Basic Concepts in Mathematics I (Sets and Algebraic Structures)
Basic Concepts in Mathematics I (Sets and Algebraic Structures)
数学通論 I（集合と代数系）2017S
数学通論 I（集合と代数系）2017S
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Course Description
Course Description
Foundation of sets and algebraic structures basic to modern mathematics. Includes sets and mappings, equivalence relations and equivalence classes, cardinal, and algebraic structures. One period of lecture and two periods of recitation weekly.
現代数学の基本概念のなかから，集合および代数系の基礎を学ぶ。集合と写像，同値関係と同値類，濃度 および代数系。毎週講義1時限，演習2時限。
Contents of Lectures 9 Lectures / 8Videos
April 12: Lecture 1 1. Introduction to Logic, 2 Sets (2 periods)
April 12: Lecture 1 1. Introduction to Logic, 2 Sets (2 periods)
Recitation 1 (1 period), Chapter 2. Logic
Recitation 1 (1 period), Chapter 2. Logic
April 19: Lecture 2 3. Direct Proof and Proof by Contrapositive
April 19: Lecture 2 3. Direct Proof and Proof by Contrapositive
Recitation 2, Ch. 2+3. Logic, and Sets
Recitation 2, Ch. 2+3. Logic, and Sets
April 26: Lecture 3 4. Existence and Proof by Contradiction, Math. Induction
April 26: Lecture 3 4. Existence and Proof by Contradiction, Math. Induction
Rec. 3, Ch. 4+5 Direct Proof and Proof by Contrapositive
Rec. 3, Ch. 4+5 Direct Proof and Proof by Contrapositive
May 10: Lecture 4 5. Prove or Disprove, Equivalence Relations
May 10: Lecture 4 5. Prove or Disprove, Equivalence Relations
Rec. 4, Ch. 6+7 Existence and Math. Induction
Rec. 4, Ch. 6+7 Existence and Math. Induction
May 17: Lecture 5 6. Functions
May 17: Lecture 5 6. Functions
Rec. 5, Ch. 8+9 Prove or Disprove, Equivalence Relations
Rec. 5, Ch. 8+9 Prove or Disprove, Equivalence Relations
May 24*: Lecture 6 7. Cardinality of Sets (i)
May 24*: Lecture 6 7. Cardinality of Sets (i)
Rec. 6, Ch. 10 Functions
Rec. 6, Ch. 10 Functions
June 7: Lecture 7 8. Cardinality of Sets (ii)
June 7: Lecture 7 8. Cardinality of Sets (ii)
Rec. 7, Ch. 11 Cardinalities of Sets
Rec. 7, Ch. 11 Cardinalities of Sets
June 14: Lecture 8 9. Proofs in Number Theory
June 14: Lecture 8 9. Proofs in Number Theory
Rec. 8, Extra Problems on Cardinalities of Sets
Rec. 8, Extra Problems on Cardinalities of Sets
June 19: Lecture 9 10. Review
June 19: Lecture 9 10. Review
Rec. 9, Ch. 12 Proofs in Number Theory
Rec. 9, Ch. 12 Proofs in Number Theory
2017, Spring
Instructor: SUZUKI‚ Hiroshi 鈴木寛（ ICU Professor Emeritus 国際基督教大学 名誉教授） | Language of Instruction: E
Major: Mathematics 数学 | Course ID: MTH232 | Course Schedule: 5/W,(6/W,7/W) | Update: 2019.05.13 Category: Major Courses
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