# Mathematics at Work

The *Mathematics at Work* seminars introduce undergraduates to some of the fields in which mathematicians are working in industry and government. Each seminar combines some serious mathematics with an explanation of its place in the speaker's company's activities, and a description of the career path of the speaker. Speakers will provide material for further reading, leading to possible topics for Second Year essays.

The seminars take place in Room MS04 in the Zeeman Building at 6.00pm on Thursdays in November, with occasional overspill to the end of October or the start of December.

**Schedule of Seminars, Autumn 2017 (provisional)**

**October 26th 2017 Dominic Vipond, Warwick Manufacturing Group Academy,** *Teaching Mathematics in Secondary Education*

**November 2nd 2017 George Dewhirst, Deloitte ***The Mathematics of Economic Development Scenarios*

**November 9th 2017 Owen Daniel, Department for Environment, Food and Rural Affairs, ***t.b.a*

**November 16th 2017 Paul Cadman Zühlke ***t.b.a*

**November 23rd 2017 Nira Chamberlain Babcock International Group ***Real world problems and the art of mathematical modelling*

**November 30th 2017 David King, Schroders Asset Management: ***t.b.a*

**Titles and Abstracts, Autumn 2017**

**Dominic Vipond ***Teaching Mathematics in Secondary Education*

Maths education is going through a period of flux; the curriculum, the way students and schools are assessed, and the way maths needs to be taught are all changing. With this turbulence comes a need for educators to adapt. Teaching to the exam is becoming more difficult, and teaching for understanding is as difficult as it has always been. Yet through all this change, many things remain the same, students are still people, and the fundamental way in which people learn hasn’t changed. It’s certainly an exciting time to be a teacher.

In this workshop, we will talk about some of the changes happening in education, and what this means for teachers. We will see a few different techniques the can be used to facilitate the understanding of students. We will explore what maths is required of students, and teachers, at different stages of the new syllabi. The ideas surrounding teaching as a career will be explored, as well as some arguments for why we need good mathematicians to be good teachers. Most importantly, we will have the opportunity to actually do some maths.

**Nira Chamberlain** *Real world problems and the art of mathematical modelling*

In my humble opinion, mathematical modelling is the most creative side of applied mathematics. To me, mathematical modelling is about looking into the real world; translating it into mathematics, solving that mathematics and then applying that solution back into the real world. However, a secret of the trade is that every mathematical model will have its assumptions and limitations. A good mathematical model will have the right amount of transparent and challengeable assumptions, which coupled with an good mathematical approach provides the framework for potential insight into real world problems. In this talk we will discuss and show examples of the art of mathematical modelling in solving real world problems.

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**Titles and Abstracts Autumn 2016**

**Julian West ***Evolving encryption*

Whenever communications data are sent across a network, there is a risk that they may be intercepted or tampered with. Rather than trying to protect the network, a more practical option is to protect the data by encrypting it. We will look at the evolution of communications methods through history and see how encryption technologies have grown up alongside communications technologies.

**Charles Tallack ***Data, systems and lives*

The NHS is one of the UK's proudest creations. It improves our health and well-being, and supports us to keep mentally and physically well and to get better when we are ill. In a typical week in England there are five million GP consultations, around 30,000 attendances at A&E, and 13,000 births.

The NHS is under enormous pressure as demand rises, patient needs change and funding is constrained. Charles's team is contributing to the transformation of the NHS by evaluating the impact of new models of care being piloted. They are modelling how the changes are supposed to work, and testing these models using advanced analytical techniques. Charles will talk abut the work of his team and other NHS England analysts to improve the NHS.

For people with an interest in applying analytical methods, the NHS provides a wealth of opportunities. There are complex systems to understand, model and improve, and data to analyse and draw insight from. Many NHS bodies employ mathematicians, including hospitals, science and research networks, and national bodies such as NHS England.

