到達目標
1. Understand the concepts of sets and statements. Develop good command over the mathematical expressions and symbols describing those concepts.
2. Understand equivalence relations. Able to prove a simple statement.
3. Understand ordered relations. Able to prove a simple statement.
4. Understand functions. Able to prove a simple statement.
ルーブリック
| Ideal Level | Standard Level | Unacceptable Level |
| Evaluation Item 1 | Have sufficient command over mathematical expressions and symbols. | Have command over mathematical expressions and symbols. | Do not have command over mathematical expressions and symbols. |
| Evaluation Item 2 | Sufficiently understand equivalence relations. Able to prove a simple statement. | Understand equivalence relations. Able to prove a simple statement. | Do not understand equivalence relations or not able to prove a simple statement. |
| Evaulation Item 3 | Sufficiently understand equivalence relations, ordered relations and functions. | Understand equivalence relations, ordered relations and functions. | Do not understand equivalence relations, ordered relations and functions. |
学科の到達目標項目との関係
準学士課程(R5までのDP) R5までDP_1 科学技術の基礎知識・応用力の修得・活用
教育方法等
概要:
Learn about naive set theory and statements which are the foundations of mathematics in general. In addition, develop the logical reasoning skill which is one of the basic skills required to learn mathematics.
授業の進め方・方法:
Classes will be conducted in lecture as well as practical exercises format. Listen intently during lectures and actively participate in group discussions during practical exercises.
注意点:
Being familiar with the symbols that appear during lectures is important for the understanding of the subsequent lectures. Solve the exercise problems on a daily basis. Develop a habit of systematic thinking of the definitions.
授業の属性・履修上の区分
授業計画
|
|
週 |
授業内容 |
週ごとの到達目標 |
| 後期 |
| 3rdQ |
| 1週 |
Relations(1) |
Explanations and exercises related to relations and relation matrices.
|
| 2週 |
Relations(2) |
Explanations and exercises related to relations and relation matrices.
|
| 3週 |
Relations(3) |
Understand and able to explain relations and their reflexive, symmetric, transitive and antisymmetric laws.
|
| 4週 |
Relations(4) |
Understand equivalence relations and equivalence classes, and able to explain.
|
| 5週 |
Relations (5) |
Understand the algebraic structures and the ordered relations formed by equivalence classes, and able to explain.
|
| 6週 |
Relations(6) |
Understand the algebraic structures that can be formed from ordered relations, and able to explain.
|
| 7週 |
Exercises |
Able to solve the applied problems learned from 1st to 6th weeks.
|
| 8週 |
Second Semester Midterm Examination |
|
| 4thQ |
| 9週 |
Mappings (1) |
Understand the definition of mapping, and able to explain.
|
| 10週 |
Mappings (2) |
Understand surjective(onto) and injective(one-to-one) mapping, and able to explain.
|
| 11週 |
Mappings (3) |
Understand composite and inverse mappings, and able to explain.
|
| 12週 |
Boolean algebra (1) |
Understand the definition and the examples of boolean algebra, and able to explain.
|
| 13週 |
Boolean algebra (2) |
Understand the boolean algebra formed by the ordered sets. Understand that a logic circuit is an example of boolean algebra.
|
| 14週 |
Exercises |
Able to solve the applied problems from the contents learned after the second semester mid-term examination.
|
| 15週 |
Exercises |
Able to solve the applied problems from the contents learned after the second semester mid-term examination.
|
| 16週 |
|
|
モデルコアカリキュラムの学習内容と到達目標
| 分類 | 分野 | 学習内容 | 学習内容の到達目標 | 到達レベル | 授業週 |
| 専門的能力 | 分野別の専門工学 | 情報系分野 | 情報数学・情報理論 | 集合に関する基本的な概念を理解し、集合演算を実行できる。 | 4 | |
| 集合の間の関係(関数)に関する基本的な概念を説明できる。 | 4 | |
| ブール代数に関する基本的な概念を説明できる。 | 4 | |
| 論理代数と述語論理に関する基本的な概念を説明できる。 | 4 | |
| 離散数学に関する知識をアルゴリズムの設計、解析に利用することができる。 | 4 | |
評価割合
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | 合計 |
| 総合評価割合 | 100 | 0 | 0 | 0 | 0 | 0 | 100 |
| Mid-term Examination | 50 | 0 | 0 | 0 | 0 | 0 | 50 |
| Final Examination | 50 | 0 | 0 | 0 | 0 | 0 | 50 |