This video will explain the concept of a mathematical proof and explain how it is different to a “proof” in other areas. As you will see, the concept of a proof within mathematics is far more rigorous and precise than in any other areas and probably what you imagine a proof to be in your mind. It doesn’t build on any of the previous videos, feel free to watch this one straight away.

## Before You Watch

## Now What?

This video is designed to give you an introduction to the basic concepts of a mathematical proof. If you wish, you can continue to develop your knowledge of statistics through some of the links below.

Alternatively you can go and have a look at some of the other videos available, such as Introduction to Algebra or Introduction to Calculus.

## But When I am Going to Use This

Probability is widely used in situations where there are a number of unpredictable events. The most obvious example is that of gambling; casinos and poker machine operators study the probability of people winning and then adjust the returns for those winnings such that they have an extremely high probability of making money.

Probability is also used in insurance to determine the premiums that must be set in order for the insurance company to make money.

Another application of probability is in quantum physics. At the very small scale, movements of particles becomes unpredictable; we therefore must use probability to determine the likelihood of a particular event happening, like for instance the probability that an atom will split and trigger the atomic bomb.

## Other Links

**Maths is Fun** introduces a method of proving things called mathematical induction. A simplified explanation is provided along with some clear, basic examples.

The **Khan Academy** has a comprehensive set of video tutorials covering a large range of mathematical and other concepts, as well as questions to test your knowledge. This link takes you to a list of resources which discuss the application of proofs across a number of different areas. Randomly choose a few that sound interesting to you and start exploring the world of proofs.

**Patrick JMT** (Just Maths Tutorials) has many video tutorials covering lots of mathematical concepts. This content investigates proof by induction. Start by choosing Example 1 at the bottom of the screen that the link takes you to.