Why Study Mathematics?

By Vicky Neale

Considering studying mathematics at university? Wondering whether a mathematics degree will get you a good job, and what you might earn? Want to know what it's actually like to study mathematics at degree level? This book tells you what you need to know. Studying any subject at degree level is an investment in the future that involves significant cost. Now more than ever, students and their parents need to weigh up the potential benefits of university courses. That's where the Why Study series comes in. This series of books, aimed at students, parents and teachers, explains in practical terms the range and scope of an academic subject at university level and where it can lead in terms of careers or further study. Each book sets out to enthuse the reader about its subject and answer the crucial questions that a college prospectus does not.

• Language: English
• Publisher: London Publishing Partnership
• Release date: Oct 27, 2020
• ISBN: 9781913019136

Vicky Neale

Vicky Neale is the Whitehead Lecturer at the Mathematical Institute, University of Oxford, and a Supernumerary Fellow at Balliol College. She teaches pure mathematics to undergraduates and combines this with work on public engagement with mathematics: she gives public lectures, leads workshops with school students, and has appeared on numerous BBC radio and television programmes. One of her current interests is in using knitting and crochet to explore mathematical ideas. She's the author of "Closing the Gap: The Quest to Understand Prime Numbers" (Oxford University Press, 2017). You can visit her website (https://people.maths.ox.ac.uk/neale/) and follow her on Twitter (@VickyMaths1729) for more information and updates.

Book preview

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Praise for Why Study Mathematics?

Why Study Mathematics? is an insightful guide for anyone considering studying mathematics at university. It explains the sort of maths you can expect to find and how it will be taught, and highlights the wide variety of career options that a maths degree opens up. It also includes important examples of where maths is used in the real world. I recommend it to all prospective maths students and their parents.

Nicholas J. Higham, Royal Society Research Professor

and Richardson Professor of Applied Mathematics,

University of Manchester

The mystery of a mathematics degree – what it is, where it leads and why it’s useful – is unlocked in this easy read. Detailed, accessible and broad ranging, Vicky Neale refines the complex and varying nature of high-level mathematics into an understandable, useful and relatable form. An ideal guide for A level maths students when pondering their next steps.

Kerry Burnham, headteacher, Exeter Maths School

Why Study Mathematics? explores in depth the various options that a maths degree has to offer as well as providing expert guidance on what to expect from a maths degree. Vicky Neale addresses all the questions that an enthusiastic mathematician considering a maths degree might have. She refutes the myth that studying maths beyond school/college is restrictive or overwhelmingly challenging. Neale’s book is both informative and engaging: it made me want to study a mathematics degree all over again, or at least revisit certain topics that are discussed. I highly recommend this book to any student or maths enthusiast wanting to study mathematics at university. Being a mathematics teacher myself, this book is definitely a resource I shall be directing A level students to.

Rebecca Blazewicz, mathematics teacher,

Bristol Grammar School

An essential read for anyone considering studying mathematics at university. Vicky Neale takes you through what to expect in your studies, and explains the practical uses and beauty of a mathematics degree.

James Grime, lecturer, public speaker and Numberphile presenter

Another great book from Vicky Neale. An extremely useful guide for students (and their advisors!) on studying mathematics at university.

Dr Kevin Houston, School of Mathematics, University of Leeds

Why Study Mathematics? is superb! It will be the very first book that I will recommend to students who wish to study mathematics at university, as it provides a very easy-to-follow guide to the many fascinating areas and branches of mathematics that could be studied during a mathematics degree and to the ever-growing number of careers that require one. Neale provides compelling insight not just into how useful mathematics is in today’s modern world, but also into what an essential and integral element of everyday life the subject is. The book provides wonderful examples of how mathematics is used in today’s ever-evolving world, from its involvement in online shopping and JPEG compression to the way it’s used to analyse climate change. The beauty of mathematics is also revealed through Escher’s paintings, many elegant equations and the intriguing world of infinities, all of which should inspire students to go and find out more.

Jason Hudson, Director of Mathematics, Wilson’s School

This book is impressively thorough in its treatment of the factors that a student might consider, both in navigating the intimidating variation of choice in mathematical courses and in exploring the essence of what maths is and the subject’s implications in a wide variety of industrial and research settings. Vicky Neale is clearly someone who not only has a deep knowledge of maths, from SIR models to JPEG compression, but also has extensive experience in helping students both in the lead up to university and beyond. I highly recommend it to any student, including both those who are just exploring their university options and those who are already set on a mathematics degree and want to explore the short-term and longer-term implications of their choice.

