2017 Exercises in Set and Topology I

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Kojima Sadayoshi  Umehara Masaaki  Nishibata Shinya  Terashima Yuji  Miura Hideyuki  Murofushi Toshiaki  Takasawa Mitsuhiko 
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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. This course is held once per week for seven or eight weeks since its credit is one.

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.


Set, Map, Family of Sets, Axiom of Choice, Equivalence Relation, Quotient Set, Cardinality, Order Relation, 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 report7
Class 8 Metric Space report8


"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.

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