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 the symbols that appear in set theory. Understand and able to describe the negation and contrapositive of a quantified statement.
3. Understand the methods to prove statements. 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 the symbols that appear in set theory.
Sufficiently understand the negation and contrapositive of a quantified statement. | Understand the symbols that appear in set theory.
Understand the negation and contrapositive of a quantified statement. | Do not understand the symbols that appear in set theory.
Do not understand the negation and contrapositive of a quantified statement. |
| Evaulation Item 3 | Sufficiently understand the methods to prove statements. Able to prove a simple statement. | Understand the methods to prove statements. Able to prove a simple statement. | Do not understand the methods to prove statements or not able to prove a simple statement. |
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, which are 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 |
| 前期 |
| 1stQ |
| 1週 |
Guidance |
Understand the content of this course, and able to explain the overview.
|
| 2週 |
Set (1) |
Understand the descriptions of sets and special sets, and able to explain.
|
| 3週 |
Set (2) |
Understand the concepts of subsets, set operations and cartesian product of sets, and able to explain.
|
| 4週 |
Logic (1) |
Understand the statements and logic operations (disjunction and conjunction), and able to explain.
|
| 5週 |
Logic (2) |
Understand the statements and logic operations (implication and negation), and able to explain.
|
| 6週 |
Set and logic |
Understand the relationship between naive set theory and logic, and can explain.
|
| 7週 |
Exercises |
Able to solve applied problems.
|
| 8週 |
Exercises |
Able to solve applied problems.
|
| 2ndQ |
| 9週 |
Statements and proofs (1) |
Understand direct proof (naive method involving systematic thinking of the definition), and able to explain.
|
| 10週 |
Statements and proofs (2) |
Understand "proof by contrapositive", and able to explain.
|
| 11週 |
Statements and proofs (3) |
Understand "proof by cases", and able to explain .
|
| 12週 |
Proposition and proof (4) |
Understand "proofs involving divisibility of integers", and able to explain.
|
| 13週 |
Proposition and proof (5) |
Understand "proofs involving divisibility of integers" and able to explain.
|
| 14週 |
Exercises |
Able to solve applied problems.
|
| 15週 |
Exercises |
|
| 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 | |
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 exam | 50 | 0 | 0 | 0 | 0 | 0 | 50 |
| Final exam | 50 | 0 | 0 | 0 | 0 | 0 | 50 |