Postgraduate Courses in Mathematics
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A survey of postgraduate courses in mathematics by the 'Guardian' newspaper (17th June 2006) reported 55 UK universities offering postgraduate mathematics degrees. The survey included degrees in other areas for which a mathematician could study, e.g. conversion courses to areas of physics, statistics or computing. In schools of mathematics a few of the exciting MSc courses which caught my eye are mathematical finance (Warwick), astronomy and astrophysics (Queen Mary), atmosphere and ocean modelling (Reading) and mathematical physics (Imperial College). All these institutions also offer pure mathematics MScs: for example for budding logicians, cryptanalysts and number theorists, an MSc in Information Security at Royal Holloway may be attractive. My department at East Anglia is typical in offering both a Pure Maths MSc and a Mathematical Modelling MSc (East Anglia). Both involve lectures and exams with coursework but also spending time on a substantial dissertation, supervised mainly in the summer. One of the outcomes from writing a successful MSc dissertation might be to win funding and carry on the research to a higher level, for another two years towards a PhD. If you are interested in studying a postgraduate course in mathematics then read on to find out more.
Mathematicians are unusually adaptable. The MSc course or PhD topic you study may be in another science department, in computing, in a branch of engineering or in the humanities. Even if you study in a maths department there is still an astonishing range of interdisciplinary courses on offer in British universities. For example, in my own department I have been supervising students this year working on musical bubbles, vortex dynamics, wave impact and volcanoes; the last in collaboration with UEA's School of Environmental Sciences. My other colleagues in applied maths supervise projects which are even more varied: e.g. arterial blood flow, sonic booms, liquid flows influenced by electric fields and the ice coating of aircraft wings. We are typical of strong research-led departments where a mixture of pure and applied mathematics lecture courses and expertise enrich students' choice and contents of higher degrees.
Higher degree courses lead to a Master of Science degree (MSc) usually after 1-2 years or to a Doctor of Philosophy (PhD) usually after 3-4 years. There are also diploma courses (Graduate Diplomas) lasting one year, normally at the level of third year mathematics.
The subject areas for MSc courses in mathematics usually reflect the special research expertise in a department. If you are applying for a PhD, then it's a good idea to visit and talk to individual lecturers about the subjects in which they might supervise you. They may suggest topics which already have funding to support your fees and living expenses. EPSRC (and other research councils) support research-active maths departments with quotas of funds to be used for the most able UK applicants to do PhDs. At PhD level the subject you work on should be primarily motivated by your interests. Apart from a strong honours degree the most important qualifications are curiosity, ambition and hard work. One of the training aspects of a PhD is you learn how to work independently on an investigation to arrive at new discoveries. Your supervisor will meet you for regular one-to-one meetings. He or she can help formulate research questions which are most likely to lead to progress, the supervisor will also help you overcome hurdles such as understanding ideas in others' research papers, but it is still hard work which wins a PhD.
Most institutions also give training in research techniques, such as how to go about nailing down incomplete references or borrowing a rare book from the British Library, or how to talk effectively to children to popularise your abstract research. Most departments also have series of research talks which give visitors and hosts a chance to present their discoveries to an audience of staff and research students. The talks can be in areas quite different from your own PhD. Towards the end of your PhD your supervisor will also help you to prepare your thesis for submission to the examiners. The high point of the project is when the student and examiners meet for the viva exam, where you defend your thesis, hopefully to the satisfaction of the examiners. Another prize from PhD research is telling the world about your discoveries, by writing them down in research papers and submitting them to learned journals. The editors accept or reject on the basis of anonymous referees. Success in the publications process is the prime way of progressing into and maintaining an academic mathematician's career. You will also talk about your PhD findings at conferences. There you also meet other mathematicians from around the world, and listen to presentations in a particular field.
A PhD in Mathematics is a qualification highly prized in education, government and business. From my own school, recent successful PhD students have gone on to postdoctoral research jobs (here and in other universities), teaching, chartered accountancy, insurance, the construction industry and retail management. Other examples of post-PhD careers are designing better sports balls and equipment, training for the Civil Service and working for the Newton Institute for Mathematical Sciences in Cambridge. As a mathematician you can look forward to being qualified for several different careers: beyond the abilities gained through a BSc, a PhD gives you expertise in one specialist area but also advanced skills. For example HOW to formulate research and HOW to find out and understand what others have done on a problem. Then having solved the problem (perhaps in close collaboration with non-mathematicians) you will be able to explain the findings to others, in clear writing (perhaps in non-technical prose) or in a well-prepared talk. Skills in computation, classification and discrimination (is this a well-posed problem?) are skills which mathematicians with PhDs take for granted, but which are highly valued in academia, government circles and successful companies.
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So if you like and are able in mathematics, and you are looking for interesting varied work in the company of bright creative people, then apply for a postgraduate course in mathematics. See websites but also visit departments to talk with lecturers and professors about the details of what they can offer you.
Contributed by:
Dr Mark Cooker,
Senior Lecturer and Admissions Director for the School of Mathematics,
University of East Anglia,
Norwich,
Norfolk
NR4 7TJ
England.
Copyright Dr M.J. Cooker 22.6.06.
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