Mathematics for Engineers and Engineers' Mathematics

This thesis is composed of two parts. In the first part, the mathematics that engineering students and mathematics students are to be taught and expected to learn is identified by means of an analysis of the content of the courses each group of students has to take, and of the types of tasks each group is given in the final examinations of these courses. The aim is to determine if there are any significant differences between the education of the two groups. In the second part, I demonstrate how professional engineers use mathematics to develop mathematical models that can be applied in solving tasks in their professional practice. Examples of mathematical models from the studies of statics, mechanics of materials, and structural analysis are presented, culminating in a discussion of the use of matrices in matrix structural analysis and the physical representation of eigenvectors and eigenvalues and what they mean to a structural engineer. The comparison, analyses, and demonstrations are performed from an anthropological point of view using the Anthropological Theory of the Didactic (ATD). From this perspective it will be shown that the similarities between the mathematical praxeologies of engineers and mathematicians are limited principally to the tasks and techniques, while the differences are found in the level of the technology and theory.