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I am a pure mathematician, and my research interests lie at the
interface between algebra, logic, and theoretical computer science. My
own chief contribution has been to develop, and exploit, a method for
concretely representing certain algebraic structures, called
distributive lattices, using what are now known as Priestley spaces.
Many different kinds of logic can be modelled by structures built on
distributive lattices, and nowadays logics are extensively used for
reasoning about computer programs and in artificial intelligence,
besides being of interest to philosophers and mathematicians. In the
other direction, new computer languages often spawn interesting
mathematics: Java is proving a good example of this. I get many chances
to travel to international conferences and to collaborate with
colleagues overseas: Priestley spaces have taken me from Hawaii to
Hungary and from Iceland to Australia.
Like most Oxford mathematics tutors I teach across a wide range of
subjects, mostly in pure mathematics. My visits to overseas universities
have given me the chance to find out how mathematics is taught in a
variety of institutions and to bring home fresh ideas to try out here. I
am the author of three undergraduate textbooks
- Introduction to Complex Analysis (Oxford University Press)
- Introduction to Integration (Oxford University Press)
- (with B.A. Davey) Introduction to Lattices and Order (Cambridge
University Press).
The first two of these are recommended reading for 2nd year
mathematics courses in Oxford; the third has formed the basis for a 3rd
year course. Any undergraduate who wishes for an additional challenge
may try reading Introduction to Complex Analysis in its Indonesian
translation. |
