It's well known that a degree in maths can open many doors in the job market. Logical thinking, numerical dexterity and problem solving are seen as ideal starter skills for a variety of jobs requiring intellectual acuity.
Law firms, business consultants, accountants and almost every corner of the IT world are among the most obvious employers beating a path to the doors of university maths departments, waiting for a stream of graduates to emerge clutching their first degrees.
But what if you want to stay in academia a little longer, do a few more sums, and stretch your brain a tad further on a maths-related postgraduate course? What are the options? And why might you want to do this, rather than join one of the attractive graduate training programmes already welcoming maths graduates with open arms and open cheque books?
The first, and often overlooked, reason is if you simply like the subject. Here, one option is a basic Masters, which will stretch, deepen and develop the pure and applied maths areas already encountered during your first degree and send you off to explore some new areas as well.
An example of this type of course is the one-year mathematics MSc at Queen Mary, University of London, a well-established course taking around half a dozen students a year. The entry requirement is a good 2.1.
"It is for people who love maths and want to keep doing it," says Dr Leonard Soicher, the course director. There's three hours' teaching a week, participants have their own study rooms, and the small size of the group makes for an intimate studying environment.
Although this type of course generally avoids specialising in vocational areas, the result of the year is often a firm decision to pursue a more directed avenue. This may be a PhD in a narrower field, a teaching post in the further education sector, or acceptance of a job outside the education world, albeit one that will exploit the intellectual powers that have been finely honed during your Masters.
However, many graduates already know that the field in which they want to work requires further study.
"If your chosen end-career requires cutting-edge maths, then you need to stay on and do postgraduate study," explains Peter Cooper, executive secretary of the London Mathematical Society.
The careers requiring more qualifications are what Cooper calls the "rocket-science finance wizardry" in the City; the sharp end of industrial research and testing; many jobs in statistics; and the burgeoning field of cryptography. Most of these career paths can be entered via a one-year taught Masters, whose content will be tailored fairly specifically to the relevant employment sector.
A trawl of areas covered in taught Masters brings up statistics as one of the most commonly offered subjects. Statisticians' posts are predominantly reserved for people with postgraduate qualifications. Most work within public sector organisations, but the corporate world also has uses for trained and qualified number-crunchers. In the pharmaceutical industry, for example, the process of bringing a drug from the trial period to generalised use involves the keeping and manipulation of precise records. Statisticians are needed to produce data that will both stand up to rigorous scrutiny from the scientific world and be attractively presented.
The Royal Statistical Society site ( www.rss.org.uk) will guide you to a list of universities offering taught Masters in statistics. Among those universities is Nottingham, where two new Masters courses started in September: MSc statistics and MSc statistics and applied probability. Either of these can be downsized to a diploma, if the dissertation, filling the final three months, is omitted.
The School of Mathematical Sciences at Nottingham is also home to a large and vibrant research community. There are around 60 postgraduate students engaged in PhDs, working across four broad areas: pure maths, mathematical physics, theoretical mechanics and statistics.
A glance at the website pages of the theoretical mechanics section provides perhaps the best evidence, for the layman, of how mathematics is at the heart of the lives we lead. Solid mechanics deals with composite materials and fracture mechanics; fluid mechanics handles acoustics, convection and plasma dynamics; and mathematical biology, a particular growth area over recent years, uses differential equations and modelling methods to predict the growth and treatment of tumours.
After graduating, many of Nottingham's PhDs move into the commercial world or public sector. "A significant proportion of our PhDs embark on careers in finance and IT," says Martin Lindsay, the school's postgraduate student adviser. "Statistics PhDs are particularly in demand from the pharmaceutical industry, and our number theory PhDs often go into cryptography, for banks or the Government Communications Headquarters." However, many stay inside the academic world, undertaking post-doctoral work either in the UK or abroad.
But it can also be worth looking outside university maths departments. Warwick University Business School, for example, has launched a new MSc in finance, which may appeal to maths graduates who fancy a career in investment banking or corporate finance.
Running the course is Professor Gordon Gemmill, who thinks the 12-month masters will appeal to people "slightly less nerdish" than those attracted to the existing MSc in financial maths.
"This course will be more general, but nevertheless intellectually challenging," he explains. Students will learn about valuing assets, managing funds in portfolios, and international finance.
Gemmill thinks the job market for people with the new qualification is healthy and much stronger than it was a year ago. It'll need to be, given the fees: £15,000 for a 12-month course.
However, if none of the above appeals, your time and expertise could well be profitably and rewardingly spent as a school teacher. Maths remains a shortage subject, and after a one-year PGCE, progression in seniority and financial terms can be very speedy. But it is not the job for everybody. A day spent at your local comprehensive, observing lessons, will help you make your decision.
Liz Jones, principal statistician for the global biopharmaceutical company UCB: 'My MSc brought me more respect with colleagues'
My first degree was via a four-year BSc statistics sandwich course at Bath University. After graduation in 1991 and a year travelling, I started work as a statistician with Smith Kline Beecham. As many of my peers there had further qualifications, I investigated ways of acquiring a postgraduate qualification myself. I found a distance learning Masters course at Sheffield Hallam University. Over two years, I completed 12 coursework modules, one dissertation, and went to Sheffield three times to sit exams. In 1995, I received my MSc in applied statistics.
I don't really know whether the second degree was that useful in teaching me new skills for my job, but I'm still very glad I did it. It probably brought me more initial respect as a junior statistician with colleagues outside the statistics department. It was also useful to have the overlap of study and work - to apply techniques learned at work to my course, and vice versa.
In my 13 years as a statistician, I've worked in different companies within the pharmaceutical sector and smaller biotec firms.