Mathematics Education for Software Engineers: It Should Be Radically Different!

Software engineering is a young engineering discipline that is different in many aspects from the classical engineering fields. For me the most distinguishing point is the kind of mathematics that serves the respective fields well. By giving examples I will try to show that classical, calculus based mathematics is of no help for defining central notions in software engineering, like ”abstract data type”. Thus, mathematics education for software engineering students should be radically different from the traditional curricula for science and engineering students. In particular, the changes to be made go far beyond putting more emphasis on discrete mathematics as done in many math curricula for computer science students. I will report on our introductory mathematics course that that we have now taught at the Polytechnic University of Upper Austria for several years. The whole first year is dedicated to teach ”The Language and Methods of Mathematics”. I will also report on experiments with using the THEOREMA language and system in the lab exercises for this course, both about highlights and problems. THEOREMA is being developed by Bruno Buchberger and his team at Risc-Linz and aims at combining general predicate logic proof methods and special proof methods in one coherent system. An important observation is that students are in no way prepared for this kind of mathematics after high school. Since computers and information technologies continue to gain more and more importance in our lives, the ability to developed software with mathematical rigour will be a crucial asset for the competitiveness of the software industry of any country in the future. This implies that changes in the high school mathematics curricula towards usability for software engineering should also be considered.