*This is part of my notes for the Edexcel S1 exam, which I will be taking in
2017*

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. … A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

– Wikipedia

The benefits of a mathematical model are many. For instance, they are quite easy and quick to produce (usually), can simplify a more complex situation, and help us improve our understanding of the real world. Because of this they enable predictions to be made about the real world.

An example of this would be spelling correction. If you train a model with enough data, it can recognise when a word doesn’t match what it has seen before, and make a suggestion about what the writer likely intended to write. Another one would be predicting the weather.

However, the real world is far more complicated than mathematics, so often models only give a partial description of what is actually going on.

### Steps to produce a model

There are several steps required to produce a model.

- Develop the model
- Make a prediction
- Collect data from the real world
- Compare the real data with the prediction
- Refine the model if needed
- If the prediction was accurate, the model can be accepted.