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 eight 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 Society would very strongly encourage schools hosting a Holgate session to consider collaborating with other local schools. **In the interests of maximising the number of schools able to benefit from the Holgate Scheme, schools are restricted to one session per academic year.

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

KATIE CHICOT | ALAN DAVIES | TONY GARDINER | PETER GIBLIN |

SIMON GOODWIN | VICKY NEALE | JOE WATKINS | JANE WHITE |

**KATIE CHICOT (BASED IN LEEDS)** - CV

**Contact:** k.m.chicot@open.ac.uk

**Mathematical Interests:** As a staff tutor at the Open University I am involved in the standard production of teaching materials and teaching. In addition I have worked on a large variety of non-standard projects. My Open University work is a unique educational role. It has allowed me to be involved with projects like the ‘Bridge2Success’ Gates project. This project was designed to overcome one of the major hurdles to returning to college education, the maths entrance test. It was nominated for the education-portal.com’s People’s Choice Award for ‘Most Interactive Resource (2012)’. It received an Honorable Mention and won the category in the Center for Digital Education 2012 Best of the Web/Digital Education Achievement Award. This project was awarded the Maryland Distance Learning Association’s *Program of the Year* award at their annual conference.

I have tried other means of communicating mathematics including co- creating the series ‘Patterns of life’ for OU iTunes. I have given a Facebook event as part of the OU Social Media Campaign and had two appearances on BBC radio 4’s 'More or Less.' I recently captained the OU’s team on BBC2’s Beat the Brain.

My research interests straddle Logic and Combinatorics. In particular I have worked with automorphism groups, the Small index property and transitivity properties all with respect to infinite designs.

I give talks in schools and also at teachers' conferences. My principal aim is to make mathematics accessible and engaging.

**Example Sessions:**

Title -*To Infinity and Beyond*

Age – 14 years to adult

Abstract-The infinitely large and the infinitely small are mind-blowing concepts that have helped mathematicians to solve some very real, and finite, problems. Katie Chicot explores the mysteries and misconceptions of infinity, from ancient puzzles to some of the very latest mathematical research, taking you to infinity…and beyond.

Title- *Big Ideas*

Age 14 years to adult

Abstract - Be prepared to let your mind expand as we look at some of the terrifying consequences of Einstein's Theory of Relativity. Time, space and reality are not what you think. To see how the universe really works we will have to ride light beams and follow in the footsteps of the greatest thinker of our time.

Title - *Your country needs you*

Age 8 years to adult

Abstract - A whistle stop tour of the history of code breaking. Students make and break codes and see how mathematics underpins all aspects of the coding arms race.

**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.

**PETER GIBLIN (BASED IN LIVERPOOL)** - CV

**Contact:** pjgiblin@liverpool.ac.uk

**Mathematical Interests**: My research area is singularity theory and its applications to differential geometry and computer vision. I have worked on many geometrical problems such as the study of light caustics by reflexion in mirrors, symmetry of various kinds, recovery of three-dimensional shape from two-dimensional images (that is the objective of ‘computer vision’) and geometrical properties of surfaces in 3- and in 4-dimensional space. In all these cases particular interest attaches to the question of what happens when something changes or moves—this might be a curve, surface, mirror, scene in the world or camera position or orientation. Naturally such questions involve a significant use of calculus, and in fact singularity theory can be seen as one of the significant directions in which differential calculus has moved in the last 50 years or so.

There is a Rough Guide to my research on my webpage, http://www.liv.ac.uk/~pjgiblin/newsletter.pdf

Most of the dozen students I have supervised for PhD worked in the area of singularity theory, and several of their theses, as well as other works by my students, are on my webpage http://www.liv.ac.uk/~pjgiblin This includes a number of essays written by high-school students under my supervision during work experience or Nuffield Bursary summer projects. A full list of my publications is also available via a link from the same webpage.

