1 February 2025 – 29 March 2025

University of Bath, UK

Supported by The Heilbronn Institute Small Grants Scheme

The Royal Institution Masterclass programme opens young people’s eyes to the diversity of mathematics, engineering and computer science. Through series of hands-on extra-curricular workshops, students all over the UK meet to explore these subjects in new and exciting ways.

Throughout a Masterclass series, students meet a range of speakers and volunteer helpers, giving them insight into possible careers and helping them to see that the science, technology, engineering and mathematics (STEM) subjects are for everyone. The Royal Institution Masterclasses aim to inspire students to continue their interest and engagement into the future. The Royal Institution work with dedicated contributors who take on a variety of roles to make Masterclasses happen in their area.

Organisers:

Chris Budd (Bath)
Jayne Stansfield (Bristol)

Speakers:

Jehan Alswaihli  (Bath):  The Magic of Symmetry
The goal of the session is to support students to explore symmetry of patterns in maths, art, and nature. This is a chance for them to enrich their understanding, improve problem-solving skills, and encourage curiosity about mathematical concepts.

James Davenport (Bath): Cryptography
We discuss examples of cryptography (secret writing) from history (Jules Caesar) and fiction (Sherlock Holmes), and the students will work on an example. These depend on the participants having an agreed secret code. But these days we want to go to an online shop and buy secretly (certainly the credit card details, even if not the “day return to Bristol”) when we don’t have any agreed secret. We demonstrate how this is possible, and the students then work on another example. We conclude with more modern cryptography, notably digital signatures.

Ben Adams (Bath): Random Walks
Choose a direction at random. Face in that direction. Take one step forward. Choose another direction at random, take one step forward. Repeat x 10. Where do you end up? Is the outcome the same every time you do this random walk? How often to you return to where you started? We’ll use maths to explore these questions, and make serendipitous connections between stock markets, stink bombs and albatrosses.

Bill Lionheart (Manchester):  Fourier: Tones and Tides
Musical sounds can be represented by a function that oscillates and can be decomposed in to a sum of simple sine waves of different frequencies. The height of the sea also oscillates with two high and low waters each day but the details of the graph of the tidal height against time also depends on the position of the moon and the sun relative to the earth. We can express this as a sum of terms oscillating with different frequencies. We will look at some examples of building up graphs form a sum of these simple sine curves. A process called “Fourier analysis”. We will make some noises into microphones and see if we can understand what the effect is of having different amounts of each frequency. We will also look at a simulation of an ingenious mechanical system that draws a tidal height curve using string and pulleys. Fourier analysis is a very important mathematical tool and without it we would not have digital communication, digital audio processing and many of the technologies that are part of everyday life.

Ilaria Bussoli (Bath):  Statistical Investigators: Hypothesis Tests
Have you ever wondered how is it decided if a cough syrup really helps with your cough and is really different from all other brands on the market? Or how is it determined if a particular player or athlete is more performant than all others? In this masterclass, we will answer these and more questions by actively engaging with one of the core tools of statistical investigation: hypothesis testing. Through hands-on exploration, you will learn about random variables and their sampling distributions, practice formulating your own hypotheses, and use probability to make smart decisions when testing them.

2 classes  by undergraduates on the Communicating Maths course TTBA