1
Introduction
1.1
How to use these notes
2
The building blocks of pure mathematics - sets and logic
2.1
Sets
2.2
Truth table
2.3
Logical Equivalence
2.4
Negations
2.5
Contradiction and the contrapositive
2.6
Set complement
3
The rationals are not enough
3.1
The absolute value
3.2
Bounds for sets
3.3
The irrationals and the reals
3.4
The supremum and infimum of a set.
4
Proof by induction
5
Studying the integers
5.1
Greatest common divisor
5.2
Primes and the Fundamental Theory of Arithmetic
6
Moving from one set to another - Functions
6.1
Definitions
6.2
Injective, surjective and bijective
6.3
Pre-images
6.4
Composition and inverses of functions
7
Cardinality
8
Sets with structure - Groups
8.1
Motivational examples - Symmetries
8.1.1
Permutations of a set
8.1.2
Symmetries of polygons
8.1.3
Symmetries of a circle
8.1.4
Symmetries of a cube
8.1.5
Rubikb