Outreach Work

At the University of Liverpool we had a succession of EPSRC grants under the ‘Partnerships for Public Engagement’ heading (or similar ones) which allowed us to employ outreach officers to develop the Funmaths Roadshow http://www.maths.liv.ac.uk/lms/funmaths/ and take it into schools nationwide (and sometimes internationally). I was the Principal Investigator on a number of these grants, before I retired. The grants also helped us to run a Maths Club http://www.maths.liv.ac.uk/~mathsclub/ which has flourished for many years now. (The University now employs outreach officers as permanent members of staff, taking over from the EPSRC grants.) My personal outreach work has revolved around going into schools to give mathematics talks, the Maths Club, and the two organizations Mathematical Education on Merseyside (MEM) http://www.maths.liv.ac.uk/~mem/ and the Liverpool Mathematical Society (LivMS) http://www.livmathssoc.org.uk I have given many masterclasses and other presentations in the University and in schools under the auspices of these organizations. I have also run interactive ‘problem-solving’ workshops where the problems/puzzles are more formal.

**Example Sessions**: As a rule I make my presentations interactive, that is involving the ‘audience’ in actually doing some mathematics. Thus a more descriptive name is often a ‘workshop’. Only rarely have I given ‘talks’ or ‘lectures’. My presentations are generally aimed at Year 11/VI form but can be for Years 8-9 which is the age of MEM Masterclass pupils. Many sample presentations (roughly Year 11/VI form) are on the Maths Club archive http://www.maths.liv.ac.uk/~mathsclub/talks.php though I rarely repeat an old talk without redesigning it to some extent. Here are a few ideas I have used in the past. I hope also to develop a presentation or two on mechanics.

1. *Card tricks that are ‘doomed to succeed’* There are many mathematically based card tricks which, though puzzling, can be explained with some elementary mathematics. This presentation can involve a smallish ‘audience’ trying the tricks for themselves or, for a larger one, volunteers can try them out. The presentation can be combined with ideas about shuffling cards and with other things that ‘must work’ such as number puzzles.

2. Counting This can involve various aspects of combinatorics: counting things in different ways to obtain striking results. Fibonacci numbers figure in this quite often, as do magic squares, partitions and probability.

3. *From maxima and minima to surface shape* This is a somewhat more formal ‘talk’ which starts with problems of maxima and minima solved without calculus and moves through properties of curves to fairly modern ideas of using mathematics to measure the symmetry of shapes and to compare one shape with another.

4. *Universal cycles* This also has connexions with card tricks, though it is mainly a mathematical topic, involving use of graphs (networks) in the plane to find sequences of 0s and 1s with special properties (de Bruijn sequences). This enables a set of five cards chosen from a pack to be identified knowing only which are the black cards. There are many ways in which this topic has been developed over the last decade, and I talk about some of them. There is opportunity for audience participation.

5. *Graphs, trees and Brussels sprouts* Graphs (networks) in the plane are studied, Euler’s theorem (vertices minus edges plus finite regions = 1 for a connected graph) is introduced and the theorem used to de-bunk a pencil and paper game, showing that the winner can be predicted from the start.

**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)

**VICKY NEALE (BASED IN OXFORD)** - Personal Website Details

**Contact:**vicky.neale@maths.ox.ac.uk

**Mathematical Interests:** I'm the Whitehead Lecturer at the Mathematical Institute and Balliol College, University of Oxford. My job combines undergraduate teaching with work on public engagement with mathematics and working with mathematically inclined teenagers. Before moving to Oxford in August 2014 I spent several years as Fellow and Director of Studies in Mathematics at Murray Edwards College, University of Cambridge, where amongst other things I worked with NRICH and the Millennium Mathematics Project. I have been a volunteer with the UK Maths Trust for many years, and have contributed to several programmes on BBC Radio 4. My mathematical interests are particularly in pure mathematics; my research background is in number theory and combinatorics. I have given numerous talks and led numerous workshops for all sorts of audiences, from groups of secondary school students of varying ages through to adults. I am keen for as many people as possible to have a taste of working mathematically, and this informs my approach to working with students. I love sharing my enthusiasm for mathematics with anyone I can!

**Example Sessions: ** I have a few standard talks that I am happy to adapt for individual audiences. These include 'Addictive Number Theory' and '7 things you need to know about prime numbers', both of which discuss some key (solved and unsolved) problems in number theory and recent progress on them. I can adapt them for slots from 30 to 60 minutes, and for audiences with different levels of prior mathematical knowledge. I gave one version of the Addictive Number Theory talk for the LMS popular lectures in 2013; a recording is available online [link to https://www.youtube.com/watch?v=gII2g4TD_7g]. A video of my talk "7 things you need to know about prime numbers" that I gave to some year 12 students is at http://mmp.maths.org/neale-7Things-Jun15-video.

