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### Advanced mathematics

# Advanced Problem Solving Module 3

##### Working through this module will help you to consolidate your existing knowledge before extending your thinking. For more details about the Advanced Problem Solving programme, READ THIS.

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

### An Introduction to Mathematical Induction

### Direct Logic

### A KS5 Proof Collection

### Dodgy Proofs

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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.

Age 14 to 18

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

Age 16 to 18

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

Age 16 to 18

Challenge Level

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

Age 16 to 18

Challenge Level

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

Age 16 to 18

Challenge Level

These proofs are wrong. Can you see why?