The Copson and Curle Lectures,

Colin M Campbell and Edmund F Robertson University of St Andrews, Scotland

Abstract

We discuss two named lecture series given at the University of St Andrews over the last thirty years. They are the Curle Lectures named after Professor Newby Curle, formerly Gregory Professor of Applied Mathematics at the University of St Andrews, and the Copson Lectures named after Professor Edward Copson, formerly Regius Professor of Mathematics at the University of St Andrews. We will discuss the range of topics of the lectures and give brief biographical information about the lecturers. We will also discuss the impact of these lecture series both on the student population and also on the wider public in St Andrews.

Introduction

In this paper we wish to discuss two named lecture series given at the University of St Andrews, Scotland over the last thirty years. One series is named after Professor Newby Curle, Gregory Professor of Applied Mathematics and a specialist in fluid mechanics and boundary layer theory, and the other series is named after Professor Edward Copson, formerly Regius Professor of Mathematics at St Andrews and an expert in classical analysis. It will be interesting to note that, although one of the professors, Professor Curle, was an applied mathematician and the other, Professor Copson, was a pure mathematician the two series both contain a mix of applied mathematics, pure mathematics and statistics.

When I (Colin Campbell) first went to the University of St Andrews in 1965 as an assistant lecturer in Mathematics I was introduced to Professor Edward Copson who thought that I was one of the students. I had to tell him that I was his new lecturer! I came to St Andrews from an undergraduate degree in Edinburgh followed by an MSc from McGill University, Montreal, Canada. One of my fellow students at Edinburgh had come straight to St Andrews, having been an undergraduate at Edinburgh and then immediately becoming a lecturer at St Andrews. How the British university job market has changed!

Professor Copson, the Regius Professor of Mathematics, was, as noted above, a distinguished classical analyst. Born on 21 August 1901 in Coventry , Edward Copson's mother was Emily Read and his father was Thomas Charles Copson , a motor engineer and inventor who worked in Coventry. Educated at St John's College , Copson was appointed by Edmund T Whittaker to a lectureship at Edinburgh in1922. He moved to St Andrews in 1930 and after a year at the Royal Naval College in Greenwich in 1934, he returned to the University of St Andrews to a chair in mathematics in Queen's College, Dundee then part of the University of St Andrews. In 1950 he became Regius Professor of Mathematics in St Andrews. From my (Colin Campbell) undergraduate days I knew him as the author of 'Introduction to the Theory of Functions of a Complex Variable', [2]. Both he and his wife Beatrice, the daughter of Edmund T Whittaker, were very welcoming to me. He was the head of Mathematics until his retirement in 1969. I (Edmund Robertson) was an undergraduate at St Andrews and was taught functions of a complex variable by Copson. When I was trying to decide where to do research I went to Copson who said, "They're about to open a new university, the University of Warwick, in my home town of Coventry and I've very excited about it. Why not apply there." I took his advice and have always been happy that I did. For a biography of Copson see [3].

The other main person in the story is Samuel Newby Curle. Following his own wishes, he was always known as Newby Curle. He was born to Samuel Curle and Edith Newby Holmes on 18 June 1930 in Sunderland, Tyne and Wear, England. Educated at the University of Manchester, he worked at the National Physical Laboratory (1954-61) and the University of Southampton (1961-67) before being appointed to the Gregory Chair of Mathematics at the University of St Andrews in 1967. He married Shirley Kingsford Campion (1934-2016) in 1956. When I (Edmund Robertson) was appointed as an Assistant Lecturer in St Andrews in 1968, going into the coffee room full of lecturers who had taught me was difficult. Newby was the one who realised this and immediately went out of his way to make it easy for me. I was always grateful for his understanding and kindness.

Newby died while out walking near Settle, North Yorkshire, on 27 June 1989. The Annual Report for the Department of Applied Mathematics of the University of St Andrews for 1988- 89 states:

The Department suffered a great loss when Professor S N Curle died suddenly in June. Over more than twenty years in St Andrews Newby Curle had done much to build up teaching and research in Applied Mathematics. His wisdom and good humour will be much missed. Friends in St Andrews and elsewhere have contributed generously to a fund in his memory and it is hoped to use the income to support a Memorial Lecture to undergraduates.

For a biography of Newby Curle see [4].

We will begin with the Curle Memorial lectures.