Dr Jamie Frost, teacher at Tiffin School, founder of DrFrostMaths and Top 10 Finalist for the Global Teacher Prize 2020

Why Study Mathematics? is awesome! It’s absolutely the book I wish I’d had as a sixth former, when, truth be told, you don’t really know what studying a maths degree is. It’s beautifully written and really engaging, and it represents a great starting point from which to explore all the different maths courses that are available. Crucially, it helps you formulate the questions you need to ask the tutors on those different courses to help you work out where will be the best place for you to study.

Sophie Carr, founder of Bays Consulting and Aperiodical’s

‘World’s Most Interesting Mathematician’

This book is essential reading for A level students who are thinking about a maths degree. The reader is given an accurate picture of what to expect on a maths degree course and what employment opportunities may follow. The descriptions and examples are perfectly chosen and do a great job of showing why the subject is so interesting and enjoyable.

David Ireland, maths teacher, Heyford Park Free School

WHY STUDY MATHEMATICS?

The Why Study Series

Studying any subject at degree level is an investment in the future that involves significant cost. Now more than ever, students and their parents need to weigh up the potential benefits of university courses. That’s where the Why Study series comes in. This series of books, aimed at students, parents and teachers, explains in practical terms the range and scope of an academic subject at university level and where it can lead in terms of careers or further study. Each book sets out to enthuse the reader about its subject and answer the crucial questions that a college prospectus does not.

Published

Why Study History? — Marcus Collins and Peter N. Stearns

Why Study Mathematics? — Vicky Neale

Why Study Geography? — Alan Parkinson

Forthcoming

Why Study Languages? — Gabrielle Hogan-Brun

WHY STUDY MATHEMATICS?

BY VICKY NEALE

Copyright © 2020 Vicky Neale

Published by London Publishing Partnership

www.londonpublishingpartnership.co.uk

All Rights Reserved

ISBN: 978-1-913019-12-9 (iPDF)

ISBN: 978-1-913019-13-6 (epub)

A catalogue record for this book is

available from the British Library

This book has been composed in

Kepler Std

Copy-edited and typeset by

T&T Productions Ltd, London

www.tandtproductions.com

Cover image

Mathematicians play an important role in understanding and tackling climate change. Mathematical modelling and statistical analysis allow researchers to review data, to make predictions about the melting of the polar ice caps and to study the population dynamics of animals such as polar bears (hence our cover image). Mathematical expertise is also relevant for managing the impact of climate change in the energy, health care, transport, agriculture, retail and finance sectors, to name just a few. Some of these topics are addressed in this book, and you'll see a polar bear in a completely unrelated context too.

CONTENTS

Acknowledgements

Introduction Why study mathematics?

PART I

THE INS AND OUTS OF A MATHS DEGREE

Chapter 1 What’s in a maths degree?

Chapter 2 What are my options for study?

Chapter 3 Who can study maths?

Chapter 4 What do maths graduates do next?

PART II

MATHS IN ACTION

Chapter 5 Applications of key mathematical ideas

Chapter 6 Further applications of maths

Chapter 7 Themes in fundamental maths

Conclusion

Further reading

ACKNOWLEDGEMENTS

I’m very grateful to the friends and colleagues who read drafts and offered me wise advice and constructive suggestions: Nathan Barker, Sue Cubbon, Charlie Gilderdale, Mareli Grady, Fiona Hamey, Lizzie Kimber, Derek Moulton, James Munro, Peter Rowlett and Andi Wang. I’m also very grateful to the team at London Publishing Partnership for their expertise and patience – Richard Baggaley, Sam Clark and Ellen White – as well as two anonymous reviewers.

INTRODUCTION

Why study mathematics?

maths is a versatile subject, with different flavours that appeal to different people with different tastes. It equips graduates with skills that employers value. It’s full of fascinating ideas and powerful applications, and the process of understanding a new mathematical concept or solving a problem using maths is enormously satisfying. Whatever your priorities – whether you’re looking to help other people, to earn a lot, to explore a creative subject or to make a difference in society – maths has something to offer you. The study of maths is rewarding in and of itself, and it gives you lots of options for the future.

