Objectives

(See the official version in catalan)

Mathematics is frequently motivated and driven by the need to solve real-world problems—often more so than might initially appear. This entails a process of "modeling" that encompasses aspects such as analyzing the problem, adopting simplifying assumptions, comparing model results with empirical data, and progressively refining the model. Indeed, various branches of science and technology are largely the product of this mathematical modeling process, which can sometimes be far from trivial. However, we may occasionally encounter a specific problem that requires the development of a tailored mathematical model—a task that might not be overly difficult to undertake. The general aim of this course is to familiarize students with this type of work.

In principle, the more mathematical knowledge one possesses, the easier it is to find a tool suited to the problem at hand. Yet, there is a common tendency to apply familiar tools unthinkingly, rather than properly analyzing the problem and developing more appropriate tools. Given this, it is entirely appropriate for this course to appear relatively early in the mathematics curriculum—before other subjects that expand the available mathematical toolkit. In any case, it is quite likely that ideas will emerge at various points which actually lead into well-established areas of mathematics.

The course is essentially practical in nature—hence the name "workshop." Its main component is a project to be carried out by students working in teams. As explained below, this task is supervised by a professor, though generally, they do not intervene directly in the project's development. At the same time—and here the course instructors will be more directly involved—other examples will be developed to illustrate various types of mathematical models as well as the general concepts of mathematical modeling.

Given the above, it is evident that this is an essentially interdisciplinary course. This fact, combined with the relatively basic prerequisites, makes it suitable not only for mathematics students but also for students from other degree programs.

In short, the Mathematical Modeling Workshop is a highly practical, interdisciplinary course that bridges the gap between mathematics and the real world, aiming to traverse that bridge in both directions.