Math 13: An Introduction to Abstract Mathematics

✍ Scribed by Neil Donaldson & Alessandra Pantano

• Year: 2015
• Tongue: English
• Leaves: 156
• Series: lecture notes
• Edition: version 2 Dec 2015
• Category: Library

✦ Table of Contents

Introduction......Page 3
Propositions......Page 9
Methods of Proof......Page 20
Quantifiers......Page 33
Remainders and Congruence......Page 41
Greatest Common Divisors and the Euclidean Algorithm......Page 47
Set Notation and Describing a Set......Page 52
Subsets......Page 58
Unions, Intersections, and Complements......Page 61
Introduction to Functions......Page 66
Investigating Recursive Processes......Page 75
Proof by Induction......Page 79
Well-ordering and the Principle of Mathematical Induction......Page 84
Strong Induction......Page 92
Cartesian Products......Page 97
Power Sets......Page 101
Indexed Collections of Sets......Page 106
Relations......Page 116
Functions revisited......Page 120
Equivalence Relations......Page 125
Partitions......Page 131
Well-definition, Rings and Congruence......Page 138
Functions and Partitions......Page 141
Cantor's Notion of Cardinality......Page 146
Uncountable Sets......Page 153