**Graham Searle ***Positron Emission Tomography*

Medical imaging has come a long way in the last 30 years. Plain X-rays remain useful, but computed tomography (CT), magnetic resonance (MR) and positron emission tomography (PET) scanners have transformed our ability to see inside the living human body. Whilst CT scanners show the body's *structure*, PET (and certain types of MR) scans allow us to look at molecular biology and *function*. These capabilities are used in a limited way in hospitals, but the real power of quantitative PET imaging is in research and development. Research PET imaginguses sophisticated physics, engineering, chemistry and mathematics to acquire 3D movies that show the distribution and kinetics of radioactive molecules injected into patients or volunteers. Once the images are acquired and the subjects have 'cooled down', we move rapidly from pretty pictures to hard numbers. Efficient optimisation techniques align 3D images and automatically identify neuroanatomical structures. Mathematical models can then extract parameters of biological significance from the data, and answer questions such as "Do people with schizophrenia have more D2 receptors in their striata?" or "Does my new drug reduce the rate of beta-amyloid in patients with Alzheimer's Disease?" This talk will give a flavour of the breadth of applications for mathematics within medical imaging, especially PET, and will include some pretty pictures of brains.

**Rob Bozeat** *Financial Derivatives*

Financial derivatives are sophisticated risk management tools created by financial institutions to allow corporate clients, institutional investors and wealthy individuals to manage their exposure to a variety of financial risks. The largest markets for financial derivatives are in Foreign Exchange and Interest Rates, but more unusual asset classes, such as Commodities and even Weather, are also traded. Derivatives transfer the risk faced by the client to the bank. This raises two interesting questions. First, how do the banks price the risk they are taking, and second, how do they manage the risk to avoid financial disaster. These questions are not easy to answer. Changes in bank regulations also mean that banks face new charges when running derivatives businesses, and hence are constantly developing and refining models to correctly price the cost of risk management. This talks provides an introduction to the mathematics of finance. I will explain how banks view risk and how they develop models to price it.

**Andrea Schiavi ***Machine Learning and Artificial Intelligence*

Machine learning and artificial intelligence have been an integral part of computer science for many years, but recently their impact upon society has increased substantially. Sectors such as banking and law, historically some of the most resistant towards change and technological innovation, are now rushing to take advantage of the opportunities that automation and machine learning can bring. As machine learning approaches commercial and widespread use, the modern era of “big data” challenges existing techniques. Simply put, two linked problems, data sparsity and an ever increasing number of dimensions, put established approaches like linear regressions and nearest-neighbour methods to the test. Mathematics increasingly shines as the key enabling element in the quest for an efficient “thinking machine” and in overcoming a challenge that is commonly referred to as “the curse of dimensionality”. This talk will explore the fundamentals of machine learning. It will stress the role played by mathematical tools and concepts, and present examples of how Eigen Technologies is using them in commercial products. As a major player in the field of artificial intelligence, we are well aware of the role that our technology could play in changing society. The discussion will explore some of the key issues that we all face as a result of these changes.

### Schedule of Seminars, Autumn 2015

**October 22nd David Basterfield npower ***Forecasting Energy Demand *

**November 5th Richard Pinch GCHQ ***Post-modern Cryptography *

**November 12th Peter Laflin Bloom Agency ***How marketing is changing Graph Theory*

**November 19th Warwick Alumni Evening**

**November 26th Ben Cox Tessella **

*Numerical solutions of non-linear PDEs for the oil and gas industry*

**December 3rd Sarah Davis GE Power*** Applications of Mathematics in Power Plant Design
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**December 10th** **Owen McCarthy and** **Amy Guyomard*** ***Frontier Developments*** Scream Ride*

### Titles and Abstracts, Autumn 2015

**David Basterfield ***Forecasting Energy Demand*

The energy industry is constantly evolving as we collectively seek to manage the energy trilemma: balancing the affordability, sustainability and security of energy supplies now and for future generations. The session will open by covering briefly the range of applications of mathematics in an energy supply business, from customer analytics to smart metering and energy trading amongst others. The main topic of discussion will be the application of mathematics to forecasting energy demand from consumers, domestic through to large business, and wind/solar generation. Forecasting demand is critical to ensure we understand the profitability of the business going forwards and to ensure we purchase the right amount of energy to meet customer needs. The financial consequences of getting it wrong are significant, hence we invest heavily in analytical capability, both people and IT systems. The session will close by introducing the *npower Forecasting Challenge* where small teams of students have the opportunity to try their hand at forecasting using real data for the chance to win a summer internship and £1000.

