# School of Mathematics

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“Richard Sykes Beckfoot SchoolI was very impressed by the Soft Stuff and Funny Fluids session especially how well the pupils engaged with the content.

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Below is a list of some of the talks in schools which we offer. As well as talks for students, we also offer talks for teachers and these are also described here. All our talks are offered free of charge. Schools outside West Yorkshire may be asked to pay transport costs.

## Talks for students

### Tides in extrasolar planets - by Dr Adrian Barker

Since the revolutionary first discovery of a planet that orbits a Sun-like star outside the solar system, astronomers have detected and partially characterised several thousand extrasolar planets. These planets have a diverse range of masses and radii, consisting of some that are as small as Earth, and some that are much bigger than Jupiter. Some planets orbit their stars very closely, much more closely than Mercury orbits our Sun. In this talk, I will introduce some of the remarkable observational discoveries of extrasolar planets over the past two decades, before describing how Mathematics can be used to understand some of their properties.

### Playing dice with epidemics - by Dr Martin Lopez-Garcia

Mathematical Epidemiology is concerned with the analysis of epidemic processes (spread of a given infection or disease), occurring in small (e.g. families), moderate (e.g. a hospital) or large (e.g. a country) populations. It allows us to forecast epidemic dynamics in these populations, and to test the efficacy of potential interventions to avoid or reduce the impact of these epidemics. During this talk, I will explain how probability theory and random processes can be used in order to virtually simulate real epidemics. To this aim, we will make use of an original "videogame" in which we simulate the spread of an infectious disease within a small group of individuals, and we will test different strategies to avoid the spread of the disease.

If students can have laptops, computers or tablets available during the activity, this could be transformed into a hands-on session.

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### Chaos, sunspots and global warming – by Prof Steve Tobias

Our nearest star, the Sun, is an active star, with solar activity leading to powerful events like solar flares and ejections of hot plasma that can be shot in the direction of Earth. Solar activity waxes and wanes in an eleven year cycle and even switches off occasionally. In this talk I will explain the mathematics behind the solar cycle, what it has to do with chaos and the double pendulum and what effect solar variability may have on the climate.

### Detonations – by Prof Sam Falle

Ordinary chemical combustion, such as that in a gas cooker, is slow and does not cause any violent disturbances. Similarly, the nuclear reactions in a power station do not usually destroy it. However, it is possible for both chemical and nuclear reactions to occur so fast that they produce a large increase in pressure with devastating consequences. In this talk I shall discuss the conditions under which this happens and show that although these are violent events, the resulting detonation waves can have some surprisingly regular patterns. These patterns are not merely pretty, they are also crucial to the existence of these waves. They can be observed in detonation waves in combustible gases and are also believed to occur in the certain kinds of stellar explosions.

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### Supernovae – by Prof Sam Falle

A supernova occurs when a star that is too massive to die quietly explodes at the end of its life. The energy released in this explosion is so great that the star becomes more than a hundred billion times as bright as the Sun for a period of six months to a year. The talk describes these events and uses the mathematical theory of explosions to illuminate the relationship between supernovae and explosions on Earth, particularly nuclear explosions.

### The Mathematics of Sex and Drugs and Rock and Roll – by Prof Alastair Rucklidge

I talk about three different topics, all with an underlying mathematical connection: differential equations. The three topics are:

- Sex - male fireflies flash in synchrony to attract females - how do they do it?
- Drugs - some of the visual hallucinations seen by drug users/migraine sufferers may be a result of pattern formation on the visual cortex.
- Rock & Roll - the double pendulum exhibits wildly chaotic oscillations.

The common thread is nonlinear differential equations, which go beyond the A-level syllabus, but the talk will indicate what students might expect to meet in a university mathematics course.

### How (not) to lie with statistics – by Dr Stuart Barber

We are bombarded with numerical information every day, and it is often hard to know what the real message is. Even worse, sometimes people set out to deliberately mislead us. This talk looks at several examples of how to spot mistakes or untruths that hide behind statistical data.

