Careers:Maths Careers

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Actuaries use maths and statistics to make financial sense of the future. For example, if an organisation is embarking on a large project, an actuary may analyse the project, assess the financial risks involved, model the future financial outcomes and advise the organisation on the decisions to be made. Much of their work is on pensions, ensuring funds stay solvent long into the future, when current workers have retired. They also work in insurance, setting premiums to match liabilities. Mathematics is also used in many other areas of finance, from banking and trading on the stock market, to producing economic forecasts and making government policy.

Art is not the first thing that springs to mind when you think about career paths for mathematicians. But evermore powerful computers have opened up breathtaking new possibilities both for visual artists and musicians. The people who design the computer graphics and the software used by artists have to be mathematically minded, and this has enabled many people to combine their passion for art with their love for maths.

Most of today's music is produced using synthesisers and digital processors to correct pitch or add effects to the sound. These tools are created by audio software engineers who work out ways of manipulating the digital sound, by using a mathematical technique called Fourier analysis. This is part of the area of digital signal processing (DSP) which has many other applications including speech recognition, image enhancement and data compression. Most of today's music is produced using synthesisers and digital processors to correct pitch or add effects to the sound. These tools are created by audio software engineers who work out ways of manipulating the digital sound, by using a mathematical technique called Fourier analysis.

Understanding the conditions that result in avalanches, and developing ways to predict when they might occur, uses an area of maths called fluid mechanics. This is one of the most widely applied areas of mathematics, and is also used in understanding volcanic eruptions, flight, ocean currents and even the stock market.

Mathematical biology or biomathematics is an interdisciplinary field of study. It models natural and biological processes using mathematical techniques and tools. Results have been applied to areas such as cellular neurobiology, epidemic modelling, and population genetics.

To be successful in business you don't only need a good product to sell, but also huge organisational talent and a knack for predicting future trends. How do you best organise your workforce to maximise productivity? What's the best design for a factory to run as efficiently as possible? Is the market ready for new ideas? You need people who can solve complex problems, assess risk, predict the behaviour of markets, and make sense of vast amounts of data. Many big organisations employ mathematicians and statisticians to help them with these tasks. Others seek outside help from business consultancies and market research, or consult experts in operational research, a part of maths concerned with finding optimal solutions to complex problems. Working in this field you experience all kinds of businesses first-hand, and there's great opportunity to branch out and develop your career. The analytical skills of a maths or stats graduate are welcome almost everywhere!

Maths, like all the sciences, has become a highly specialised field. It is next to impossible for a lay person to understand all its uses and the latest advances. Science communicators, writers and journalists are here to make maths and science accessible for the general public. They work for broadsheet newspapers and popular science magazines such as the New Scientist, help to put together and host TV programmes, write popular science books and help put on science exhibitions. For a career in this area you definitely need a maths or science degree, and this is what you should concentrate on while you are at university. Having said that, there are many opportunities for students to try their hand at science communication, for example by taking part in science writing competitions, or by becoming a volunteer helping to put on science festivals.

Creating virtual worlds and making the people that inhabit them behave as we would expect involves a lot of maths. The virtual landscapes and things within them are three-dimensional mathematical objects, and these objects behave and interact according to the equations for the rules of physics that apply within the game. These rules might cover gravity, speed and force, and even stop your character falling through a solid floor but allow them to sink in quicksand. This type of mathematics is also used in computer graphics for movies, and maths plays an important part in many areas of IT, including programming, designing hardware and project management. Computer games designers create the virtual worlds and make the people that inhabit them behave as we would expect. The virtual landscapes and things within them are three-dimensional mathematical objects, and these objects behave and interact according to the equations for the rules of physics that apply within the game.

Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. Mathematicians, with their training in logical and precise thinking, are highly prized in this field.

You often hear about consultants being called in by government departments or business, but what do they actually do? Statistical and mathematical consultants use their training to solve problems in a wide range of areas, such as predicting future infrastructure requirements, improving manufacturing processes and using the large amounts of information now held by businesses to help them make better decisions Statistical and mathematical consultants use their training to solve problems in a wide range of areas, such as predicting future infrastructure requirements, improving manufacturing processes and using the large amounts of information now held by businesses to help them make better decisions.

Cryptography is the practice and study of hiding information. Cryptography is considered to be a branch of both mathematics and computer science. Not just for spies anymore, cryptography applications include the security of ATM cards and computer passwords.

The defence sector is an important employer of mathematicians: it needs people who can design, build and operate planes and ships, and work on other advanced technologies. It also needs clear-thinking and analytical strategists. A lot of the work in this area is shrouded in secrecy, but we did manage to get some profiles for you.

Studying economics requires you not only be able to handle data and work with figures, but also to understand the concepts underlying economic questions. You will use maths to calculate compound interest, and arithmetic series to calculate growth of investments. You will need to use calculus to optimise cost and profit calculations, and to use maths to express and analyse supply and demand problems.

Being a student, you're in a prime position to judge whether returning to school after university appeals to you. But remember that there are lots of different aspects to teaching. You could teach adults, for example, or those with special needs. Then there's university: as a lecturer, at least half of your time is devoted to research, which brings you to the forefront of maths and science in general. You can also get involved in the education sector at a different level and become one of those who decide what goes into the curriculum, or assess how well the education system functions.

