# Mathematics and Statistics

## An introduction to the tutors and students

## Why study statistics?

Statistics is an exciting area of modern mathematics. Are humans the cause of global warming? Which genetic mutations are associated with common human diseases? Statistical models and modern computational techniques can help to answer such questions. One reason statisticians are now in high demand is that data storage has plummeted in cost and efficiency (you only need to compare the early punch cards used in the 1920s, which could store around 70 bytes of data in a piece of card 18.7cm by 8.3cm, to current USB drives - the biggest of which stores 1TB (10^12 bytes) on a 7.2cm by 2.7cm stick). As data is cheap, people (and companies) start collecting it and in order to do any meaningful analysis they must use statistics. Statistics is used by companies like Netflix to tell you what other films you might like to watch, Amazon to tell you what other products you might want to buy, and Google to translate from one language to another.

## What's in the course?

The first year course in Maths and Statistics is the same as the first year course in Mathematics. This gives you a solid grounding in both pure and applied maths, from integration to multivariable calculus. From the second year on, students have a wider range of statistics options (including simulation and statistical programming) as well as compulsory statistics courses (applied statistics, which includes computer practicals). In the fourth year, you undertake a research project in an area of statistics, probability, or operations research. The project is a great opportunity to carry out a substantial piece of statistical work, whilst giving you the communication skills to explain statistics. This latter component is particularly important for statisticians, as statistics is frequently misused and misunderstood in the media.

If you want to see a complete list of the courses available, take a look at the course handbook.

## Who is this course good for?

- If you want to apply maths to real world situations, using modelling and programming.
- If you enjoy having your intuition confused (see the Efron's dice problem below).
- If you want to go into actuarial work, health, or finance.

## Problems to think about

**Probability**

Efron's dice are a set of four dice, with the following numbers on their six sides:

A: 4, 4, 4, 4, 0, 0

B: 3, 3, 3, 3, 3, 3

C: 6, 6, 2, 2, 2, 2

D: 5, 5, 5, 1, 1, 1

Looking at each consecutive pair of dice (e.g. A and B, B and C, and so on), what is the probability that each dice beats the next?

If I take A, what is the best die for you to pick in order to maximise the likelihood of you winning? Is this always the best die to pick?

What is the expected value (that is, the average score) for each die?

Can you find a set of four dice that have the same odds of winning against each other, but also have the same expected value? What does this tell us about data analysis?

## For more information

Have a look at the Department of Statistics website, and have a read through their departmental prospectus. They also have a list of frequently asked questions.

There are many good websites explaining statistics. Some of the more accessible include Understanding Uncertainty, Significance magazine, and Five Thirty Eight.