School of Mathematics

Mathematics Masterclasses

Our Royal Institution Mathematics Masterclasses, jointly organised with Heriot-Watt and Napier Universities, are interactive and hands-on super-curricular classes designed to stimulate and encourage young people in the art and practice of mathematics. Masterclasses are designed to stretch and inspire keen and talented pupils from all over the Edinburgh and Lothian regions, allowing them to broaden their mathematical knowledge and develop a sense of enjoyment in the subject. Classes are led by top experts from academia and industry, and cover a broad range of mathematical topics.

Our Mathematics Masterclasses series, jointly organised with Heriot-Watt and Napier Universities, runs for eight weeks in the autumn term, starting in mid-September. Every Saturday morning, a different speaker is invited to share their favourite part of mathematics, which could be an interesting game they've played, an aspect of their cutting-edge research, a magic trick, or an unexpected connection between maths and another subject. Classes are never just a dry lecture, but are highly interactive and a great opportunity for pupils to develop critical thinking and problem-solving skills.

Schools from the Edinburgh and Lothian regions are invited to nominate up to two S2 pupils to take part in the series; we usually accept around 90 pupils, from a mix of state and private schools. Parents cannot nominate their child directly, but are encouraged to speak to their child's teacher if they are interested. Pupils are selected based on their enthusiasm for mathematics and their work ethic rather than purely on their mathematical ability. You can find out more about Royal Institution Masterclasses here.

Pupils taking part in Mathematics Masterclasses

Programme for 2017 series

Date Speaker     Title     Description
30th September     Gavin Reid

What are the chances?!


Probability is fundamental to many real-life mathematical problems. We'll look at how we can use it to more scientifically quantify uncertainty and apply these ideas to understand how a clever punter might beat a bookie, the chances of winning the lottery, and how you might use maths to win in a game show!

7th October Philipp Rueter Knots in Math


Knot theory is the mathematical study of knots. The knots in this context are a bit unlike the knots we know from real life, in that we always take them to be a closed loop with a knot in it. The simplest knot is then the "unknot", which is just a circle. We can also draw more complicated pictures of knotted loops and can try to untie those. Or, given two different pictures of knots, we can try to decide, if they actually show the same knot.

We will first try to answer these questions for some examples and then try to formalize a bit what we learned. We will also see how coloring knots can help with some of these questions.








Break over school holidays.

28th October Chris Sangwin How     Round is Your             Circle?


Mechanisms are all around us, but we often take them for granted, or don't even notice they exist. Many rely on rotating parts. That is, one circular part which fits inside another. To work smoothly and without wearing out they need to be made very accurately. In some situations this is critical to safety.  How do you test if something is round? The mathematics needed to answer to this question involves the shape of the 50p coin, the NASA Space Shuttle Challenger explosion in 1986 and how to drill a square hole.

4th November Catherine Ramsay

The Elemental Solids


Meet the three dimensional shapes that have captured the interest and imagination of mathematicians for thousands of years. We will discover their mystical origins, investigate their properties and prove important results about these and other polyhedra in a hands on exploration of the beauty and order of euclidean geometry.

11th November


Des Johnston


The Game of Life


The Game of Life was invented by a British mathematician, John Horton Conway, in 1970. It is played on a square grid like a chess board on which cells live, die or are born according to simple rules. In many ways these cells behave like living things, in spite of the simplicity of the rules that govern their fate, and this led to the name of "Life" for the game. The masterclass session first introduces the Game of Life and explains the rules. We will then play Life on a computer, exploring different starting patterns and even the effect of changing the rules, and also explore the game on paper.

18th November Dorothy Winn

Combinatorics - Learning to Count


Combinatorics is all about counting - any problem which starts "How many...." is likely to be answered using Combinatorics. How many ways are there to order the numbers 1 to 10? How many ways are there to escape from a given maze? How many shapes are made up of four squares? Or five squares? We will work out some of the fundamental principles of Combinatorics in a hands on session with lots of engaging problems.

25th November Mark Wilkinson

The Maths of Social Media


It might surprise you, but the way in which the internet is used by society gives rise to many interesting (and often very tough!) mathematical problems. For instance, in what manner and how quickly does information spread through social media? Can one effectively stop the spread of "fake news"? How can one even identify "fake news" on sites such as Facebook? In this Masterclass, we shall learn the basic mathematical language of graphs, which are important mathematical structures that mathematicians use to model the internet. We shall then tackle some mathematical problems that even employees of Google might find intriguing!

2nd December Mairi Walker Mapping the world


Maps have been used for thousands of years to help us explain and explore the world around us. But how well does a map actually represent the surface of the Earth? In this masterclass we will explore different ways of mapping the world, and see how the problems we encounter lead us into an entirely new world of geometry.


The final masterclass will end with a closing ceremony at which pupils who have regularly attended the masterclasses will be awarded a certificate. Parents are invited to this masterclass, and the morning will finish with a celebratory buffet.

The Edinburgh & Lothians Mathematics Masterclasses are supported by the University of Edinburgh, Heriot Watt University, Napier University and the Royal Institution. We are very grateful to the Glasgow Mathematical Journal Trust and the James Clerk Maxwell Foundation for their financial support of our 2017 series. If you are interested in offering us financial support for future years then we would be glad to hear from you!