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。

Apr 11 Lecture 1　1. Introduction to Logic, 2 Sets (2 periods)

Recitation 1 (1 period), Chapter 2. Logic

Apr 18 Lecture 2　3. Direct Proof and Proof by Contrapositive

Recitation 2, Ch. 2+3. Logic, and Sets

Apr 25 Lecture 3　4. Existence and Proof by Contradiction, Math. Induction

Rec. 3, Ch. 4+5 Direct Proof and Proof by Contrapositive

May 02 Lecture 4　5. Prove or Disprove, Equivalence Relations

Rec. 4, Ch. 6+7 Existence and Math. Induction

May 09 Lecture 5　6. Functions

Rec. 5, Ch. 8+9 Prove or Disprove, Equivalence Relations

May 16 Lecture 6　 7. Cardinality of Sets (i)

Rec. 6, Ch. 10 Functions

May 23 Lecture 7　8. Cardinality of Sets (ii)

Rec. 7, Ch. 11 Cardinalities of Sets

May 30 Lecture 8　9. Proofs in Number Theory

Rec. 8, Extra Problems on Cardinalities of Sets

Jun 06 Lecture 9　10. Review

Rec. 9, Ch. 12 Proofs in Number Theory

Jun 13 Lecture 10　11. Review

Old Final