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### Paradoxes and unplayable games – by Prof. Jonathan Partington

It is often observed that Mathematicians spend a lot of time playing games, and indeed many parts of Mathematics have their foundations in game playing. My object in this talk is to give some examples of games which either can't be played (though that needn't stop you), or if they can be played, will at least cause a few surprises. Examples that may be considered include Colonel Blotto's game, Auctioning a Five-Pound Note, Mornington Crescent, and the Prisoner's Dilemma. Some paradoxes will be explained, while some are just too strange.

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### Funny fluids and soft stuff: polymers, pizzas and Bird's custard – by Dr Daniel Read

Many of the materials we encounter on a daily basis - gloopy substances such as shower gel, pizza cheese, tomato ketchup, plastics or paint - exhibit flow properties that seem halfway between that of a liquid and a solid. This talk (illustrated by a number of demonstrations) gives an introduction to the rich variety of flow phenomena that are possible, and to the mathematics that can be used to describe them.

### Maths and Magic – by Dr Kevin Houston

It is possible to shuffle a pack of cards so that the cards from two halves are perfectly alternated. While this shuffle looks perfectly fair, it is almost as unfair as you can get. The shuffler can work out the destination of each card and, with a bit of thought, can deal winning hands of cards effortlessly. The possibilities in cheating and in card magic are immense! In this talk we will look at this "perfect" shuffle and the interesting mathematics behind it. (Involves audience participation.)

### Win a Million Dollars with Mathematics – by Dr Kevin Houston

A million dollars is on offer for each of six mathematical problems. It used to be seven, but Grigori Perelman, solved one of them, the Poincare Conjecture. Surprisingly he has refused to take the million dollar prize!

In this talk I will look at the some of these problems, why they are important and their relevance to the real world. The problems cover subjects such as computers, fluids, and prime numbers. (Involves audience participation.)

### Chaos: complicated behaviour from simple equations – by Prof David Hughes

The mathematical theory of Chaos considers systems governed by well-defined rules but that, somewhat surprisingly, are not predictable over any long period of time. The most well known chaotic system is the weather. Although the equations governing the dynamics of the atmosphere are well known, it is only possible to predict the weather for a few days ahead. I shall consider a much less complicated simpler system than the weather, but one that still shows all the beauty and complexity of a chaotic system. The mathematics is in some sense very simple, but it leads to some of the most interesting questions being pursued by research mathematicians.

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### Fibonacci and his rabbits – by Dr Tom Roper, President-elect of the Mathematical Association

The workshop begins by looking for number patterns in Pythagorean Triples and then moves onto the famous Fibonacci sequence. Group work is used throughout and there is some history to be encountered along the way. The workshop has been used successfully with year 8 pupils attending a master-class right through to sixth form students taking A-level mathematics. The level of mathematics is adjusted to the abilities and experience of the students. Pens, pencils and paper plus at one point some scissors is all the apparatus that is required.

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### Polyhedra – by Prof John Truss

A polyhedron has a finite collection of faces, which are (parts of) planes in 3 dimensions, together with edges (where 2 faces meet) and vertices (where 3 or more faces meet), and by the corresponding 'solid' we mean the region of 3-dimensional space enclosed by the polyhedron. In the lecture I shall describe one of the most famous classifications, which has been known about from ancient times, namely the classification of all the regular and semi-regular solids (in 3 dimensions). The regular ones are called 'Platonic', and the semi-regular ones are 'Archimedean'. Models of all of these will be produced.

(This talk is suitable for sixth-formers; a simpler version is also available for younger children).

### Packing Problems – by Prof Chris Jones

How do you pack spheres together to get them into as small a volume as posible? What is the best possible packing fraction that can be achieved? How big is the smallest square into which you can fit seven circles of unit diameter? Questions like these have fascinated mathematicians for hundreds of years, but many can be explored using the geometry of simple triangles and the properties of regular solids. This talk can be given in a form suitable for year 9 students, as well as at a more sophisticated level for sixth formers.

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### Untangling Knot Theory - by Dr Richard Elwes

It is not only mountaineers, scouts, and sailors who study knots, but also mathematicians. In fact, knot theory has turned out to be an extraordinarily deep subject. In particular, the question of determining whether two knots are essentially the same turns out to be surprisingly difficult. This subject also has numerous and diverse applications, from the knotting of our own DNA to quantum physics. In this session we will meet several mathematical techniques for analysing and classifying different knots.