The Newby Curle Memorial Lectures

In what follows we will give the title of the lecture and give a brief biography of the speaker. The following Curle Memorial Lectures have been given:

1990 Professor Sir James Lighthill

The first Curle lecture was given by Professor Sir James Lighthill, who was Newby Curle's PhD Supervisor at the University of Manchester. The lecture on 'Aerodynamics' was introduced by the Principal of the University of St Andrews, Professor Struther Arnott.

Born in France in 1924 Michael James Lighthill was educated at Winchester College and at Trinity College Cambridge. After positions at the University of Manchester he became director of the Royal Aircraft Establishment at Farnborough in 1959. He was a founder and, from 1965-67, first president of the Institute of Mathematics and its Applications. In 1969 he moved to the Lucasian Chair of Mathematics at the . From 1979 to 1989 he was Provost of University College London. His life came to a sad end in 1998 in a swimming accident as he attempted to swim round the Island of Sark in the Channel Islands.

1992 Professor T Brooke Benjamin

The second Curle lecture was given by Professor T Brooke Benjamin (Oxford). It was given on 8 December 1992. He talked on 'Averaged hamiltonian methods in fluid mechanics'.

Born in Wallasey, England in 1929 T Brooke Benjamin was a student at the (BEng 1950), (MEng 1952) and King's College, Cambridge (PhD 1955). He was a fellow of King's from 1955 to 1964. From 1979 until his death in 1995 he was Sedleian Professor of Natural Philosophy at the Mathematical Institute, Oxford and a fellow of the Queen's College, Oxford. He was well known as a mathematical physicist and mathematician, particularly in fluid mechanics. He had an early joint paper with Sir James Lighthill on surface waves (Proc. Roy. Soc. London 1954) [1].

1994 James D Murray

The third Curle lecture was given by Professor James D Murray (Princeton) on 'Mathematical Biology'.

Born in Moffat, Scotland in 1931 he studied at the University of St Andrews where he graduated with a BSc in Mathematics in 1953 and with a PhD In 1956. His doctoral advisor was Andrew Ronald 'Ron' Mitchell whom we both remember well. After posts at Durham, Harvard, University College London and Oxford, James Murray became professor of mechanical engineering at the University of Michigan in 1965. In 1969 he became professor of mathematical biology at the and founder and director of the Centre for Mathematical Biology. In retirement as well as being an Emeritus Fellow at Corpus Christi College, Oxford, he is also professor emeritus of applied mathematics at the University of Washington. His area of research is the many and varied aspects of mathematical biology.

1996 Robin Wilson

The fourth Curle Memorial Lecture to undergraduates in St Andrews was given by Dr Robin Wilson (Open University) who gave an entertaining and informative talk on graph theory.

Born in 1946, he was at school at University College School, Hampstead, London. Robin is a graduate of Balliol College, Oxford and has both an MA and a PhD from the University of Pennsylvania. He is an emeritus professor in the Department of Mathematics at the Open University. He also has a First Class Honours degree in Humanities with Music from the Open University. His research areas are graph theory, particularly colouring problems, and the history of mathematics, particularly British Mathematics and mathematics in the 17th century. He is also interested in the history of graph theory and combinatorics.

2000 Sir Brian Hoskins

The fifth Curle Memorial lecture was given by Professor Brian Hoskins FRS, President of the Royal Meteorological Society on 20 April 2000. The title of his talk was 'Forecasting weather and climate: a chancy business'.

Born in 1945, Brian James Hoskins was educated at the University of Cambridge with a BA in 1966 and a PhD in 1970. He has been at the University of Reading since 1976. From 2008- 2014 he was the first Director of the Grantham Institute for Climate Change at Imperial College, London. From 1998-2000 he was President of the Royal Meteorological Society. He received a knighthood in 2007.

In a report on the lecture by Professor Hoskins we have the following description.

Brian Hoskins discussed how over fifty forecasts are made at one time to work out the probability of different kinds of weather in a few days time, yet only one of these forecasts (if any!) are given to the public. We are screened from information deemed to be too complicated, or commercially profitable, yet this information could be of great practical use to many of us. The subject of climate change was also discussed, and he showed that the consensus prediction is for continued global warming (and associated sea-level and associated sea-level rises) due principally to carbon dioxide emissions.

2004 Chris Budd

The sixth Curle Memorial lecture was given by Professor Chris Budd (Bath). The title of his talk was '101 uses of a quadratic equation'.