I am also happy to lead interactive workshops. I have a repertoire of problems suitable for various age groups and looking at various mathematical ideas, all based on my desire for the students to do as much as possible for themselves, so that they can experience the excitement and challenges of working on mathematical problems. I particularly like using open-ended activities that give lots of scope for exploration, conjecturing, proof, asking questions, and so on. Examples include sessions on modular arithmetic, continued fractions, Euclid's algorithm via an interactivity [link to http://nrich.maths.org/psum/picture-this/], and several based on my favourite NRICH [link to http://nrich.maths.org/] problems such as Take Three From Five [link to http://nrich.maths.org/1866], Sticky Numbers [link to http://nrich.maths.org/6571] and Got It [link to http://nrich.maths.org/1272]. I enjoy various forms of mathematical craft, and have created an interactive workshop based on one such activity, curved stitching. I can adapt this for different levels of mathematical experience, but in all cases the participants explore how straight lines can be used to draw curves, and some of the underlying mathematics.

I am used to discussing with an event organiser what they are looking for and what the expected audience will be like, in order to select appropriate activities. I feel most comfortable working with teenagers and adults but am happy to work with secondary school students of any age, and to discuss possibilities for younger students.

**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.

**JANE WHITE (BASED IN BATH)** - CV

**Contact:** k.a.j.white@bath.ac.uk

**Mathematical Interests:** I am interested in mathematical modelling of problems arising from the healthcare sciences with a focus on control and monitoring. There are two strands to this work: control of infectious diseases and drug absorption and monitoring.

With the infectious disease modelling, I am interested in exploring the impact of different control strategies on population level infection profiles. For example, should the HPV vaccination programme be extended to include teenage boys? With a limited budget, should intervention focus only on high risk cohorts or does population surveillance also contribute to infection control? What can control engineering techniques tell us about whether we can control infection outbreaks in a population?

My work on drug absorption and monitoring uses mathematical models to understand the problems associated with using the skin as a route for drug delivery and subsequent drug monitoring. The skin is potentially a very important organ for delivery and monitoring drugs non-invasively. But it is also a highly heterogeneous barrier which functions to prevent flow in and out of the body. Mathematical models help to determine the conditions, such as the type of drug molecule, that will facilitate the use of the skin for delivery and monitoring.

Alongside my research and teaching activities, I have been involved in working with schools and colleges to provide mathematical opportunities for students in the school sector.

I am a member of the Wessex Masterclass committee and have delivered sessions to year 8 students on a range of applied themes including population growth and introductory mechanics.

As the departmental link for widening participation, I have delivered a number of lectures and workshops for students in KS4 including sessions on curve sketching and graphical interpretation; number bases; and rate equations. I have motivated the sessions by linking the mathematics to my research in the context of the biological and healthcare sciences and, on occasions, to the art of card tricks.

At KS5, I have developed the departmental outreach programme for A level mathematics students which includes a series of real world mathematics sessions for year 12 students and a year-long problem solving and STEP programme for year 13 students. I have also been the academic lead for a mathematics programme to supplement the curriculum for BTEC enhanced diploma students in local FE colleges studying computer science, engineering and sports science.

**Example Sessions: ** Interactive talks for groups of pretty much any size and content tailored to the audience (I have put suggestions in brackets below); typically lasting 50 minutes

·Number bases and card tricks (Year 6 – 8)

·The logistic map and its applications to biology (Year 7 – 10)

·Name that curve! (Year 9 – 10)

· Population growth/infectious diseases (Year 12)

Workshops for groups up to around 25-30 students, KS3 & KS4; typically 90 minutes

· Practical introduction to matrices. Motivated by examples from population biology, and moving onto investigating properties of matrices (multiplication, inverse etc.)

· Maths at the drugstore. To encourage students to think seriously about studying A level mathematics if they might want to study nursing, pharmacy etc. Dilution problems, safety measures etc. Ideas of half-life and exponential decay.

PGCE students/CPD for teachers

· The optimal way: a ubiquitous phenomenon. A general interest talk for teachers to motivate A level teaching, particularly of calculus and integration.

If you have another idea, please do get in touch and I will see if I am able to help.

Submitted by Duncan Turton on