Recent developments in mathematics and computer science offer a sound, if unfamiliar, basis for the development of computer-controlled systems. The professional systems engineer should become as competent in these fields as he is (expected to be) in traditional mathematics and physics. The paper emphasises their application in the early phases of product development (requirements analysis and functional specification)-a prerequisite for their successful use in design and implementation. Some important aspects of 'embedded' computer systems, such as concurrency, have not been discussed because space does not allow an adequate introduction to their formal treatment