Christopher John Budd was born in 1960. Educated at St John's College Cambridge with an MA degree in mathematics in 1982, he was awarded a DPhil degree from Oxford University in 1986. He is currently Professor of Applied Mathematics at the University of Bath and Professor of Geometry at Gresham College. He is co-director of the interdisciplinary Centre for Nonlinear Mechanics at the University of Bath. He is also active in promoting interdisciplinary collaboration both nationally and internationally. His research interests involve the analysis, application and numerical analysis of the solution of nonlinear differential equations with a particular emphasis on problems which arise in industry. As part of his outreach he has been chair of the UKMT ( Mathematics Trust) from 2016–2019.

The following announcement of Professor Budd's lecture was made:

The 2004 Curle Memorial Lecture will be held at 5.15 pm on Wednesday 27 October 2004 in Physics Lecture Theatre A, North Haugh, St Andrews. The talk '101 uses of a quadratic equation' will be given by Professor Chris Budd. As well as being Professor of Applied Mathematics at the University of Bath, Chris Budd is a prolific populariser of mathematics particularly to young people. This has been recognised by his honorary appointment to the chair of Mathematics at the Royal Institution of 'Christmas Lecture' fame.

The following is a report of the lecture:

The Curle Memorial Lecture for 2004 was given on the 27th of October by Professor Chris Budd. Chris holds the chair of Applied Mathematics at the University of Bath and also at the Royal Institution - recognising his esteem in the popularising of mathematics. The lecture series was set up in memory of Professor Newby Curle who held the Gregory Chair in Applied Mathematics from 1967 until his death in 1989. This year's talk entitled '101 uses of a quadratic equation' was aimed primarily at a general audience. The speaker was introduced by Bob Grundy who outlined the history of the event. Chris gave one of the most stimulating mathematics lectures in St Andrews for many years. To a large and enthusiastic audience he outlined the history of the quadratic equation from Babylonian mathematics to modern ideas on chaos. The talk finished with a fascinating demonstration of the chaotic motion of the double pendulum. Ken Falconer, a former colleague of Chris's when both were at Bristol, gave a vote of thanks.

2006 David Acheson

The seventh Curle Memorial lecture was given by Dr David Acheson (Oxford) on 10 October 2006. The title of his talk was '1089 and All That'.

Born in 1946 David John Acheson was educated at Highgate School, King's College, London (BSc Mathematics and Physics, 1967) and the University of East Anglia (PhD 1971). He was appointed a Fellow in Mathematics at Jesus College, Oxford in 1977 and became an Emeritus Fellow in 2008. His research has varied through geophysical and astrophysical fluid mechanics, magnetic fields and differential rotation in stars and 'magnetorotational' instability. From 2010 to 2011 he was President of the Mathematical Association.

Here is a review of Dr Acheson's lecture:

The title of the lecture comes from a simple arithmetic magic trick which entertained the lecturer as a child - seemingly different sums that always give the answer '1089'. Start with any 3-figure number (say 625). Reverse it (526), subtract the smaller from the larger (099), reverse it (990) and add the two together (1089). The trick is not difficult, but it was the inspiration for a wonderful lecture in which mathematics was presented as a game and an adventure, irrespective of whether it is elementary or advanced. For David Acheson, the "elements of mystery and surprise run through a great deal of mathematics at its best," and accordingly he took the audience on a journey from first steps to the frontiers.

2008 Sir Steve Cowley

The eighth Curle Memorial lecture was given by Professor Steve Cowley (Imperial College). The title of his talk was 'Fusion Power: The era of burning plasmas'.

Steven James Cowley was born in 1959. Educated at Corpus Christi College Oxford (BA 1981), he went to Princeton University as a Harkness Fellow and graduated in 1985 with a PhD for research into tokamaks. After periods at Culham, Princeton and UCLA he went to Imperial College London. Thereafter he has been head of the EURATOM/CCFE Fusion Association and CEO of UKAEA. In 2018 he was appointed director of the Princeton Plasma Physics Laboratory. In 2018 he received the award of Knight Bachelor.

