*The LMS is currently looking for new Holgate Lecturers. For more information, click here.*

The Holgate Lectures and Workshops sessions scheme provides session leaders who are willing to give a talk or run a workshop on a mathematical subject to groups of students or teachers. The sessions are of mathematical content and are not, for example, careers talks. Rather they are intended to enrich and enhance mathematical education, looking both within and beyond the curriculum. Holgate session leaders do not charge a fee for giving talks, but local organisers are expected to pay travel expenses and subsistence costs, together with any local costs of organising the session. The LMS will pay an annual honorarium to the session leaders.

The scheme is named in memory of Philip Holgate, who helped ensure the success of the LMS Popular Lectures.

The Education Committee has chosen the below five individuals to act as session leaders. The profiles below show their background and mathematical interests and provides contact details for anyone interested in organising a Holgate Session. The talks provided below are firmly intended as indicative and not comprehensive. Session Leaders will work with local hosts to develop and adapt sessions to the needs of the audience. The LMS strongly encourages schools hosting a Holgate session to consider collaborating with other local schools.

**In the interest of maximising the number of schools able to benefit from the Holgate Scheme, schools are asked not to arrange more than one session per academic year, and not to contact multiple lecturers for the same event.**

Local hosts of a Holgate Session will be asked by the Society to complete a brief questionnaire about the session that will allow the Society to gather some feedback and develop the scheme.

Those interested in hosting a Holgate Session should contact the Session Leader directly by e-mail to discuss content and how the Session Leader can best work with hosts.

### HOLGATE SESSION LEADERS

STEPHEN CONNOR | ALAN DAVIES | TONY GARDINER | SIMON GOODWIN | JOE WATKINS |

**STEPHEN CONNOR (BASED IN YORK)** - CV

** Contact:** stephen.connor@york.ac.uk

**Mathematical Interests:** I'm a senior lecturer in the Department of Mathematics at the University of York, and my main research interests lie in the area of applied probability. Probability is a topic that humans seem to struggle with -- we often don't have a very good feel for how likely it is that something will happen, and are surprised by "coincidences" more often than we probably should be. I really enjoy studying a subject that involves so much fascinating theory, yet also relates to everyday life.

Particular interests include the study of how long it takes for a random process (such as a particle performing a random walk, or a pack of cards being repeatedly shuffled) to approach some sort of equilibrium. This is a problem that is also important in other subjects, such as chemistry and physics. In addition, I am interested in methods for using computers to simulate the long-term behaviour of random systems which are too complex for us to study analytically. Applications here include analysis of queueing systems with lots of servers, and restoration of "noisy" images.

As well as teaching and conducting research, I am a STEM Ambassador and the "Schools Liaison and Widening Participation Officer" for my department. I have led many interactive sessions at schools in and around York (for children aged 6 -- 18), given a number of public lectures, and have recently helped to organise Royal Institution Maths Masterclasses for North Yorkshire.

**Example Sessions:**

I generally prefer to run interactive sessions; if asked to give a lecture then I always endeavour to make this entertaining as well as informative! The suggestions given below are indicative only: I'm very happy to discuss other possibilities.

Title: *How many shuffles does it take to randomise a deck of cards?*

Age: 14 -- adult

Abstract: How many times should you shuffle a pack of cards? How do casinos (try to) ensure that their cards are well shuffled? Why should we care? And what has this to do with mathematics?

This session works best as a lecture: in it I give an idea of how these questions can be answered, and why the answers are interesting, using a heady concoction of (relatively simple) probability, group theory, combinatorics, analysis, and maybe even a little magic.

Title: *Surprising uses of randomness*

Age: 14 -- adult

Abstract: A look at how random numbers can be used to solve a variety of problems, from approximating the area of the UK, to image restoration, to decrypting simple codes.

Title: *Patterns and proofs*

Age: A-level students

Abstract: An introduction to the idea of mathematical proof through problem solving. This session encourages students to spot patterns in numbers and puzzles, and to then turn their observations into theorems; this should help students with the concepts of proof by induction and proof by contradiction, and give an insight into the world of university-level mathematics.

Title: *Skill vs luck*

Age: 8 -- 16

Abstract: Is your favourite sports star really skilful, or just lucky? How can we use probability and statistics to tell whether a run of great results is pure fluke? Students will spend some time investigating patterns in repeated tosses of a fair coin, before using the knowledge acquired to critically assess real-life data.

