Year 12 masterclasses

Session Title

Led by

Date

How to hold a pizza: lessons from Gaussian curvature
Behind the perfect pizza slice, is the mathematician who knows how to hold it. In this masterclass, we will learn about Gaussian Curvature and what that means when we bend a two-dimensional object (or pizza!). The consequences of this remarkable result have allowed us to manufacture strong materials, but have also demonstrated the endless problem of drawing accurate map projections of the world.

Thomasina Ball

Warwick Mathematics Institute

24/01/2026

Fantastic Ramsey numbers and how to find them

Here is a claim: In any gathering with at least 6 people, irrespective of how these people are chosen, there will always be either 3 people who all know each other or 3 people who are all strangers. This looks weird and sounds more like a sociological property. But in fact, this is a completely mathematical fact!

Here's a second question: What is the relation between the numbers 6 and 3 in the above claim? Does it work for 8 and 4? In this talk, we will discuss how to think about such problems and maybe if we get time, mention a related question which has troubled mathematicians for 75+ years!

Akshat Mudgal

Warwick Mathematics Institute

31/01/2026

Why Swings Swing: Mathematics of Repeating Motion

Why does a pendulum keep swinging? Why does a pendulum keep swinging? How can a stretched soap film pull itself back into shape? And why does motion inside the Earth follow the same rules as a mass on a spring? And why does motion inside the Earth follow the same rules as a mass on a spring? In this masterclass, we will explore how mathematics helps us understand oscillatory motion — movements that repeat again and again.

Using , everyday examples, we will try to discover, how many different physical systems can be described by the same mathematical idea called simple harmonic motion. We will see how energy moves between different forms, why equilibrium matters, and what changes when motion is slowed down by friction or resistance.

This session is designed to show how a few mathematical ideas can explain a wide range of physical phenomena, and how mathematics turns motion into something we can predict, understand, and even play with.

The outline of my talk is:

• Introduction to oscillatory motion through familiar examples (pendulum, swing, motion through a tunnel dug across the diameter of the Earth).
• Differential equation form of simple harmonic motion.
• Energy viewpoint: exchange between kinetic and potential energy and the role of equilibrium.
• Key property of SHM: time period independent of amplitude.
• Contrast with non-SHM systems (e.g. motion in a V∝x4 potential where the time period depends on amplitude).
• Comparison of time periods across different SHM systems.
• Brief discussion of damped oscillations and how friction changes motion.

Ravi Singh

Warwick Mathematics Institute

07/02/2026

Pattern detectives: Uncovering the symmetries of designs
Look closely at the world around you and you will find patterns everywhere: on wallpapers, carpets, clothes, and even in nature. Hidden beneath these designs lies a mathematical secret: every repeating pattern is built from symmetries. In this masterclass, you will become a pattern detective, learning how to identify the symmetries in real examples of patterns found in architecture and fashion.

Alvaro Gonzales Hernandez

Warwick Mathematics Institute

28/02/2026

Mathematical modelling (and a jar of wet sand)
Mathematical models are everywhere in modern life eg: in weather forecasting, streaming services' algorithms, and designing race cars. But how do mathematicians come up with these models? How do they decide what type of model is appropriate and how much detail to include? In this masterclass, we will discuss frameworks and analytical tools for mathematical model design and use these to model some real-world problems: pendulums, water droplets... and my jar of wet sand...

Ellen Luckins

Warwick Mathematics Institute

07/03/2026

Modular arithmetic is a simple, yet ingenious way to do arithmetic that has deep and diverse applications throughout mathematics and the sciences. For example, modular arithmetic has applications in number theory, cryptography, chemistry and even music.

In this lesson, we will learn the basics of modular arithmetic, quickly progressing to solve problems involving clockwork, the days of the week and finding the last digit of very large numbers! The elegance of these solutions should hopefully convince the students to adopt modular arithmetic as part of their mathematical toolbox and inspire them to learn more about the subject 😊.

Sunny Sood

Warwick Mathematics Institute

21/03/2025