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 inclusion relations of sets.
  3. You can do topological discussions on an abstract space.
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: inverse image, surjection, injection, composition Review the previous session in advance. Check out "Map" in advance. 190minutes
7. Cardinality: countable set, diagonal argument, power set, cardinality of the continuum Review the previous session in advance. 190minutes
8. Mid-term exam Review Session2 1-7 in advance. 190minutes
9. 1-dim Euclidean space 1: \epsilon-neighbourhood, adherent point, accumulation point, inner point, exterior point, boundary point, closure Check out "Geometry and Equations" in advance. 190minutes
10. 1-dim Euclidean space 2: closed set, open set, Bolzano-Weierstrass' theorem, Heine-Borel's theorem Review the previous session in advance. 190minutes
11. n-dim Euclidean space: inner product, Schwarz inequality, Euclidean distance, Heine-Borel's theorem Review the previous session in advance. 190minutes
12. Metric space 1: example Review the previous session in advance. 190minutes
13. Metric space 2: topology Review the previous session in advance. 190minutes
14. Final exam Review Sessions 9-13 in advance. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Midterm exam Final exam Total.
1. 50% 25% 75%
2. 25% 25%
Total. 50% 50% -
Evaluation method and criteria
Mid-term exam and Final exam.
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.
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
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 applicatable
N/A N/A
Last modified : Mon May 06 04:02:19 JST 2019