**ALAN DAVIES (BASED IN NORFOLK AND HERTFORDSHIRE)** - CV

**Contact**: a.j.davies@herts.ac.uk

**Mathematical Interests**: After a first degree in mathematics from Southampton University, Alan took a masters degree and a doctorate in structural engineering and numerical computation respectively from Imperial College. He has spent most of his working life as an academic at the University of Hertfordshire, formerly the Hatfield Polytechnic. He had short spells in industry working as a research engineer in the aircraft industry and as a process engineer in the food industry. During his time in Hatfield his major teaching activity has been with undergraduates and postgraduates in mathematics, science and engineering.

Since 1993 he has been the organiser of the Hertfordshire Royal Institution Mathematics Masterclasses for year 9 pupils. As a consequence of this work he has gradually increased his contacts with schools and now runs regular mathematics workshops for years 5 and 6 in primary schools and years 7-13 in secondary schools. The workshops and lectures usually reflect his interest in applied mathematics, in particular mechanics, however he has a general interest in all areas of mathematics and runs sessions on many other topics. He has also developed a series of public lectures on applications of mathematics and physics to a variety of problems aimed at a general audience, ages 8 to 108.

**Example Sessions:**

All sessions can be adapted to the audience background and age and can be straight lectures, usually with suitable demonstrations, or they can be hands-on workshops.

Further details, of these and other sessions, can be found on the Mathsdiscovery website, http://www.mathsdiscovery.co.uk

**Rainbows**

We shall see a wide variety of rainbow phenomena some of which will be familiar to all of us, others will be not so well-known. We shall explain the double bow and why the colours are always in the same order. We’ll see rainbows in places other than in the sky and we shall answer the question “Can you see that rainbow?” This talk can be expanded to include other atmospheric phenomena such as haloes, glories, the green flash etc.**Anamorphic art**

Anamorphosis is a transformation technique by which pictures are presented in a manner in which they are difficult to interpret. In order to recognise the picture it must be viewed from a specific point. Typical of the idea is the advertising logo seen on sports fields. The picture is painted in such a manner that the three-dimensional nature of the field is transformed to a two-dimensional picture on the television screen. Conical anamorphosis leads to some interesting pictures on the surface of a cone and can be understood by all ages.

This session is best delivered as a hands-on workshop and is appropriate for all ages. There will be a wide variety of examples and all participants will have plenty of opportunities to produce an anamorphic image.**Mechanics**

In this session we shall introduce the basic laws of mechanics via a lecture demo. Many people find mechanical concepts non-intuitive and a helpful way to overcome this is to perform simple mechanical experiments, usually using very simple equipment.

The session can be adapted to suit a specific theme, e.g. we have a session called ‘The mechanics of superheroes’.**The fascinating number π**

The number π has been a fascination for mathematicians for some four thousand years. The amount work involved has been enormous and the associated literature is vast. We shall look at the historical development of some of the ideas focussing on specific aspects such as Archimedes’ mathematical description and how a dartboard can be used to make an estimate of the value of π. The decimal expansion of a transcendental number such as π should be random and we shall look at some of the repurcussions.

**TONY GARDINER (BASED IN DORSET, BUT HAPPY TO TRAVEL)** - CV

**Contact:** anthony.d.gardiner@gmail.com

**Mathematical Interests**: Tony is a mathematician who has been closely involved with schools for many years. He has worked in group theory, algebraic graph theory, number theory, analysis, history and philosophy of mathematics, and mathematics education. His publications include numerous resources for schools, mainly for more able students - including Mathematical puzzling (Dover), Understanding infinity (Dover), Discovering mathematics (Dover), The mathematical olympiad handbook (Oxford), and the series Extension mathematics (Oxford 2007). He started the national pyramid of Challenges and olympiads and ran them for 10 years. A new book (with Alexandre Borovik) The essence of mathematics - through elementary problems should appear shortly

**Example Sessions**: I hesitate to give a list of possible titles - since I would prefer to design each talk (in consultation with the teacher issuing the invitation) to suit the intended age group and their background. This attempt to design the session appropriately may be achieved via an initial e-mail exchange followed by telephone contact.

Mathematics requires exposition - so any session needs to be structured. However, school students have limited experience of accessing mathematics solely through exposition; so each session is likely to require a degree of student activity (though the underlying style could range from an extended structured exposition to a workshop).

