Taking a postgraduate degree opens up a range of rewarding and challenging careers

Although the completion of a first degree in maths already opens up numerous intellectually stimulating and financially rewarding avenues in the world of work, there are plenty of good reasons for talented mathematicians to stay on and study their subject further.

And society needs this intellect to be directed at real challenges. For example, work now going on in maths departments at British universities includes research on the differences in twins' heartbeats inside the mother's womb, the efficiency of microwave ovens, and the safety-related problems created by ice forming in an aircraft's wing.

Broadly speaking, there are five channels available for postgraduate study: statistics, operational research, applied maths, pure maths and financial maths.

There is a constant supply of employment openings, in government and industrial spheres, where a solid command of complex statistical methods is required. Operational research entails the harnessing of mathematical models to solve organisational problems in management or financial areas, or in areas where random human behaviour is involved.

Applied maths is the close cousin of physics, and entails work in real industrial and scientific environments. More esoteric is the pure maths field. But, although such subjects as analysis, topology and advanced algebra may appear remote, their study at the highest level is crucial to the solution of real-life problems. Finally, there are numerous courses these days on financial maths, which study the movement of shares and the intricate behaviour of the financial markets.

Postgraduate courses initially divide into two types: taught courses leading to a Masters, and research-based, usually longer, PhDs. Although this is not a hard and fast rule, it is generally the case that entry onto a PhD course will require the student to demonstrate Masters-level proficiency first, although this may be in the form of an M Math first degree, taking four years instead of three.

All universities with maths departments offer postgraduate opportunities, and all have abundant, and usually clear, information on specific courses or research possibilities on their websites. Bath University, for example, which has 60 students on postgraduate courses, lists the research specialities of members of staff, which provide pointers to potential PhD topics for prospective postgraduates.

Professor Chris Budd, who runs the MSc in modern applications of mathematics, says postgraduate study offers specific and general benefits.

"There are a large number of jobs in industry which require PhD-level expertise. And, more generally, the challenge of doing a PhD is a very good one. You have to work on your own and as part of a team."

Alongside Oxbridge, Warwick's maths department is among the largest in the UK. There are 100 postgraduates active in varying fields at any one time. By far the biggest group are doing an MSc in financial mathematics, one of the most sought-after postgrad courses in the country.

This MSc has elements of maths, physics, economics, business and statistics, and aims to prepare students to go into intellectually demanding and highly remunerative jobs in leading financial companies. Study areas range from Brownian motion to theories of how stock markets work.

It's very intensive and expensive, with fees of about £12,000, but the head of the course, Sebastian van Strien, says successful students find it easy to get jobs that will, very quickly, help them get their money back. To get on the course, you need a minimum of 2.1 degree in a subject containing a lot of maths, but, in addition, you'll have to pass a tough test set by Warwick to weed out those who just won't be able to cope with the complexity or the pace of the course.

Funding for most maths postgraduate research work comes from the Engineering and Physical Sciences Research Council, but the first stage is to approach a university, which will then channel you in the direction of available grants.

One way of supplementing income while on a Masters or PhD is to do paid teaching of undergraduates. The danger here is that the time devoted hinders your own work. Individual universities will have their own approaches to how much of this teaching is appropriate for each postgraduate student.

The rule of thumb is that you must not take your eye off the main reason why you have stayed on past your first degree, namely to advance your own understanding of, and prowess at, the subject significantly. It's on this yardstick that your success will be measured, by your supervisors and by yourself!

'At first some of it sounded very abstract, but then you see how it fits into the real financial world'

Joel Fine

Joel Fine, 26, is just finishing a PhD in pure maths at Imperial College, London. His area of study was differential geometry, more specifically using calculus to find ways of measuring distances on abstract four-dimensional objects. He was funded for three years by the Engineering and Physical Sciences Research Council at about £10,000 a year; he supplemented his income by teaching undergraduates and some on Masters courses at Imperial, receiving about £13 an hour with an additional £11 an hour for marking.

Although he got a First at Oxford in his original degree, he was initially shocked at how hard the PhD was. "My knowledge seemed to stop at about 1920 and I was supposed to be working at around the level maths was in 2000."

However, he has really enjoyed the experience and is now looking for post-doctorate research posts in his specialist area at either Oxbridge or Imperial.

Jason Cook

Jason Cook, 29, is studying a one-year MSc in financial maths at Warwick University. He came to the course after working in the City for four years, wanting to know more about the theory of how the financial markets behave. His first degree was in physics at Bath. He found the course very intellectually challenging. "It requires a lot of dedication and you have to put in the hours. In the first term, I didn't understand everything and some of it sounds very abstract. But as you meet things for the second or third time, it starts to make sense and you can see where it fits in to the real financial world."

He accepts that for some recent graduates, the fees (£12,000) seem steep, but points out that earning power after successful completion of the course should be substantially raised.

Andrew Hill

Andrew Hill, 25, has been part of the maths community at Bath University since 1997. After completing his four-year M Math first degree, he did a one-year Masters in modern applications in mathematics, a course concentrating on the uses of higher mathematics in industry. He is now in the middle of a four-year PhD with joint sponsorship from an industrial partner and the Engineering and Physical Sciences Research Council. His area of study concerns the inner workings of microwave ovens, in particular developing mathematical models to try to understand more fully the interaction between the magnetic field and the food that's being cooked. "It's very interesting, particularly because I spend a lot of time away from Bath working with the people in industry."