T201 : Set and Topology I" simultaneously.