Personal profile

Research overview

algorithm design; algorithm implementation; computational group; computing; coset enumeration; finite simple group; group presentation; group theory; permutation; semigroup; monoid; history of mathematics

Research interests

My early research interests were in infinite group theory, particularly in the study of groups of infinite matrices. I then worked on applications of computing to group theory and more recently I have made major contributions to semigroup theory. I have used existing implementations of group theory algorithms to study groups. In particular, I have studied presentations of groups either starting from a given group and finding a presentation with certain properties or starting with a particular presentation and attempting to determine the structure of the group. I have written various computer programs to solve specific group theoretic problems, with earlier work based on FORTRAN but recent work using the GAP system (Groups, Algorithms, Programming). For example, I have been involved in the design and implementation of algorithms for finding presentations of subgroups of finitely presented groups. I have written a Reidemeister-Schreier program and I have collaborated with colleagues at the AustralianNational University (ANU) in the development of a Tietze transformation program. I have also discovered and implemented an algorithm for determining presentation of subgroups which is more general than the Reidemeister-Schreier and the modified Todd-boxeter coset enumeration algorithm. Versions of these algorithms are now implemented within GAP. My most recent work includes the design and implemetation of algorithms to enumerate semigroups and theoretical work on fiinitely presented monoids and on automatic monoids.


See the the algebra group website for more infomation.

Other expertise

With John O'Connor, I am one of the two developers of the award winning Mathematical MacTutor software.


I am one of the maintainers of the MacTutor History of the MacTutor History of Mathematics Archive on the World Wide Web. I have written most of the biographies and articles on the history of mathematics on that site. This has won many awards for its breadth of cover and innovation.

Industrial relevance

mathematical consultancy;building computer packages; designing web sites

Academic/Professional Qualification

Ph.D., University of Warwick; M.Sc., University of Warwick; B.Sc., University of St Andrews; Edinburgh Mathematical Society; London Mathematical Society; European Mathematical Society; Royal Society of Edinburgh; Institute for Learning and Teaching (ILT)

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