Course title
330023001
Logic and Set Theory

 TAKEUCHI Shingo
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
IoT Course DP-4a・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Software Course DP-4b・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Media Course DP-4c・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Data Science Course DP-4d・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Mechatronics Course DP-4・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Architecture and Architectural Engineering Course DP-4a・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Environmental Systems and Urban Planning Course DP-4b・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Bioscience Course DP-4a・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Biomedical Engineering Course DP-4b・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Sports Engineering Course DP-4c・3 専門分野と他分野を関連付ける素養
主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Mathematical Sciences Course DP-4・1 研究者・技術者としての基礎的素養
代数、幾何、解析、応用数学、情報数学などの専門知識を修得し、課題を抽象化して数理的な問題設定をすると共に、適切な理論的考察・計算的手法を用いて問題解決策を構築できる。
Purpose of class
Modern mathematics is founded on the concept of sets. For example, while high school mathematics primarily involves investigating the properties of individual sequences or functions given to us, university mathematics often takes the opposite approach: it considers and uniformly handles collections such as “sets of sequences” or “sets of functions” that share the same properties. In this course, we will learn the conventions for working with sets and the logic necessary to apply them.
Course description
In the first half, after learning the fundamentals of “logic and sets,” we define “equivalence” (or “equivalence in cardinality”) between two distinct sets by considering ‘mappings’ from one set to another. Particularly important are “countable sets,” which are sets equivalent to the set of all natural numbers N, and “uncountable sets,” which are infinite sets not equivalent to N. In the latter half, we learn about “families of subsets” (sets of sets), their union and intersection, and the concept of “quotient sets” obtained by partitioning sets using “equivalence relations.”
Goals and objectives
  1. To be able to describe propositions using logical symbols.
  2. To be able to prove propositions about sets and mappings.
  3. To be able to partition sets using equivalence relations.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 25% 25%
2. 25% 25% 50%
3. 25% 25%
Total. 50% 50% -
Evaluation method and criteria
Mid-term exam and Final exam. When the minimum and maximum scores of the midterm and final examinations are m and M, respectively, a student is considered to have passed if m≥30 and M≥60, where M is the grade.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Propositional logic, equivalence of propositions Regardless of whether you do your prep work, make sure you review. 190minutes
2. Set Regardless of whether you do your prep work, make sure you review. 190minutes
3. Proposition functions and predicate logic, universal quantifier ∀ and existential quantifier ∃ Regardless of whether you do your prep work, make sure you review. 190minutes
4. Mapping 1 (mappings and set operations, etc.) Regardless of whether you do your prep work, make sure you review. 190minutes
5. Mapping 2 (surjective, injective, bijective, etc.) Regardless of whether you do your prep work, make sure you review. 190minutes
6. Mapping 3 (surjective, injective, bijective, etc.) Regardless of whether you do your prep work, make sure you review. 190minutes
7. Midterm exam and feedback Review lecture notes and ensure you can solve the textbook’s example problems and exercises. 190minutes
8. Equality of sets Regardless of whether you do your prep work, make sure you review. 190minutes
9. Set cardinality, countable sets, uncountable sets Regardless of whether you do your prep work, make sure you review. 190minutes
10. Power set, family of subsets Regardless of whether you do your prep work, make sure you review. 190minutes
11. Union and Intersection of families of subsets Regardless of whether you do your prep work, make sure you review. 190minutes
12. Binary relation Regardless of whether you do your prep work, make sure you review. 190minutes
13. Equivalence classes, quotient sets, partitions of sets Regardless of whether you do your prep work, make sure you review. 190minutes
14. Final exams and feedback Review lecture notes and ensure you can solve the textbook’s example problems and exercises. 190minutes
Total. - - 2660minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback outside of the class (ScombZ, mail, etc.)
Textbooks and reference materials
Textbook: Yohei Komori, Sets and Topology (Nippon Hyoronsha). For reference books, please refer to the “Reference Books for Courses Taught” section on the laboratory website.
https://sites.google.com/shibaura-it.ac.jp/shingo/
Prerequisites
Nothing in particular.
Office hours and How to contact professors for questions
  • Every Wednesday during the academic term, after the fourth period (it is advisable to contact me in advance when visiting).
  • Please make active use of the Learning Support Center.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
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
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sun Mar 22 04:01:39 JST 2026