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Personal profile

Research overview

My background is in formal pure mathematics, with a great deal of computer experience. My research covers the application of computers to problems, in abstract algebra, I work on developing general algorithms such as vector numeration, on applying known algorithms and mathematical ingenuity to solve specific large problems such as finding the maximal subgroups of very large sporadic groups, and on the development of the GAP (groups, algorithms and programming) system.

For a mathematician, I am very practically minded. I have little interest in developing algorithms in the abstract without attempting to implement them and I write programs to produce the best possible performance rather than simply to demonstrate the algorithms

I am Director of the Centre for Interdisciplinary Research in Computational Algebra (CIRCA) at the University of St Andrews. The Centre undertakes mathematical research with computer assistance, develops new techniques for computation in abstract algebra and develops and distributes software implementing these techniques. The Centre also organises conferences, seminars and training courses and coordinates the international efforts to develop maintain and promote the GAP (groups, algorithms and programming) software package.

Other expertise

I have a good general knowledge of computer science and practicalities of personal computers (PC) and workstations, especially Linux. I have a good layman's knowledge of physics, chemistry and astronomy.

Future research

A serious look at some aspects of GAP from the point of view of an expert in programming languages and type systems

Experimental integration of GAP with persistent object stores and hyper-programming techniques

Industrial relevance

GAP has been used in electronic textbooks. There might be a demand for a commercial computational algebra toolkit. There might be consultancy or support business opportunities in this area

Academic/Professional Qualification

Ph.D., University of Cambridge; M.A., University of Cambridge; , Certificate of Advanced Studies, Mathematics, University of Cambridge; B.A., University of Cambridge; American Mathematical Society; Edinburgh Mathematical Society; London Mathematical Society


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