I regularly work with students of school age, in a range of outreach programmes including summer schools, master classes, mentoring, etc.

## 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.

## Summer and Easter schools

- Sutton Trust Summer Schools, Cambridge

From 2015 - 2017, I taught and/or helped to organise the Maths Sutton Trust Summer Schools. When I was teaching, it was Number Theory: from modular arithmetic to cryptography. - Teach First Futures, Maths Stream, Cambridge

From 2014 - 2016, I taught the maths stream of a Teach First Futures Easter School, together with some applied colleagues (different ones in different years). We taught some basic group theory the first time, and then Number Theory (as above), and also Differential Equations. - Deutsche SchülerAkademie, Germany

In 2012 and 2013, I taught a course (together with my friend Julian Vogel) on abstraction in mathematics (Abstraktion in der Mathematik). Course 4.1, page 42 in the 2012 programme, and course 3.1, page 34 in the 2013 programme. We covered a lot in the 2 1/2 weeks, and had lots of fun doing it!

## Mentoring, classes and support programmes

- Mentor for in2science UK

In 2020 I mentored two groups of Year 12 students interested in studying maths or physics at University. In2Science promotes social mobility and diversity in science, technology, engineering and maths. - AMSP problem classes, University of Leicester

From 2018 onwards, I have been giving advanced problem classes for Year 13 students from schools around Leicester. The students work on problems together which stretch them a bit beyond the level of their school problems. - Royal Institution Maths Masterclasses in Cambridgeshire

From 2015 to 2017, I gave some masterclasses to 11/12-year-olds in Cambridge, on modular arithmetic and cryptography. - Maths Masterclasses, University of Cambridge

In 2016 and 2017 I gave one of two 1h talks in the Maths Masterclasses, to about 300 A-level students. These subject masterclasses are a great way for students to explore what a subject might be like at university. - Talks to students

I've given several talks to students, which you can find on my Talks page.