# Advanced Problem Solving Module 3

## Advanced Problem Solving Module 3

Proof is at the heart of mathematics. This module introduces you to some different proof methods, together with some opportunities for you to have a go at writing your own proofs. Don't expect to write a perfect proof on your first attempt; most formal proofs begin life as a messy outline, which are written up neatly later.

### An Introduction to Proof by Contradiction

##### Stage: 4 and 5

An introduction to proof by contradiction, a powerful method of mathematical proof.

### An Introduction to Mathematical Induction

##### Stage: 5

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.

### Direct Logic

##### Stage: 5 Challenge Level:

Can you work through these direct proofs, using our interactive proof sorters?

### Can You Prove It?

##### Stage: 5 Challenge Level:

Here are a collection of statements to prove, to help you to practise writing out clear mathematical proofs.

### Dodgy Proofs

##### Stage: 5 Challenge Level:

These proofs are wrong. Can you see why?