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School of Environment and Society
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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Suzuki Sakie Gotoda Takeshi Miura Hideyuki Murofushi Toshiaki Umehara Masaaki Tsuchioka Shunsuke Takahashi Jin Ichiki Shunsuke Nishibata Shinya
- Class Format
- Exercise
- Media-enhanced courses
- Day/Period(Room No.)
- Wed3-4(S421)
- Group
- -
- Course number
- MCS.T202
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 1Q
- Syllabus updated
- 2021/3/19
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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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.
