## Arrival

On arrival at Royal Holloway you will be directed to the upstairs of the Windsor Building by our friendly student helpers. You will be registered and given an information pack. After registration a light breakfast will be provided. There will be a chance to relax and meet our student volunteers and other students before the first talk.

For information on getting to Royal Holloway, please see our Travel page.

**Booking**

Exploring Maths 2018 is a free **invitation only** event. If you would like to attend please contact us. Attendance should be organised by a teacher or other authorised representative of your school.

Exploring Maths 2018 is free.

All students must have signed parental permission to attend the event. This is the responsibility of the organizing school, and Royal Holloway accepts no responsibility for unauthorised attendance.

The organizing school is responsible for ensuring that students attend if places are booked on their behalf.

If you need to cancel your attendance at the event after May 31 2018 we reserve the right to levy a cancellation charge of £100 against the school to cover administration costs. If not all places reserved by the school are taken up we reserve to right to levy an administrative charge of £50. Any charges will be submitted to the organising school by invoice, payable within 30 business days of receipt.

## Timetable

**09.00**Registration and refreshments**09.40**Welcome from the Principal, Professor Paul Layzell**09.45**Introduction to the day, Professor Stefanie Gerke**10.20**Hidden Maths in Technology, Matt Parker**11.30**Small Group Talks**12.00**Lunch**12.30**Tours of campus from outside the Windsor Building**12.30—13.00**Further Mathematics (for teachers only), Mr Steve Collins**13.15—13.45**Small Group Talks**14.00**Mathematics at University, Professor Jens Bolte**14.45**The Music in a 2000 year old proof, Professor Rüdiger Schack**15.45**Close and questionnaires

## Main Talks

### Matt Parker: *Hidden Maths in Technology*

There are numbers all around us that make our modern lives possible. From rescuing your lost words in text messages, to taking selfies. We will discuss barcodes and check digits, error correction, binary numbers & ASCII, and digital images. This session will show students the mathematics behind modern technology and emphasise the importance of learning maths for future tech careers.

*Possibly the only person to hold the prestigious title of London Mathematical Society Popular Lecturer while simultaneously having a sold-out comedy show at the Edinburgh Festival Fringe, Matt is always keen to mix his two passions of mathematics and stand-up. Originally a maths teacher from Australia, Matt now lives in the UK and works both as a stand-up comedian and a maths communicator.*

### Professor Jens Bolte: *Mathematics at University*

Are you interested in studying Mathematics at University? This session will deal with the types of course available and the qualifications required, the ways in which university mathematics is different from or similar to mathematics at A-level, and the careers available.

*Professor Jens Bolte has been at the Department of Mathematics at Royal Holloway for more than 10 years. His research area is Mathematical Physics and he is particularly interested in the quantum mechanics of particles moving on networks.He has previously worked on the quantum description of chaotic dynamics and approximations of quantum dynamics in terms of classical dynamics.*

### Professor Rüdiger Schack: *The* *Music in a 2000 year old proof*

Are all quantities in mathematics ratios of integers, such as 5/7? The ancient Pythagoreans thought so. For them, mathematics, cosmology, and music were firmly based on the integers. The Pythagorean world view was thrown into crisis in the 5th century BC when it was discovered that some distances, and by implication some musical intervals, cannot be expressed as ratios of integers, that is, they are “irrational”. It took more than 2000 years for mathematicians and musicians to fully come to terms with the discovery of irrational numbers. This talk will present a simple and beautiful proof that the square root of 2 is irrational, and through it explore connections between music and mathematics.

*Professor Rüdiger Schack has been teaching at Royal Holloway’s Mathematics Department for more than 20 years, including 5 years as Head of Department. He has made numerous research contributions in the field of quantum theory ranging from foundations to optics and cryptography. Recently he was a panelist at the World Science Festival in New York. His musical interests include singing in a choir and playing piano and harpsichord.*

## Small Group Sessions

**11.30**and

**13.15**. Each talk will be given twice

*Mathematics and the Laws of Nature: A Variation on the Theme of Wigner*, Professor Jens Bolte*Big Numbers and Securing the Internet,*Mr Benjamin Curtis*Prime Numbers, Perfect Numbers and Amicable Numbers*, Professor Rainer Dietmann*The Birthday Paradox and its applications*, Ashley Fraser*Beyond the Third Dimension*, Further Mathematics Support Programme, Mr Mark Hughes*Exploring Mathematics with MATLAB*, Dr Alexey Koloydenko*The shape of space,*Professor Brita Nucinkis*Fun Maths Roadshow and Problem Solving*, Further Mathematics Support Programme, Mr Steve Collins*The MU Puzzle*, Professor Rüdiger Schack*The Liar Game*, Dr Mark Wildon*Further Mathematics for Teachers*, Mr Steve Collins. For teachers only, from**12.30**to**13.00**

The abstracts (i.e. short summaries of the talks) are below.

