Course title
V06403001
Fundamentals of Mathematics

 takeuchi shingo
Course description
In this lesson, you will learn the logic necessary to describe propositions, ideas necessary to demonstrate inclusion relations of sets, and distance spaces which are the Euclid spaces and its abstraction. Further abstraction (topological spaces) is learned in "Geometry I" class.
Purpose of class
Modern mathematics is based on the idea of "sets". For example, in mathematics up to high school, it was the main to investigate the properties of individual sequences and functions given, but in university mathematics, conversely, to consider sequences having the same property ("the set of such sequences"), and functions having the same property ("the set of such sequences"), etc. By introducing the concept of inner product and distance into such a set, we will consider the abstraction (distance spaces) of Euclid space by making something similar to the world we know well.
Goals and objectives
  1. You can describe propositions logically.
  2. You can demonstrate properties of sets and maps.
  3. You can demonstrate properties of sets in Euclidean spaces.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Logic 1: propositional logic, truth table Check out "Logic" in advance. 190minutes
2. Logic 2: predicate logic, \forall, \exists Review the previous session in advance. 190minutes
3. Set 1: Fundamentals of sets Review the previous session in advance. Check out "Set" in advance. 190minutes
4. Set 2: family of sets, direct product Review the previous session in advance. 190minutes
5. Set 3: equivalence relation, equivalence class Review the previous session in advance. 190minutes
6. Map 1: inverse image, surjection, injection Review the previous session in advance. Check out "Map" in advance. 190minutes
7. Map 2: composition Review the previous session in advance. 190minutes
8. Attention on Mid-term assignment Review Session2 1-7 in advance. 190minutes
9. Cardinality: countable set, diagonal argument, power set, cardinality of the continuum Review "surjection" and "injection". 190minutes
10. 1-dim Euclidean space 1: \epsilon-neighbourhood, adherent point, accumulation point, inner point, exterior point, boundary point, closure, closed set Check out "Geometry and Equations" in advance. 190minutes
11. 1-dim Euclidean space 2: open set Review the previous session in advance. 190minutes
12. n-dim Euclidean space: \epsilon-neighbourhood, Heine-Borel's theorem Review the previous session in advance. 190minutes
13. Metric space: distance function, example Review the previous session in advance. 190minutes
14. Attention on Final assignment Review Sessions 9-13 in advance. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term assignment Final assignment Total.
1. 30% 10% 40%
2. 20% 10% 30%
3. 30% 30%
Total. 50% 50% -
Evaluation method and criteria
Mid-term assignment and Final assignment. As a criterion, if you determine that you understand 60% of the content covered in the class, your final score will be 60 points.
Textbooks and reference materials
Ken Kuriyama, "Ronri, Syugou to Isoukuukan nyumon", Kyoritu-shuppan.
Prerequisites
Check out "Logic", "Set", "Map", and "Geometry and Equations" in your high-school textbook.
Office hours and How to contact professors for questions
  • Lunchtime on every Tuesday.
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
Last modified : Sun Mar 21 16:02:57 JST 2021