School of Mathematics

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.

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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.

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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.

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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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How computers throw dice – by Dr Stuart Barber

Computers are, in theory, completely predictable (though they often don't seem that way).  Yet they often need to come up with random outcomes - a simple example would be dealing a deck of cards for a game of "spider".
So how do completely predictable computers come up with unpredictable results?  This talk will look at how computers generate randomness, how to check that numbers really are random, and what these random numbers can be used for.
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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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What did Fourier do and what do people do now? – by Prof. Jonathan Partington

Fourier noticed that waveforms can be split up into simpler waves (sines and cosines), which correspond to musical harmonics. The application he found was in the theory of heat conduction. Since then, harmonic analysis, as it is called, has become a very important and lucrative business. For example, signal processing and image reconstruction are vital in applications such as CD players, mobile phones and medical scanning. However, nowadays there are other basic functions (wavelets) that have become fashionable as an alternative to sines and cosines, and we shall say something about them too.
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Big networks and small worlds – by Dr. Thomas Wagenknecht

From the internet and facebook to railway lines and the Royal Mail, networks dominate our modern life. The mathematical theory of networks is known as graph theory and its history began in the 18th century when the famous Swiss mathematician Leonhard Euler solved the problem of 'The Seven Bridges of Koenigsberg'.

In the talk we use Euler's solution of the problem to introduce basic concepts of graph theory. We then consider modern applications of the theory and discuss the concept of small-world networks, which leads to a mathematical explanation for the idea of 'six degrees of separation'.

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Cobwebs, pendulums and butterflies – the maths of chaos – by Dr. Thomas Wagenknecht

Is your life predictable or does it sometimes feel a bit erratic? Find out about Chaos Theory and learn how mathematicians try to understand unpredictable and complex natural phenomena, and how they try to make the best of our, well, chaotic world.

In this talk we discuss examples that demonstrate how simple equations like the logistic map and mechanical systems like the double pendulum can give rise to very complicated behaviour. We describe methods that can be used to illustrate and analyse this behaviour mathematically and discuss its consequences for science, life, the universe and everything.

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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.

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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.)

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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.)

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Dead Greek Mathematicians – by Dr Kevin Houston

The ancient Greeks not only knew that the world is round, they had a very good estimate for the size. One of them even proposed that the Earth goes round the sun. This talk is about bringing the dead Greek mathematicians back to life and seeing that they knew a lot more than they are given credit for.  We'll see Pythagoras as a cult leader, Archimedes as a hero battling Roman invaders and how a librarian measured the size of the earth with surprising accuracy. (Involves audience participation.)

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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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Modelling in shape and space – by Dr Tom Roper

The way we see things is governed by how we measure. In our everyday world we measure using the theorem of Pythagoras. But supposing we did not use Pythagoras? What if we used some other way of measuring, what would the world about us look like then? The workshop explores how shapes change, how loci change when we change the way we measure space. The only mathematics needed is the theorem of Pythagoras. The only apparatus required rulers, pencils (some coloured) and lots of centimetre squared paper.

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Fibonacci and his rabbits – by Dr Tom Roper

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).

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Infinity – by Prof John Truss

We are used to the idea of 'infinity' in an informal sense; for instance, we may say that a decimal expansion goes on 'for ever'. All same, at school we are told be careful about talking about infinite objects, and some of the famous mathematical 'fallacies' are based on some aspect of infinity. Provided they are carefully handled, infinite numbers and sets form an essential part of contemporary mathematics. In this talk I shall try to make sense of what an 'infinite decimal expansion' is, and I shall also show that not all infinite sets have the same 'size', that is, some are of a higher order of infinity than others.
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Decimal patterns – by Prof John Truss

A fraction is a number of the form a over b where a and b are whole numbers (which for the purposes of this talk we suppose to be positive). This may always be expanded as a finite or infinite decimal. This talk explains some of the very beautiful patterns which arise. In particular it is explained which fractions have finite or infinite expansions at which stage those with finite expansions terminate why those with infinite expansions eventually recur, and what is the length of the block in which they recur how to generalize these remarks to other bases, e.g. binary. (This talk has often been delivered as a 'masterclass', so is suitable for younger children).

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Knot Maths – by Dr David Salinger

A mathematical knot is a model of a piece of string with an ordinary (or not so ordinary) knot loosely tied in it and then having the ends of the string spliced together to form a tangled loop. Two questions are: when can an apparent knot be unravelled to form an unknotted loop and when are two apparently different knots the same? We explain a little about why neither question has yet received a satisfactory answer.
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Coding messages – by Dr David Salinger

The principles of public key cryptography go back to Pierre de Fermat in the 17th century. We describe those principles and their connection with prime numbers.
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Infinities – by Dr David Salinger

In mathematics there is more than one kind of infinite number. We’ll see that the number of whole numbers is less than the number of numbers on the number line. This fact was first demonstrated by the German mathematician Georg Cantor at the end of the 19th Century.

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Modelling the Deep Interiors of Planets – by Prof Chris Jones

Space missions have given us a great deal of information about our solar system, but many important questions remain. How did the planets form? How are their magnetic fields created? What drives the powerful winds and violent storms in the giant planets? Mathematical models of the interiors of planets are helping to answer these questions, and these models are in turn leading to new developments in Mathematics.

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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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