**Richard Pinch ***Post-modern Cryptography*

Traditional symmetric or secret key cryptography has historically been the province of government, diplomatic and military users with a requirement for confidentiality. More recently asymmetric or public key cryptography has been developed and taken up to meet the requirements of life in cyberspace. Businesses and private individuals are now using it, often unknowingly, to achieve authentication as well as confidentiality. New threats and opportunities are emerging with the advent of quantum technology. I will describe how cryptography is being used today and some of the challenges for the future.

**Peter Laflin** *How Marketing is Changing Graph Theory*

Graph Theory is put to good use in lots of very unexpected ways. For example, you would not be able to perform an Internet search without Graph Theory being used to understand which webpages are more important than others. Graph Theory is also used to help suggest the products you might buy whilst shopping online and it is now being used to help brands make their marketing campaigns be more successful.

In this seminar, Peter Laflin, Chief Data Scientist at Bloom Agency, will give a brief introduction to Graph Theory. As the world of marketing is changing, in the face of more data and a greater need to accurately measure the impact of marketing activities, the world of graph theory faces a challenge. Since the 1700’s, when Euler first posed a graph theoretic question, the node and edge set have remained fixed in the problems being studied. We now need to solve problems where the nodes and edge sets come and go over time which means we need to think differently about the maths we use to solve our problems. Peter will explain how the world of marketing is challenging the world of mathematics to change, to provide the tools needed to solve the commercial questions posed of businesses in the 21st century.

Bloom are successfully using this new mathematics for clients like SKY and ITV. Peter’s talk will feature case studies which will show how innovation in mathematics is delivering successful campaigns.

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**Ben Cox ***Numerical solutions of non-linear PDEs for the oil and gas industry*

This talk takes a look at the huge role that mathematics plays within an international analytics, software and consulting services company. At Tessella, we often need to design innovative solutions to some very challenging problems in the science and engineering domains. This means that graduates with the right mix of mathematical rigour and insight are vital to our continued success and growth. This seminar will address why mathematicians are so important to Tessella, drawing upon a couple of case studies from our work for a major client within the energy sector. The examples highlight the use of Newton's method of numerical solution to solve a system of partial differential equations modelling fluid flow in oil and gas reservoirs. In this case, an understanding of this method - not to mention some key mathematical traits - was crucial in improving the performance of a benchmark reservoir simulator that is used to model a variety of oil recovery mechanisms.

**Sarah Davis** *Applications of Mathematics In Power Plant Design*

Market competition, long term increasing fuel costs and growing concerns about emissions are driving the requirement for more efficient and environmentally friendly power plants. The world is experiencing a “data explosion” due to the rapid advances in computer technology enabling the sensing, acquisition, storage and analysis of massive data-sets. This data can arise directly from physical sensors or from increasingly sophisticated computer models capturing the variations of complex phenomena. More data, in turn, requires the use of increasingly elaborate mathematical techniques for data analysis. This talk discusses a number of such techniques and how they are used today in power plant design.

**Owen McCarthy and Amy Guyomard** *Scream Ride*

Since the beginning of the computer games industry, mathematical techniques have been used to bring complex games to life. In everything from drawing a line on a pixel display to simulating physics in complex rigid-body collisions, game developers employ knowledge from many fields of mathematics: linear algebra, physics simulation, and numerical analysis to name a few. However, unlike in many other applications, we have to solve problems robustly in less than 1/30 of a second.

This talk covers an overview of the broad applications of mathematical techniques in modern computer games and how Frontier Developments used mathematics to bring the fully destructible world of ScreamRide to life.