Why study mathematics?

Author 
Vicky Neale

A friend of Plus, Vicky Neale, has written a book about why people study maths at university, and to give a taste of what it's like to study a maths degree. We asked her to tell us about her book and why she wrote it...

Why Study Mathematics? by Vicky Neale

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.

At school, there are standard requirements about what students have to learn: there's a national curriculum. This isn't the case at university. Universities have significant flexibility when it comes to how they organise degree programmes. There's a huge variety of courses – offering differences in mathematical content and emphasis, in teaching style and in assessment methods – that can lead you to a maths degree. This means that it's really important to research the available options before you apply, to find courses that'll suit you.

There's a lot of flexibility about which topics are covered in a maths degree. In the UK, the only topics specifically mentioned in the QAA benchmark statement (which sets out expectations for maths degrees) are calculus and linear algebra. Beyond that, it's up to individual universities to design appropriate degree courses.

Different people have different mathematical tastes. Some like nothing more than to get their hands on a large data set, to interrogate it in order to see what conclusions they can draw, and to consider the robustness of those conclusions. Others are motivated by a particular application and spend time exploring which mathematical tools can help to answer the questions they find exciting in that area. Others still are fascinated by the beautiful, fundamental questions in this subject (it's surprising just how many fundamental questions there are for which we still don't have complete answers) and devote themselves to curiosity-driven maths.

Within a maths degree, you're likely to have opportunities to experience all of these facets. However, degree programmes do differ in the emphasis they place on each aspect of maths, as well as in the number of options they offer to students, so it's really worth thinking about what style of course will suit you. Are you motivated by the use of maths in industry and other applications, and therefore interested in building a mathematical toolkit for that purpose, or would you relish delving into the background theory of how and why the tools work? You’re not restricted to one or the other: many courses combine elements of both. But when you're researching courses, it can be helpful to consider the extent to which each might be described as "theory-based" or "practice-based", because viewing courses through that lens might help you to focus on the ones that'll suit you.

You might have heard people talking about there being a jump in difficulty from school maths to university maths. While there are certainly differences between the two, this isn't the same as the latter representing a massive step up in difficulty. Some of the differences might be to do with teaching approaches, with the style of questions you're being asked to tackle, or with the amount of independent study you’re being expected to undertake. Others might be due to the fact that you're meeting new topics.

It's important to remember that universities know the move from secondary to higher education involves a transition to new material and new ways of working: degree programmes are designed to support students making this transition. Universities are familiar with the profiles of their incoming students and what they can expect them to know or to be able to do, and they tailor their programmes accordingly. Having said that, you'll still need to adapt to new ways of working, to be willing to persevere and to ask for support when you need it. There's no need to panic, though. Over the course of a three- or four-year maths degree, you'll become increasingly independent and develop your study skills and mathematical sophistication. You don't need to have done all this before the first day of your degree!

Deciding which subjects you'd like to pursue is just one of the many factors you'll need to consider when choosing a course of study. For instance, there are a variety of ways these subjects can be combined to form a degree that suits your interests. And there are many other factors to consider, such as how teaching and assessment are structured, what opportunities you’ll have to interact with staff and your fellow students, and what the career possibilities are.

I wrote Why Study Mathematics? in the hope that it will help you to find out more about maths at university. In Part I (from which the extract above is taken), we 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 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. One chapter concentrates on topics that are common to pretty much all maths degrees, illustrating the relevance of differential equations to modelling the spread of disease, connections between linear algebra and JPEG image compression, and the surprising use of non-real complex numbers to very real problems in aerodynamics. Other chapters illustrate further aspects of the mathematical sciences, from the use of operational research to facilitate kidney donation to the role of data science in genetics and retail, from compressed sensing to improve medical imaging to non-Euclidean geometry and uncountably infinite sets. Don't worry if you haven’t heard of all these mathematical ideas – these are topics you might meet in a maths degree, not ones you need to understand before you study one!

If you're a student looking to make a decision about university, or you are supporting someone who is making that decision, I hope that this book will give you a clearer picture of why a maths degree is a good option for many people. And if you are 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.

Book details:
Why Study Mathematics?
Vicky Neale
paperback, kindle — 208 pages
London Publishing Partnership (2020)
ISBN 978-1913019112

You can also watch a short interview with Vicky when she told us about her favourite mathematical moments.


About this article

Vicky Neale

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, crochet and other craft to explore mathematical ideas – her two cats enjoy joining in.