Math 13: An Introduction to Abstract Mathematics

✍ Scribed by Neil Donaldson & Alessandra Pantano

• Year: 2019
• Tongue: English
• Leaves: 176
• Series: lecture notes
• Edition: version 15 Feb 2019
• Category: Library

✦ Table of Contents

Introduction......Page 3
Propositions......Page 9
Methods of Proof......Page 21
Quantifiers......Page 36
Remainders and Congruence......Page 45
Greatest Common Divisors and the Euclidean Algorithm......Page 52
Set Notation and Describing a Set......Page 58
Subsets......Page 65
Unions, Intersections, and Complements......Page 68
Introduction to Functions......Page 74
Investigating Recursive Processes......Page 85
Proof by Induction......Page 89
Well-ordering and the Principle of Mathematical Induction......Page 95
Strong Induction......Page 104
Cartesian Products......Page 109
Power Sets......Page 113
Indexed Collections of Sets......Page 118
Relations......Page 130
Functions revisited......Page 135
Equivalence Relations......Page 141
Partitions......Page 147
Well-definition, Rings and Congruence......Page 155
Functions and Partitions......Page 159
Cantor's Notion of Cardinality......Page 164
Uncountable Sets......Page 172