*Mathematics and the Laws of Nature: a Variation on the Theme of Wigner,* Professor Jens Bolte

At least since Galileo Galilei, the laws of nature have been formulated in mathematical language. The mathematical physicist E. P. Wigner once gave a talk on this subject, under the title “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, in which he elaborates on “why the success of mathematics in its role in physics appears so baffling”. In this talk I shall explain Wigner’s ideas in examples, from the very simple ones to some of the more “baffling” ones. Among the latter is P. A. M. Dirac’s prediction of anti-matter, solely based on the mathematical consistency of the (Dirac-) equation that he developed in 1928.

*Big Numbers and Securing the Internet*, Mr Benjamin Curtis

*Big Numbers and Securing the Internet*, Mr Benjamin Curtis

Big numbers keep the internet safe. In this talk we will begin with a discussion about large numbers, and how we can put them into context. For example we can understand how large the number 10 is, but it is much more difficult to understand how large 13,700,000,000 is. We will then discuss exactly how large numbers need to be in order to secure the internet, as well as how these numbers are used. We will consider a simple example of how some mathematical problems get ‘harder’ as the numbers get bigger. Finally, we will look at how future developments in computers will mean that we need a different way to secure the internet in the future.

*Prime Numbers, Perfect Numbers and Amicable Numbers*, Professor Rainer Dietmann

Primes are amongst the most fascinating objects in mathematics. In this session we want to discuss some of their basic properties such as the fact that there are infinitely many prime numbers. This can for example be demonstrated by using so-called Fermat numbers, which were conjectured to be all prime until Euler found a counterexample in 1732. Another interesting class of primes, Mersenne primes, are closely connected to so-called perfect numbers which are subject to many interesting unresolved conjectures and are related to so-called amicable numbers.

*The Birthday Paradox and its applications*, Ms Ashley Fraser

How many people do you have to invite to a party so that there is a 80% chance that there are at least 2 that have the same birthday? The number is surprisingly small and this is known and the “birthday paradox”. Today the birthday paradox is used to compromise passwords and we will discuss how these attacks work and how to prevent them.

*Beyond the Third Dimension*, Further Mathematics Support Programme, Mr Mark Hughes

Have you ever wondered what lies beyond the third dimension? In this journey through the dimensions, we will be exploring a branch of mathematics called topology (sometimes playfully referred to as ‘geometry on a rubber sheet’). We will explore some shapes that can’t exist unless you add more dimensions. We will discover that transitioning from the third to the fourth dimension is not much harder than transitioning from the second to the third dimension. We will also find that time isn’t necessarily the fourth dimension, despite physicists’ claims.

*E xploring Mathematics with MATLAB*

**, Dr Alexey Koloydenko**

MATLAB is a powerful package for scientific computing, typical of the facilities available in mathematical laboratories. We make considerable use of such packages, both in teaching and in research. Algebra and calculus can nearly all be done ‘automatically’ on the computer rather than by hand, thereby avoiding ‘getting the sign wrong’ or ‘forgetting the factor of 2’ that plague all of us at times. This is particularly important in applications where the equations can spread over several pages at a time. In this introduction, you will be guided through some basic algebra and calculus examples, including 2D and 3D graphs and a demonstration of solving a real life problem.

*The shape of space,*Professor Brita Nucinkis*Fun Maths Roadshow and Problem Solving*, Further Mathematics Support Programme, Ms Cath Moore

This is a hands-on workshop where students can experience a variety of problems in small groups. There will be the opportunity to demonstrate maths, logic, communication and teamwork skills as different tasks covering a variety of topics are tackled. This workshop is ideal for any student in the first year of A level Maths or Further Maths.

*The MU Puzzle*, Professor Rüdiger Schack

*The MU Puzzle*, Professor Rüdiger Schack

Starting from a given sequence of letters and four simple rules, can one arrive at the word MU? We will show that this simple mathematical puzzle leads to surprising insights into the nature of mathematical proof and the limitations of computers. And, of course, we will also solve the puzzle.

*The Liar Game*, Dr Mark Wildon

Ask a friend to think of a secret number between 1 and 15. How many questions with yes/no answers do you need to discover your friend’s number? How many questions would you need if your friend is permitted to lie in one answer? We will answer these questions and learn how to play these games optimally, using the mathematics of coding theory to detect lies.

*Further Mathematics for Teachers*, Mr Steve Collins

This is an informal opportunity for current or potential teachers of Further Maths to share ideas and to find out how the Further Maths Network can support them. It will also provide an opportunity for teachers to get together and discuss different aspects of Further Maths teaching.