### 2020　Exercises in Set and Topology I

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Undergraduate major in Mathematical and Computing Science
Instructor(s)
Umehara Masaaki  Nishibata Shinya  Miura Hideyuki  Murofushi Toshiaki  Suzuki Sakie  Tsuchioka Shunsuke  Takasawa Mitsuhiko  Takahashi Jin  Ichiki Shunsuke
Course component(s)
Exercise    (ZOOM)
Day/Period(Room No.)
Wed3-4(W833)
Group
-
Course number
MCS.T202
Credits
1
2020
Offered quarter
1Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
Class 1 Set and Set Operation report1
Class 2 Map, Family of Sets, Axiom of Choice report2
Class 3 Equivalence Relation and Quotient Set report3
Class 4 Cardinality report4
Class 5 Countable Set/Uncountable Set, Cardinality of the Continuum report5
Class 6 Order Relation, Well-Ordered set, Zorn's lemma report6
Class 7 Euclidean Space and Metric Space report7

### Out-of-Class Study Time (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)

"Set and Topological Space (in Japanese)" by Shigeyuki Morita published by Aasakura Shoten.

### Reference books, course materials, etc.

The person in charge will hand out materials accordingly.

### Assessment criteria and methods

By scores of reports and class performance. If you register for "MCS.T201: Set and Topology I", its score will be counted as a part of contributions also. Details will be announced in the first lecture.

### Related courses

• MCS.T201 ： Set and Topology I

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

The students who register for this course are strongly encouraged to do for "MCS.T201: Set and Topology I" simultaneously.