Methodological conceptualization of mathematical modelling

The experience of the author and colleges, as mathematicians working in interdisciplinary groups, have shown the necessity to make the process of mathematical modelling more precise and to establish its different phases. In this way, the specific role of the mathematician in working teams can be better understood by the other members of the team and his or her specific capabilities can be used more efficiently. The proposed structuration of the mathematical modelling process is resumed in a following diagram, especially when computational schemes are the desired result (see Figure 1).

The discussion tends to delineate a concept of modelling from a standpoint where the difference between mathematics as a language and mathematics as a science, having its own dynamic and semantics, plays a fundamental role.