Mathematics for Formal Methods, a proposal for education reform

It is widely recognized that there is a body of mathematics which is crucial to the underpinning of computer science, software engineering, and information and communications technology. For the most part, at undergraduate level, such mathematics is generally considered to consist of discrete mathematics, including formal logic. At a research level, one expects to find abstract algebra, category theory, topos theory, etc. In this paper we discuss a body of mathematics which is foundational to formal methods per se and used for the modelling of the usual sort of system artefacts: monoids and their morphisms. In particular we show how a single notion of distribution leads to better insights into many of the standard models in use. This discussion leads naturally to salient remarks on both the need for, and suitable direction to be taken in, a proposed education reform with a particular emphasis on mathematics for Information Technology.