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.
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.
- You can describe propositions logically.
- You can demonstrate properties of sets and maps.
- You can demonstrate properties of sets in Euclidean spaces.
| Mid-term exam | Final exam | Total. | |
|---|---|---|---|
| 1. | 30% | 10% | 40% |
| 2. | 20% | 10% | 30% |
| 3. | 30% | 30% | |
| Total. | 50% | 50% | - |
| 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. | Mid-term exam and review | 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. | Final exam and review | Review Sessions 9-13 in advance. | 190minutes |
| Total. | - | - | 2660minutes |
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.
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in outside of the class (ScombZ, mail, etc.) |
Ken Kuriyama, "Ronri, Syugou to Isoukuukan nyumon", Kyoritu-shuppan.
Check out "Logic", "Set", "Map", and "Geometry and Equations" in your high-school textbook.
- During class periods, every Wednesday after 4th period (it is advisable to call in advance when visiting).
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
- 4.QUALITY EDUCATION
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Wed Apr 02 04:09:36 JST 2025