The following announcement of the lecture was made:

University of St Andrews, Curle Memorial Lecture 'Fusion Power: The era of burning plasmas'. Professor Steve Cowley, Director, UKAEA Culham Laboratory. 5.15 pm Monday 1st December 2008. Physics Lecture Theatre A. In a decade, the international fusion experiment ITER will start operating in the south of France. This historic experiment will generate up to 500 MW of fusion power and provide a proof of principle for fusion energy. Fusion has the potential to provide a large fraction of our energy for millions of years. Prof Cowley will describe the scientific progress in fusion - from Sir Arthur Stanley Eddington's prophetic predictions in 1920 to the remarkable results that have led to ITER. He will outline the challenging problems that must be solved to make fusion power a commercial option, and worldwide efforts to find their solution.

2011 Sir Ian Diamond

The ninth Curle Memorial lecture was given by Principal Ian Diamond (Aberdeen). The title of his talk was 'The evolving history of the UK Census: 1801-2011 (and beyond?)'.

Ian David Diamond was born in Kingskerswell, Devon in 1965. He obtained BSc and MSc degrees from the LSE (London School of Economic and Political Science) in 1975 and 1976 and his PhD degree from the University of St Andrews in 1981. He has spent his career as a professional statistician. From 2010-2018 he was Principal and Vice Chancellor of the University of Aberdeen. Since retiring from that position he has been, among many different roles, Chair of British Universities and Colleges Sport. He is also a qualified football referee. We both remember playing five-a-side football with him and enjoying many tussles on the pitch. In 2013 he became a KB (Knight Bachelor).

The lecture was given on Tuesday 8 February 2011. It should have been given in November 2010 but was postponed because of bad weather. The 2010 announcement was as follows:

The School of Mathematics and Statistics presents The Curle Lecture 2010. Professor Ian Diamond (Principal, University of Aberdeen). The evolving history of the UK Census: 1801- 2011 (and beyond?). 5.15pm Monday 29th November, Physics Lecture Theatre A. The Curle Lecture is a biennial event hosted by the School of Mathematics and Statistics at St Andrews in memory of Professor Samuel Newby Curle, who was appointed Gregory Chair of Applied Mathematics in 1967 and who died in 1989. This year's Curle Lecture will be given by Professor Ian Diamond, Principal of the University of Aberdeen. Professor Diamond was previously Chief Executive of the Economic and Social Research Council. He was also Chair of the Research Councils UK Executive Group (2004-2009). Before joining the ESRC, Professor Diamond was Deputy Vice-Chancellor at the University of Southampton. He is a graduate of St Andrews, having studied here for his PhD in Statistics. This is a public lecture to which all are welcome. The COPSON LECTURES

In a letter to the first Copson lecturer Marcus du Sautoy Edmund wrote: Dear Marcus, I would like to invite you to give the first Copson Lecture at the University of St Andrews in the first semester of 2005-6. Let me give you some background. Edward Copson was my professor at St Andrews. He died in 1980. Recently his family have given the university money to fund an annual 'Copson Lecture'. We would like to have this lecture aimed at say the school/university level so that it would be attractive to our undergraduates, school pupils in the last couple of years at school, and to as wide a spectrum of mathematically literate people from the community as possible. We would be delighted if you would be the first Copson Lecturer.

The following Copson Lectures have been given:

2005 Marcus du Sautoy

The first Copson lecture was given by Professor Marcus du Sautoy (Oxford) on 11 October 2005 entitled 'The Music of the Primes'.

Marcus du Sautoy was born in 1965. His first degree is from Wadham College, Oxford and his DPhil degree is also from Oxford. Formerly a fellow at All Souls College, Oxford and Wadham College, Oxford he was appointed in 2008 to the Simonyi Professorship for the Public Understanding of Science and a fellowship at New College. He is well known as a broadcaster and populariser of mathematics, see for example his book 'The Music of the Primes'. One special link to us in St Andrews is that he was a main speaker at 'Groups St Andrews 2001 in Oxford'.

Marcus sent us the following Abstract.

Prime Suspect

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97…

Prime numbers are the atoms of arithmetic. At school, we are taught that they are divisible only by themselves and the number one. What we are rarely taught is that they represent one of the most tantalizing enigmas in the pursuit of human knowledge. How can one predict when the next prime number will occur? Is there a formula which could generate primes? These apparently simple questions have confounded mathematicians ever since the Ancient Greeks.

Prime numbers are the most important numbers in mathematics. Every number is built by multiplying together these indivisible numbers. For example 105 is built by multiplying the primes 3, 5 and 7. The primes are for the mathematician what atoms are for the chemist. They are the hydrogen, helium and lithium of the world of numbers. Chemistry has been very successful at producing a list of all the atoms that exist in Nature. Called the Periodic Table, it lists 109 chemical elements from which all molecules can be built.

