Lecture 1

Lectures notes will be posted on moodle after 24 hours, to encourage note taking.

Wait till after lecture 3/4 before starting example sheet 1.

0.1 Contents

Chapter 1. Elementary (Introductory) Number Theory

Primes, modular arithmetic.
No knowledge will be assumed except the meaning of these terms

Chapter 2. The Reals

Chapter 3. Sets and functions

Some important terminology will be introduced.

Chapter 4. Countability

Chapter 0. Proofs

A proof is a sequence of true statements without logical gaps, that establishes some conclusion.
We haven’t defined logical gaps etc …, we have to start somewhere and have agreed upon assumptions (axioms)

We want to prove things because

we want to know they are true;
We hope to gain insight into why they are true;
we might be lucky and the proof is beautiful.