Schools and public outreach

Combining mathematics and history, this session uses a model of the Enigma machine to show how messages were kept secret during the Second World War.

Session leader: Chris Hughes

Put your secret-keeping skills to the test!

This session is an easy introduction to the mathematics of codes, from simple Caesar cyphers to modern-day cryptography.

Session leaders: Stephen Connor and Chris Hughes

How long does it take for a fingernail to grow? How many layers are there in a croissant?

In this session, we use some simple maths to investigate how things around us grow at different speeds, using fingernails, knitting, croissants and Covid-19 as examples.

Session leader: Stephen Connor

A simple coin-tossing game with some very counter-intuitive properties. This session explores these properties, and shows how to use the binary number system to work out optimal game strategies.

Session leader: Stephen Connor

We use Venn diagrams and simple probability to understand how statistics arising from medical tests and court cases can be misinterpreted.

Session leader: Stephen Connor

With this activity we'll explore the sometimes surprising behaviour of infinity, and in particular the existence of different sizes of infinity.

Session leader: Emilie Dufresne

Combining mathematics and history, this session explains how the Second World War Enigma machine worked, why it was considered to be ultra secure at the time, and how a simple mathematical theorem concerning permutations enabled it to be broken by the Allies.

Session leader: Chris Hughes

Using probability, logarithms and differentiation, this session uses a simple dice game to establish the Kelly principle, 'the Fundamental Theorem of Betting,' - and shows how hard it is to make money through gambling.

Session leader: Niall MacKay

Pick a number. If it's even, halve it. If it's odd, multiply by three and add one. Repeat. Do we always, eventually, reach one? This is the '3x+1 problem' or 'Collatz conjecture' -- and no one has any idea how to prove it. In this session, aspects of the problem are described and worked out on the board, combined with a "game" on a big table in which we try to reverse-engineer the problem using cards each with an integer on one side and its image under the map described above on the other.

Session leader: Niall MacKay

We can offer mock interviews for students applying to Oxford or Cambridge for whom the process may be alien or intimidating and who have no other source of comparable support.

Session leaders: Niall MacKay and Michael Bate

An introduction to group theory via bell-ringing and the 15 puzzle.

Session leader: Michael Bate

The maths of ecosystems, climate change and how to go to the toilet!

Session leader: Jon Pichford

A gentle introduction to the mathematics of card shuffling, involving probability, permutations and a little magic.

Session leader: Stephen Connor

The maths hidden underneath this simple conundrum has direct relevance to real problems in ecology and evolution such as:

• How fast should a fish swim?
• Why do elderly people break their bones so easily?
• How do bacteria learn to gamble?

Session leader: Jon Pitchford

A workshop in which students are challenged to spot patterns and conjecture solutions to problems involving cake cutting, drawing graphs, and sharing gold between pirates.

Session leader: Stephen Connor

An exploration of prime numbers, from historical results to modern day advances, including how these fascinating numbers are now crucial to the security of the internet through public key cryptography.

Session leader: Chris Hughes

In this simple slide-based talk, we use first-order differential equations and a little statistics to understand the tactics and outcome of the Battle of Britain

Session leader: Niall MacKay

This workshop introduces students to the idea of mathematical proof. We talk about why mathematicians care so much about proof, and see examples of some famous theorems. We then look at proof by contradiction and by induction, with the students working through plenty of examples of each type.

Session leaders: Stephen Connor and Benito Aubry