The term "engineering" covers an incredibly wide range of things: there's engineering in building and construction, engineering to do with anything that flies, swims or moves on the roads, engineering in the electronics and communications sector, engineering in the utilities — you name the area, there'll be an engineer in there somewhere. If you study engineering, you will use maths for most of your courses. Whether you are doing civil, mechanical, electrical or materials engineering, you will need to use geometry, calculus and algebra to work with mathematical formulae for physical forces, electrical currents and other phenomena. For example, when studying civil engineering you will have to calculate the force distribution for different structures, such as truss bridges. This will involve a combination of trigonometry and solving the equations of forces on the bridge. On other occasions you will need to use integration to calculate the centre of mass of an object, or to use differential equations to understand the flow of water through pipes.

In modern finance maths is of paramount importance. The financial world relies heavily on accurate forecasts of the future and these are based on rigorous mathematical models. Finding the optimal way for a company or individual to organise assets requires a keen analytical mind and very good problem solving skills — something that maths graduates have in abundance.

Life is a risky business. Insurance companies and the actuarial profession make a living by protecting individuals and companies from the consequences of these risks. As an actuary you can apply your expertise to all kinds of areas, whether it's investment banking or looking after those at the lower end of the social scale.

Computers are the ultimate maths machines. In the 17th century the mathematician Gottfried von Leibniz realised that you can calculate anything you want only using 0s and 1s, and he presented the first ever calculating machine to the Royal Society in London. Today, a world without computers is hard to imagine. You don't need much maths to use them, but to design them and develop the software used by anyone from bankers to artists you do. Scientists, engineers, architects and medical professionals all rely on computer simulations in their work. The people who put these simulations together have to be experts not only in computer science, but also in maths. Every second an enormous amount of information is transmitted over email, the internet and other tele-communication devices. It's maths that makes them work efficiently and keeps the information safe.

Medicine, the pharmaceutical industry and the health service rely heavily on maths and stats. It's vitally important that experiments are set up safely and accurately. Once an experiment has been done, the data resulting from it needs to be analysed meticulously. And the government health service needs accurate information to plan its budget and make sure that no patient slips through the net. Medical students have to take courses in statistics, which is not surprising given that much of today's medical knowledge is evidence-based. They need to critically interpret data, such as the results of trials of new medical practice, to judge the reliability of tests and to assess the risks of treatments. Maths is also used in medical research, for modelling tumour growth and the effects of therapy, for planning treatment, and for understanding and interpreting medical scans.

Meteorologists use mathematics to model the factors that affect the weather to make short term predictions. They also study how changes in these will impact on the climate. They use numerical analysis and computer modelling techniques to solve the equations in the models to produce results, from the next day's weather forecasts on TV, to long term predictions involving the greenhouse effect and global climate change. Rather confusingly, this is part of an area of mathematics called fluid mechanics: in this case the "fluid" is the atmosphere. "Partial differential equations" are used to model the flow of fluid and to find patterns governing its behaviour. Statistical analysis also plays an important role in helping to predict climate change. Environmental statisticians are crucial in analysing and interpreting meteorological data, resulting in a better understanding of the consequences of global warming. Meteorologists use mathematics to model the factors that affect the weather to make short term predictions. They also study how changes in these will impact on the climate. They use numerical analysis and computer modelling techniques to solve the equations in the models to produce results, from the next day's weather forecasts on TV, to long term predictions involving the greenhouse effect and global climate change.

Mathematics is even necessary in many of the non-lab sciences, such as psychology and archaeology. Archaeologists use a variety of mathematical and statistical techniques to present the data from archaeological surveys and to distinguish patterns in their results that shed light on past human behaviour. Statistical measures are used during excavation to monitor which pits are most successful and to decide on further excavation. Finds are analysed using statistical and numerical methods to find patterns in the way the archaeological record changes, both over time and geographically, within a site and across the country. Archaeologists also use statistical tests to test the reliability of their interpretations.

To make a car go faster you need to improve its aerodynamics, and this requires mathematics to describe the motion of the air as the car drives through it, and how that motion affects the car's performance. This area of mathematics is also used to understand flight and can even improve sporting performance.

Maths and stats have applications in almost any field you can imagine, but before they can be applied somebody has to develop them — and the somebodies who do this are research mathematicians and statisticians. Most work at universities and divide their time between research and teaching. Some work together with industry or government to come up with solutions to real-life problems, while others explore the lofty heights of pure maths, which may not find applications for another hundred years. As a researcher you work at the cutting edge of your field and have ample opportunity to travel the world and meet the best minds around. You're in daily contact with students and can help along the next generation of mathematicians, something that is very rewarding in itself. Exploring new mathematical territory can be hard work and requires a real passion for the field, but the moment you come up with a new idea or theory all of your own can't be beaten by anything else.

Space science involves a whole range of activities. You can be a researcher exploring the nature of planets and stars and the shape of our universe, you can build space ships, satellites or space probes and - most glamorous of all - you can be an astronaut and venture into space yourself. All of these require a background in physics or engineering, which ultimately boil down to maths. Maths provides a perfect entry-point into the field.