We have a variety of talks available for schools, colleges and other interested parties. These talks, which will be presented by a researcher (or research student) from the Department, can be presented either at the University of Sussex or at an alternative location (e.g. your school) if within a reasonable travel time (approximately 90 minutes) from the University.
All our activities are suitable for Key Stage 4 and 5 (e.g. GCSE and AS/A-level/sixth-form) students.
All our talks are approximately 45 minutes in length, allowing time for questions at the end.
Available talks include (abstracts are shown towards the bottom of the page):
- Taking chances!
- How likely is that?!
- Sending secret messages
- Getting the right message
- Soap bubbles, snow flakes and walking on water
- Painting maps and colouring zebras: A journey into the secret life of plane curves!
- Turning spheres inside out: The mystery of surfaces
- The maths of animal spots and stripe patterns
- Dynamical Systems: between attractivity and chaos
- Synchronisation in technology and nature
- Clouds and coastlines
Talk overviews
Taking chances!
Dr John Haigh
Random chance influences many activities in life. By looking at several different situations, we see how an understanding of the workings of probability helps us come to good decisions in the face of uncertainty, or to gain an advantage in friendly games involving chance. Suitable for GCSE students.
How likely is that?!
Dr John Haigh
Random chance influences many activities in life. By looking at several different situations, we see how an understanding of the workings of probability helps us come to good decisions in the face of uncertainty, or to gain an advantage in friendly games involving chance. Suitable for A-level students.
Sending secret messages
Prof James Hirschfeld
The science of sending secret messages is Cryptography and goes back over 2000 years. Secret messages are widely used in modern communication. Electronic authentication, banking, and credit cards are just a few applications.
The mathematics behind this often relies on properties of prime numbers. In this talk relevant properties of prime numbers are described. Both ancient and modern methods of Cryptography are outlined.
Getting the right message
Prof James Hirschfeld
The mathematics of correcting errors in a transmitted message was first described in 1948 and is known as Coding Theory. It is widely applied in modern communication. Credit cards, digital radio, mobile phones, sending photographs from satellites all use error-correcting codes. The mathematics behind this is linear algebra, that is, solving linear equations. In this talk, some simple examples are explained, such as the use in credit cards.
Soap bubbles, snow flakes and walking on water
Dr Omar Lakkis
Molecules are bit like people - some attract each other and some repel each other. Water molecules are attracted to each other and "stick together" which is why rain comes down in droplets, but water and oil molecules don't like each other and repel each other. The pressure (or force) that binds molecules together is called "surface tension".
A new and developing branch of mathematics looks at surface tension and time evolution of surfaces: for example how crystals and snowflakes grow. And add enough cornstarch to water and the surface tension increases (because water and starch love each other and form giant molecules known as polymers), so much so that the miracle of walking on water becomes reality.
Mathematics makes it possible to simulate these phenomena on a computer. By doing so, scientists can understand these phenomena better and engineers can design manufacturing of crystals processes better.
Painting maps and colouring zebras: A journey into the secret life of plane curves!
Dr Ali Taheri
A circle has an "inside" and an "outiside"; any two points in the inside can be joined by a continuous curve lying completely in the inside, and likewise any two points in the outside can be joined by a continuous curve lying completely in the outside but any continuous curve joing a point in the inside to a point in the outside must hit the boundary circle at some point. The same is ture of a square, a rectangle and an ellipse, but not of the "figure 8" or an "anunuls". What is the difference? How will things change if one considers a more complicated shape?
If one want to colour the black stripes of a zebra or a colour green the map of an island can one do so all at once without having to lift the pen? How can one decide if two points on the Zebra's skin are to be painted black or two points on the map are to lie on the island and not one in the surrounding sea?
Topology provides an answer: The Jordan Curve Theorem! The story begins with ...
Turning spheres inside out: The mystery of surfaces
Dr Ali Taheri
A soap bubbles, a chocolate doughnuts and a ginger pretzel are all examples of surfaces in our day-to-day lives. Geometric objects such as curves and surfaces and their "higher dimensional" analogues have fascinated mathematicians and physicists for centuries. For example a soap bubble has an inside face (which you can't touch) and an outside face (which you can touch). The same thing applies to the surface of a doughnut and pretzel: there is an inside face and an outside face. But not every surface has to have two separate faces! Think about the Mobius band: an ant can walk along the band and cover both sides without having to jump across the band. A natural question thus is: If a surface has two separate faces can one swap them by turning it inside out without having to damage the surface? Think, e.g., about turning your jumper, pants or gloves inside out! You dont have to tear it to do so! But can you do this to a bubble? Thus sometimes the answer is yes and sometimes "NO". Really? Well I'll show you an amazing way of doing this!
The maths of animal spots and stripe patterns
Dr Anotida Madzvamuse
For many centuries, the science of pattern formation in nature has fascinated experimentalists and theoreticians alike. Despite this enormous interest, the question of how patterns form remains unanswered. What is a pattern? What is responsible for its formation? Is it genetics or cells differentiating or is it the environment? Is growth important? In many cases patterns are well ordered raising the possibility of the existence of common principles underlying there formation. For example, spots of the leopard, butterfly wing patterns, spots and stripes on sea shells, fish patterns and so on. In order to understand the emergence of these patterns, biologists, experimentalists and mathematicians must work together to understand complex biological and chemical processes. In this presentation, we present an array of some of the spectacular patterns observed in nature and present plausible mathematical mechanisms that can generate these patterns through the use of a computer.
Dynamical Systems: between attractivity and chaos
Dr Peter Giesl
Dynamical systems arise everywhere in nature: they describe populations of foxes and rabbits, the movements of planets, weather forecast, even acrobatics. They are systems which evolve with time. Such systems can have very different long-time behaviour: either they can tend to a certain state, e.g. foxes and rabbits die out eventually, or just one of them survives. Or they can tend to a periodic orbit, e.g. a planet moving around the sun. They can also be chaotic, such as the famous Lorenz system, describing weather. In this talk we will see a variety of dynamical systems in pictures and movies, and we will understand what "attractive" and "chaotic" really means!
Synchronisation in technology and nature
Dr Konstantin Blyuss
Synchronization is a universal phenomenon arising when in a large system of connected units, suddenly they start to behave as one. This spans all scales and types of systems: from schools of fish to swarms of birds and fireflies, to neurons in the brain and people walking on a bridge. This talk will introduce and discuss some examples of how synchronization arises and how it can be studied mathematically.
Clouds and coastlines
Dr Adrian Martin
In many areas of mathematics, in particular classical calculus, we deal with objects which are in some sense fairly smooth. Nature, on the other hand, presents us with objects that are very much not smooth, such as clouds and coastlines. We can model these mathematically using the concept of fractals (which are pretty popular on posters). But in order to develope a theory of fractals we first need to take another look at the concept of dimension, and discover that it is not as simple as we may first have thought.