Below are the summer schools and workshops sponsored by MathFIT during 1999-00. Text is included to give a flavour of the events.
Algebraic and co-algebraic methods in the mathematics of program construction
"A recent trend in the mathematics of program construction has been towards higher levels of genericity, allowing greater abstraction in programs and more recurring patterns to be captured. In this regard, algebraic constructions and inductive proof techniques have been popular for a long time, but there has been considerable interest recently in the dual co-algebraic constructions and co-inductive proof techniques. Further research is required in several aspects of this work. The mathematical basis of the calculus, especially for infinite structures, still poses many challenges; for the purposes of program specification, a basis in allegory theory, i.e., relation algebra, is preferable to a basis in category theory, but this still needs further investigation; also (and most importantly) the insights and methods suggested by the theory have to be cast into a form of practical use to computer programmers."
Contact: Dr Jeremy Gibbons, Oxford University
Date: 10-14 April 2000
"The radio spectrum is a limited resource. Spectrum is required for both new and expanding radio services. This makes the allocation of spectrum increasingly difficult. Although different radio services differ significantly in their specifications, most services have in common that discrete radio channels are assigned to users. The frequency assignment problem is concerned with assigning channels in as efficient a way as possible, while guaranteeing a specified level of service. Of the alternative mathematical formulations of this problem, the most natural one uses graph theory with vertices representing transmitters and edges joining pairs of transmitters which are constrained. Weights on the edges give the required channel separations. Thus the problem becomes a generalisation of the well-known graph colouring problem and many results from this area have been used in channel assignment (even in very restricted cases the problem is computationally intractable). A great deal of research has been carried out to design algorithms, using meta-heuristics and discrete mathematical programming, to produce good solutions to the problem."
Contact: Dr Steven Noble, Brunel University
Date: 25-27 July 2000
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