School of Computing and Mathematical Sciences

# Outreach

Discover our various outreach projects, designed to share our enthusiasm for mathematics with school and college students.

## Covid-19 Special: virtual workshop and project

Remainders of Security: from modular arithmetic to cryptography. In this workshop, you will learn a bit about cryptography, and also some modular arithmetic, also called clock arithmetic. Cryptography is needed everywhere in our modern world: for example for safe internet communication (including WhatsApp), protecting government or industry secrets or sensitive customer data, and for things like internet shopping. The entire e-commerce industry is based on the idea that we can communicate sensitive information safely and securely. But there are also weird uses you would never have thought of: for example a contact tracing app that tells you when someone you had contact with later tested positive with Covid-19, but without you, them or the government being able to use it to track everyone’s data.

The workshop is structured with short videos and some worksheets which you can do on your own or in a group. The basic stream is fun and accessible to any student from about 12 years old or so. Anyone who is interested in some more mathematical detail can do some of the "optional loops" to go deeper into the material. Children who can read well but are less than 12 might try just the three items in Part II of the left-hand column, starting from "Introduction to Cryptography".

Year 12 project on Cryptography: Cryptography is needed everywhere in our modern world: for example for safe internet communication (including WhatsApp), protecting government or industry secrets or sensitive customer data, and for things like internet shopping. The entire e-commerce industry is based on the idea that we can communicate sensitive information safely and securely. But there are also weird uses you would never have thought of: for example a contact tracing app that tells you when someone you had contact with later tested positive with Covid-19, but without you, them or the government being able to use it to track everyone’s data.

In this project, you start with a workshop on modular arithmetic and cryptography, including the famous RSA encryption algorithm. You can then explore the topic in one of many directions, picking something that interests you from a list of our suggestions. Find out about the history of cryptography, the enigma code used in World War 2, or explore more modern techniques such as the Diffie-Hellman Key Exchange or Digital Signatures. Crack code using Frequency Analysis or take part in a cipher challenge.

## Current activities and events

Our undergraduates are involved in the Undergraduate Ambassadors Scheme (UAS) and the Students in Classrooms Scheme whereby students are placed in schools to inspire and encourage younger students. UAS is incorporated into the module MA3511 Communicating Mathematics, and as such may be chosen as part of the Mathematics degree course.

If you are a mathematics teacher in Leicester or Leicestershire and would like to get involved with either UAS or the Student Associate Scheme, please contact Dr Josh Cork.

In conjunction with the Advanced Mathematics Support Programme (AMSP), we deliver regular problem-solving classes for Year 12 and 13 students. This programme is aimed especially at widening participation students. We like to show you the beauty and elegance of mathematics by discussing fascinating problems.

### Sample talks for schools

#### Maths and what it can do for you

I will discuss why the study of mathematics can be so rewarding, both intellectually and financially. Using my own career journey by way of example, you will hear how a mathematical education is a great career investment in an exciting and rapidly-changing world that is increasingly dominated by the digital domain. The talk ends with some words of advice for entering university, no matter which subject you choose to follow (although we do hope it’s maths!).

#### The beauty of shapes - encounters with the weird world of topology

I will be guiding you on a visual expedition into the weird world of topology, which deals with classifications of abstract geometrical shapes in many dimensions. You will see how, using mathematics, we can find ways to orient ourselves in this strange world and classify all the weird shapes we encounter. You will meet lots of interesting polyhedra, tasty doughnuts, one-sided paper stripes, weird bottles, beautiful surfaces given by algebraic equations and many other animals from the topological zoo.

#### Chaos and fractals

I will introduce the concept of 'chaos' and how it leads to very complicated geometric structures called 'fractals'. Fractals are very peculiar and have unusual properties. For example, a fractal can contain as many points as an interval, yet have no length. Also, the dimension of a fractal is not 1 (like a line), 2 (like area), or 3 (like volume), but somewhere in between. Finally, I will give you a recipe for how to construct fractals and you can try to construct your own.

#### Euler's formula

In this elementary talk, we discuss the beauty of polyhedral shapes and how to classify them using a simple counting trick via Euler's formula.

#### Juggling mathematics

Learn to juggle by numbers, with one, two or four hands, with or without the help of the computer. We introduce the mathematical language used by jugglers worldwide to communicate, model and develop their routines since the 1980s. The workshop will include hands-on practical sessions, both real and virtual. Design your own original juggling patterns and put them into practice!

#### Statistics, beauty, the golden ratio and mathematical analysis

In this talk, we will look at the average ratio of proportions of the human face, and how many we need in a sample to get a good approximation to an average. We will then look at a puzzle and see how the solution to the puzzle relates to the ratio above. Finally, we will look at how to compute this ratio as the limit of a sequence.

#### The chances of finding Richard III

Assessing how likely it was that we would find the remains of Richard III at the point at which it was decided to go ahead with the excavation, using a Bayesian probability approach.

#### Mathematical puzzles and games

Many mathematicians become interested in mathematics through games and puzzles. In this talk I will introduce some games and puzzles which require particular forms of mathematical thinking to solve. It will be in workshop format with lots of interaction. Students will need to bring a pen and some paper.

#### Dirichlet's principle: what have hairs to do with pigeonholes?

We will show that obvious statements like "if you have fewer pigeon holes than pigeons and you put every pigeon in a pigeon hole, then there must result at least one pigeon hole with more than one pigeon" can be formalised into a powerful counting argument, Dirichlet's principle, with lots of surprising applications in mathematics and daily life.

#### Mathematics and how to make your first million

Mathematicians that have solved difficult and long-standing problems have been honoured not only with immense respect from their colleagues, but also with worldwide fame. I will talk about the story of one mathematician who solved one of the most famous maths problems, which, had he solved it some years later, could possibly have won him a \$1,000,000 prize. I will finish with 7 other unsolved problems that could make a millionaire of the people who solve one of them.

#### Mathematics undergraduates involved in ambassador and teacher-training scheme at local schools

Several of our final-year mathematics undergraduates are involved each year in an ambassador and placement scheme with local schools in Leicestershire. This is a joint initiative between Mathematical Sciences, the School of Education and local schools focusing on outreach and widening participation in the region, as well as on the training of future mathematics and science teachers.

As part of the 3rd year module MA3511 Communicating Mathematics, students each year are placed in schools and tasked to inspire and encourage younger high-school students, normally from years 8 and 9. For several years the main partner school in this scheme has been the Thomas Estley Community College in Broughton Astley. The end of the placement is always celebrated with a special outreach and widening participation event where pupils from Thomas Estley and other local community schools, together with their parents and teachers, engage in hands-on activities to explore the fascinating world of mathematics beyond their usual school curriculum. This year the final event took place on Thursday 22 March 2019 and more than 30 students with their parents from all over Leicestershire took part.  Over the course of two hours, the high-school students were given the opportunity to experience hands-on the fascination and beauty of mathematics and to get an idea about some very modern (and very ancient!) topics and ideas.

Feedback was overwhelmingly positive. For example, students and parents exclaimed "Fun and interesting... a great insight into the subject", "A great evening that was very informative, great hands-on maths sessions" "Great evening, the undergraduates' delivery was excellent!".

Everyone is already eagerly looking forward to next year’s edition.

### Levelling Up: Access Leicester

The Levelling Up Scheme, being piloted by the London Mathematical Society (LMS) thanks to a generous donation from Dr Tony Hill, and in collaboration with Durham University and the University of Leicester, is supporting the provision of online tutoring and pastoral support for A-level mathematics students from under-represented and disadvantaged backgrounds.