Modelling the Real World: A Didactic Proposal for an Interdisciplinary Mathematical Modelling Course

Abstract

This paper presents a comprehensive didactical proposition for an interdisciplinary mathematical modelling course designed for first-semester undergraduate students. The aim is to provide detailed curriculum design, teaching materials, and implementation guidelines directly adaptable by other universities. The course framework integrates Problem-Based Learning methodology with mathematical modelling across six disciplinary modules: operations research, macroeconomics, microeconomics, sociology, epidemiology, and complexity sciences. This proposition includes a structured 17-week curriculum with specific learning objectives, detailed problem scenarios, and assessment rubrics. Each module contains concrete examples, such as transportation network optimisation, economic growth modelling using the Solow model, social network analysis, SIR disease spread models, and chaos theory applications through the Lorenz attractor. The proposition emphasises developing critical thinking, problem-solving, and interdisciplinary collaboration skills through real-world mathematical applications. The course design implements a student-centered approach where instructors serve as learning facilitators, supporting autonomous project development while fostering analytical and technological capabilities required for contemporary workplace demands. Complete evaluation criteria, implementation guidelines, and transferable pedagogical materials enable adoption across diverse institutional contexts.