There are many factors to consider when choosing what to study at university and where to study it (and this follows a careful decision about whether your next step is to attend university or to pursue another path). You might already know from your experience at school or college that you have a particular interest or strength in a certain subject, or you might be choosing between a few options. Or, as some subjects are available at degree level but not at school or college, you might be researching these as well as looking into how subjects that you’ve previously studied develop and change at university. (As you’ll see in this book, maths at university includes a broad range of topics, many of which you won’t have encountered at school.) In addition, you might have a particular career path in mind, or you might be looking to ensure that you keep your job options open.

This book will help you to find out more about maths at university. In Part I, we’ll explore the practicalities of a maths degree. What’s involved in studying a maths degree? What topics might you study? What teaching methods and types of assessment might you encounter? How do you choose between the wide variety of maths degree courses on offer? What makes a good maths student? What careers are open to maths graduates?

In Part II, we’ll look more closely at some of the topics you might study at university, providing a taste of the theoretical underpinnings of maths and offering insight into its diverse applications: in medicine and health care, in digital communication, in engineering, in tackling climate change, and more. My choice of subjects is inevitably centred on mathematical nuggets that I find fascinating, and I’ve tried to pick examples of topics and applications that don’t often come up at school or college in order to give you a glimpse of further horizons, rather than to remind you of things you already know well. Don’t worry if you don’t follow all the mathematical ideas – these are topics you might meet in a maths degree, not material you’re supposed to understand already!

I’ve included some suggestions for further reading at the end of this book. These include books that you might want to read before starting a maths degree as well as websites to inspire you and to help with your decision making. There’s a lot out there for aspiring mathematicians, from engaging YouTube videos by Numberphile to stimulating maths problems by NRICH and the UK Mathematics Trust, from case studies by Maths Careers to biographies of mathematicians throughout history by MacTutor.

Perhaps you’re reading this book as a student looking to make a decision about university. Or maybe you’re reading it because you’re supporting a family member making this decision, or because you’re a teacher working with students trying to choose a university course. Whatever your situation, I hope that this book will give you a clearer picture of why a maths degree is a good option for many people.

If you’re the one who’s thinking about embarking on this adventure, then I would like to wish you all the very best with your mathematical studies.

Last-minute note

I’m putting the finishing touches to this book in the spring and summer of 2020, under ‘lockdown’ in the UK because of the Covid-19 pandemic. As you’ll see in a few pages’ time, Chapter 5 starts with a discussion of the use of maths to study the spread of disease. Believe it or not, this was always the plan for this chapter, long before Covid-19 emerged, and the first draft now looks uncomfortably prescient.

The vital role that mathematical modelling has to play both in predicting how this disease might unfold and in simulating the effect of different strategies is being featured on the national news, along with discussions about ‘flattening the curve’ and the reliability of statistical data on cases so far.

In addition to modelling the spread of this disease, maths graduates have been developing software and planning logistics for the National Health Service (NHS) and supermarkets; teaching and safeguarding young people; analysing and managing risk in all areas of business; keeping the finance sector open; and supporting the economy, all of which are making a powerful difference during this pandemic.

The world around me as I write is strange and unfamiliar. I’m not allowed to leave my house, except to take a daily walk or to buy groceries. My students are scattered around the world, most having left Oxford at the end of term, just before lockdown was introduced. They’re doing an extraordinary job of continuing to study maths and make excellent progress under difficult circumstances. I teach them from my kitchen table, using technology to bridge geographical gaps that now seem very wide.

No doubt you’re wondering what this means for the future of university study and specifically of maths degrees. While university planning is well underway for the 2020/21 academic year, we don’t really know what this will look like yet. I’m certain that it will have to involve a mixture of online and face-to-face teaching and learning. I hope that, in the long term, we’ll take the best aspects of the former and adapt them to improve our maths degrees in the future, using technology to enhance our lessons, but not to replace those activities best done in person. Maths lecturers from different universities are already coming together to exchange ideas about how best to organize teaching and to support students’ learning in light of our changing circumstances.

While all university courses might look a little different over the next few years, maths degrees will still offer a stimulating, inspiring, satisfying and rewarding programme of study as well as a