##### 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.

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### An introduction to proof by contradiction

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

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### An introduction to mathematical induction

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

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### Direct logic

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

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### A KS5 proof collection

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

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### Prepare for university - pure mathematics

Helpful preparation for those intending to study a course involving pure mathematics at university.

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### Prepare for university - applied mathematics

Helpful preparation for university for those intending to study a
course involving applied mathematics at university.

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### NRICH and Olympiads

A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.