Whatever the chosen format, any session would be intended to offer an unfamiliar, but important, glimpse of serious mathematics.

If I were to indicate the possible range of topics it would certainly include various gems from recreational mathematics, from number theory, from geometry, from algebra, from combinatorics, and from analysis - all with added historical flavour. All are likely to emphasise the connection between apparently separate topics that is characteristic of mathematics.

**SIMON GOODWIN (BASED IN BIRMINGHAM)** - CV

**Contact details:** s.m.goodwin@bham.ac.uk

**Mathematical interests:** My research is in the areas of pure mathematics called representation theory and group theory, which are concerned with understanding symmetry. Given the abundance of symmetry in nature and in mathematics, representation theory has far reaching connections and applications in mathematics and sciences. In my teaching at the University of Birmingham I enjoy sharing my enthusiasm when teaching the first and second year courses on algebra. In these courses we develop the theory of fundamental algebraic structures, like groups and rings, whilst seeing applications and motivation for this abstraction. I have developed and run interactive workshops in variety of areas of mathematics and aimed at different age ranges. In these workshops I like to share my enthusiasm and get the audience to experience the joy of mathematical problem solving and discovery. When I'm not doing mathematics, I like to spend my time outdoors and enjoy cycling, running and walking - though sometimes I'll be thinking about maths at the same time.

**Example sessions:** Titles of interactive workshops that I have previously run are given below; here interactive means that the participants do some of the maths. A target age group is given though these sessions can also be adapted to be suitable for other age groups. Further details are available on request and many other topics can be covered.

Mathematical mindreading (year 10-11)

Puzzles, probability, permutations and paradoxes (year 12-13)

Symmetry, shuffling and solutions (years 10-11 and years 12-13)

The Fibonacci sequence, the golden ratio and the worst game of snakes and ladders (years 10-11)

Using maths to win at gameshows (years 10-11)

What are the chances? (years 10-11)

**JOE WATKINS (BASED IN CANTERBURY)** – CV

**Contact details:** J.Watkins@kent.ac.uk

**Mathematical Interests**

My research interests have tended to focus around spectral theory, specifically on the relationship between spectral determinants and zeta functions. This has included the study of such functions within Quantum Mechanics, which was the main focus of my PhD research. I have also completed some work in the mathematics of juggling and the link between this and musical tiling (inspired by the work of a University of Kent student, Rachael Whyman).

Since then I have become more interested in how mathematics can be used within Social Sciences, both as a precise tool for measurement but also as a means of providing accessibility to people who are non-expert in such disciplines. Consequently I have begun a research programme to investigate how colour can be rigorously and consistently used in order to provide intuitive interpretations of large datasets, thereby mitigating the need for technical analysis. This has included the development of a simple heat-mapping technique and several projects to demonstrate the usefulness of this method.

I also have an interest in investigating how research can be effectively communicated and understood through Public Engagement and Outreach events, and to what extent such work can be influential in encouraging students to study STEM subjects at A-Level and beyond.

**Examples of Sessions Offered**

The following are examples of sessions that can be offered. All talks or workshops tend to feature an interactive element and are as hands-on as possible. The sessions below are examples and I can work with local organisers to develop sessions according to need.

The Mathematics of Juggling

This session provides an introduction to the ‘Siteswap’ notation, which describes the mathematics of juggling in a very neat, simple way. As well as learning how to speak this language, participants will understand the hidden and beautiful rules that determine exactly which juggling patterns are possible and which are little more than nonsense. This talk suits most audiences from Secondary School upwards and can be run for a very large group.**The Art of Codebreaking**

After understanding some basic concepts of modular arithmetic, this session uses computer graphics to demonstrate why encryption is so powerful. We investigate additive, multiplicative and exponential methods of encryption, demonstrating why the final choice is ultimately the most secure system to use for sending secret messages. This talk would be suitable for a mature audience or for Secondary School students with an interest in mathematics.**Build a Theorem**

How do we define a triangle? Of course, everybody knows what a triangle is, but putting this into words is a lot more subtle than you might think. After exploring the basis of writing a good mathematical definition, we show how simple algebraic concepts can be used to give powerful results about geometry and tessellations. This talk would work best for a smaller audience of enthusiasts, preferably with experience of A-level or higher.