Despite several millennia of investigation mathematicians are still struggling to understand their own mathematical Periodic Table of primes. The reason they are so hard to understand is that, unlike atoms, the primes go on for ever. In the first great Theorem of mathematics, the Greek mathematician Euclid proved that there are infinitely many prime numbers. Gone is the hope of just making a list of 109 primes, like the chemists, from which all numbers can be built.

Understanding the primes goes to the heart of what it means to be a mathematician. Mathematics is the science of patterns. Most people have the impression that mathematical research consists of doing long division to a lot of decimal places. But this is as crazy as thinking that professional musicians just play their scales faster and higher than anyone else. Mathematicians spend their lives striving to look for patterns, for logic and order in the chaos that surrounds us. Faced with the primes stretching out to infinity, mathematicians are hunting for some structure and pattern which can help us understand how Nature chose these elusive numbers.

The trouble is that as one looks through a list of primes it is very hard to predict when the next prime will appear. The numbers look more like lottery ticket numbers than numbers with some pattern. As one stares out to the infinite depths of the universe of numbers, the primes look as random as the stars in the night sky.

What makes a good mathematician is someone who can think laterally, who can look at the problem in a new way. In the nineteenth century a German mathematician called Bernhard Riemann found a new perspective on the primes which he believed would explain how the primes are laid out amongst all the numbers. Like the cosmologists who discovered the source of the stars in the night sky, Riemann uncovered what he believed was the Big Bang behind the primes.

Looking at the primes' apparent chaos from a fresh perspective, the German mathematician got an inkling of a subtle underlying harmony – the music of the primes. On the strength of his expert intuition, he made a bold prediction about the primes' hidden music, later dubbed the Riemann Hypothesis. Sadly, no one knows if Riemann actually found the key to the puzzle of prime numbers. He died before providing the proof, and his housekeeper burned many of his personal papers.

Since his death, scores of mathematicians, plus more than a few physicists and high-tech pioneers, have set out to conquer the Riemann Hypothesis. Today, the victor stands to gain one million dollars - courtesy of a Boston businessman - along with the glory. The story of humankind's attempts to master the primes reads like an unsolved murder mystery. It is a story of strange journeys, last minute escapes from death and the unquenchable thirst for knowledge. Its dramatis personae include a French spy, a Hungarian Jew fleeing Nazi persecution, a clerk from India, and John Nash (played by Russell Crowe in A Beautiful Mind) - whose 'prime obsession'may have contributed to his mental breakdown.

Mathematicians study the primes because of their beauty and universal character, like a common language of the cosmos. But today there are very commercial reasons for studying the primes - they are the key to modern codes. Every time someone sends their credit card number securely across the Internet, they are using properties of the primes to keep that number secret. To crack codes on the Internet, a hacker has to find a way to discover the primes that built an e-business's code number. It's like the chemist who wants to know what atoms make up salt. Chemistry has successfully invented a machine called a spectrometer which takes the salt and tells the chemist that Sodium and Chlorine are the atoms which built this molecule.

But the mathematicians have so far failed to discover a fancy prime number spectrometer which can quickly take a large number and tell you the primes that built that number. Understanding the primes holds the prospect not only to unlock the greatest mathematical enigmas of all time but could bring e-business crashing to its knees. Mathematics is still waiting for the person who can make that elusive breakthrough and make the primes sing.

2007 John Haigh

The second Copson lecture was given on 10 December 2007 by Dr John Haigh (Sussex) entitled 'How likely is that?'.

John Haigh was an undergraduate at Brasenose College, Oxford with a BA in 1963 and an MA in 1968. He was a postgraduate at Gonville and Caius College, Cambridge 1963-65 and the University of Sussex with a PhD from Cambridge in 1968. He has spent his career at the University of Sussex. His area of research is probability and statistics.

Announcing the lecture, it was stated that this year's Copson Lecture will be given by Dr John Haigh of the University of Sussex on Monday 10th December at 5.15pm in Lecture Theatre A of the Physics Building. This lecture was established in memory of Edward Copson, Regius Professor of Mathematics in the University of St Andrews from 1950-1969, and aims to bring to St Andrews a distinguished mathematician with the reputation of being able to communicate mathematical ideas to a non-specialist audience. Dr Haigh is an expert on probability who has written a popular book on the subject 'Taking chances: winning with probability' and has given one of a series of popular lectures for the London Mathematical Society. Jointly with fellow sports lover Rob Eastaway he has also written 'Beating the Odds; the hidden mathematics of sport'. He sums up his lecture entitled 'How likely is that' as follows; "Answers to questions about probability are often surprising and may even seem paradoxical. But a logical approach shows why these answers arise." This is a public lecture to which all are welcome.