(image: Celtic or pseudo-Celtic decorative knot to fill square box, author: AnonMoos, public domain)

### The Maths that Makes the Modern World - by Dr Richard Elwes

From searching the internet to managing a manufacturing company, everyone knows that maths plays a central role in today's hi-tech civilisation. But what sort of maths? In this talk we'll meet a few familiar ideas from algebra and geometry which seem simple and elegant on first sight. But when massively scaled up and implemented on powerful computers, we'll see how these techniques have truly changed the world.

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### How to win the lottery with mathematics - by Dr Phil Walker

In this one-hour interactive session, we will first play a game with some cards with a particular mathematical structure. We will then look at a simpler set of similar cards, and investigate the structure of the cards' design. This will lead us to discover that the cards cover a space of combinations in a particular way. We then discuss the way that lotteries work: we will calculate the odds of winning in a very simple lottery, including the expected payoff, and we will find that the cards in front of us could help us to choose a set of tickets that would guarantee a winning combination. We conclude with a story of people who did this with a real-life lottery and, as a cautionary tale, a calculation of the odds and expected payoff when playing the UK National Lottery.

This session touches on the following topics from the Mathematics National Curriculum:

* Reasoning: conjecturing about patterns and relationships (KS3+)

* Problem solving: making and using connections between different parts of mathematics (KS3+)

* Problem solving: applying appropriate concepts to unfamiliar and non-routine problems (KS3+)

* Probability: using a model to predict outcomes (KS4)

### Playing smarter with probability - by Dr Phil Walker

In this interactive session, we will play a dice game that requires players to evaluate probabilities and expected payoffs. We will then use pieces from the game to run some probability experiments, before doing some probability calculations to compare with our experimental results. We will discuss the optimal strategy for the game. At the end of the session, students can play some more rounds of the game in order to apply what we have covered.

This session touches on the following topics from the Mathematics National Curriculum:

- Problem solving: model situations mathematically (KS3+)
- Probability: simple probability experiments (KS3+)
- Probability: calculate theoretical probabilities (KS3+)
- Probability: using a model to predict outcomes (KS4)

### Complex Fluids: the elegant workings of soft matter - by Dr Mike Evans

Why does jelly wobble? Why do rubber balls bounce? And how do opals form? The answers to all of these questions lie in combinatorics. Simply by counting the different ways to arrange their molecules, you can understand the behaviour of many complex materials.

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### The Light-Speed Barrier - by Dr Mike Evans

We discuss the ways in which Einstein's special theory of relativity imposes a limit on the speed of motion, and just how much of a barrier it is.

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### Murder in the Sunshine State: Correlation, Causation and Simpson’s Paradox - by Dr Peter Thwaites

There is a very high correlation between the behaviour of financial markets and both sunspot activity and the length of women’s skirts. But are there causal links between these variables?

Terry Speed said that "considerations of causality should be treated as they have always been treated in statistics: preferably not at all but, if necessary, then with very great care". Florida murder data suggests very strongly that White defendants convicted of multiple murder are significantly more likely to receive the death penalty than Black defendants so convicted. We analyse the data a little bit more carefully!

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## Talks for teachers

### Beginning to teach mechanics at A Level – by Dr Tom Roper, President-elect of the Mathematical Association

The session will look closely at Newton’s Laws, the necessary assumptions made in mechanics and provide ways of revealing, examining and addressing misconceptions prevalent in all of us, teachers and students. The use of some very simple apparatus in the teaching of mechanics will be demonstrated and there will be ample opportunity for participation and discussion. Some examples of the way mechanics can provide powerful models of aspects of the real world will also be considered where time permits. The session could be run over half a day or a full day depending upon the needs of those attending.

### Getting A level Mathematics students to think – by Dr Peter Thwaites (formerly a secondary school Head of Mathematics)

Mathematics is not all bookwork and sums, and A level Mathematics can be made much more interesting by the use of activities which make students think. In this session we consider mechanics as a practical activity (involving bathroom scales …); tackle a “Pure” investigation featuring networks and leading to a watertight proof; and discover how real (US murder & death penalty) data can be very misleading.

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