2009 Peter Cameron

The third Copson lecture was given on 14 December 2009 by Professor Peter Cameron (QMUL) entitled 'Sudoku and Mathematics'.

Peter Jephson Cameron was born in Queensland, Australia in 1947. Educated at the University of Queensland and the University of Oxford he is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London. Among many distinctions he has been awarded in 1979 the London Mathematical Society's Whitehead Prize and was a joint winner of the 2003 Euler Medal. His many areas of mathematical research include group theory, combinatorics, coding theory and model theory. Of local interest is that he was a main speaker at Groups St Andrews 2005.

Prof Cameron sums up the lecture as follows.

In the Independent newspaper, the instructions for Sudoko say "There's no maths involved." You solve the puzzle with reasoning and logic. But, as any mathematician will tell you, maths is just reasoning and logic! There is indeed quite a lot of mathematics in Sudoku. In the lecture, I will explain some of the history, and show that mathematicians and statisticians could have invented Sudoku years before the retired architect Howard Garns actually did. Time permitting, I will also talk about a variant called 'Symmetric Sudoku' invented by Robert Connelly, which is closely connected with error-correcting codes and finite geometry.

2017 Vicky Neale

The fourth Copson lecture was given on 22 September 2017 by Dr Vicky Neale (Oxford) entitled 'Closing the Gap: the quest to understand prime numbers'.

Vicky Neale obtained her PhD from the University of Cambridge in 2011. She then taught at Cambridge while being Director of Studies at Murray Edwards College. In 2014 Vicky Neale became Whitehead Lecturer at the Mathematical Institute, University of Oxford and Supernumerary Fellow at Balliol College. She is also been actively involved with UKMT (United Kingdom Mathematics Trust). One of her particular interests there has been helping to organize EGMO (the European Girls' Mathematical Olympiad).

The lecture was announced as follows.

Prime numbers have intrigued, inspired and infuriated mathematicians for millennia, and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety. Join Vicky to learn about recent progress towards proving the famous Twin Primes Conjecture, and to hear the very different ways in which these breakthroughs have been made - a solo mathematician working in isolation, a young mathematician displaying creativity at the start of a career, a large collaboration that reveals much about how mathematicians go about their work.

From the School of Mathematics Newsletter October 2017 we have the following entry. The Copson Lecture 2017 with the title 'Closing the Gap - the quest to understand prime numbers' was given by Dr Vicky Neale, University of Oxford, on 22nd September. Attendance by students, staff and the general public was very good. This was the first Copson Lecture since 2009 and provided an excellent example of how mathematical research and the processes behind it can be explained to a wider audience. The School also plans to revive our second public lecture series, the Curle Lectures, in 2018.

Summary

It is interesting to note that of the nine Curle and four Copson lecturers to date, 10 received part of their education at either Cambridge University or Oxford University (or both). Of the remaining three, two spent considerable parts of their careers at Oxford.

It is to be hoped that in the near future both the Curle and the Copson lectures will be revived and provide a nice example of outreach for Mathematics in St Andrews. We are pleased to note that the lectures have covered a wide range of mathematical topics from some very obvious 'applied' talks, some talks that are of a statistical nature and some that are 'pure mathematics'. The topics, and the lectures themselves, have all been designed to be of interest to all those who do not necessarily have advanced mathematical knowledge.

REFERENCES

[1] T B Benjamin and M J Lighthill, On conoidal waves and bores, Proc. Roy. Soc. London Ser. A 224 (1954), 448-460.

[2] E T Copson, An Introduction to the Theory of Functions of a Complex Variable, Oxford University Press.

[3] J J O'Connor and E F Robertson, Edward Thomas Copson, MacTutor History of Mathematics. https://www-history.mcs.st-andrews.ac.uk/Biographies/Copson.html

[4] J J O'Connor and E F Robertson, Samuel Newby Curle, MacTutor History of Mathematics. https://www-history.mcs.st-andrews.ac.uk/Biographies/Curle.html