Unit MATHEMATICAL MODELS FOR APPLICATIONS
- Course
- Mathematics
- Study-unit Code
- 55A00070
- Curriculum
- Generale
- Teacher
- Diletta Burini
- Teachers
-
- Diletta Burini
- Hours
- 42 ore - Diletta Burini
- CFU
- 6
- Course Regulation
- Coorte 2026
- Offered
- 2026/27
- Learning activities
- Caratterizzante
- Area
- Formazione matematica modellistico-computazionale avanzata
- Sector
- MATH-04/A
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The course introduces methodologies and tools for the mathematical modelling of living systems and collective phenomena. After an overview of the main levels of mathematical description, particular emphasis will be placed on kinetic approaches for systems characterized by interactions among individuals and by adaptive and emergent behaviours. Applications and case studies will be used to illustrate the strengths and limitations of different modelling frameworks.
- Reference texts
- N. Bellomo, A. Bellouquid, L. Gibelli, N. Outada. A quest towards a mathematical theory of living systems. Cham, Switzerland: Springer International Publishing, 2017.
- Educational objectives
- The course aims to provide students with advanced tools for the mathematical modelling of living systems and collective phenomena. At the end of the course, students will be able to compare different mathematical descriptions of the same phenomenon, understand the role of individual interactions in generating emergent behaviours, and critically interpret models developed in different application domains. Particular attention will be devoted to kinetic approaches for the description of systems composed of many interacting entities. The course also aims to develop the ability to read, understand and discuss research articles in the field of mathematical modelling.
- Prerequisites
- Students are expected to have a basic knowledge of mathematical analysis, linear algebra and differential equations, together with familiarity with the main tools of mathematical modelling. Useful prerequisites include notions of ordinary and partial differential equations, probability and dynamical processes.
- Teaching methods
- The course combines classroom lectures with theoretical and practical activities. Lectures are devoted to the presentation of the main concepts and methods of mathematical modelling, while the theoretical and practical activities involve the analysis and discussion of research articles, case studies and models developed in different application domains. Particular attention is devoted to the critical reading of the scientific literature and to the presentation and discussion of results by the students. All teaching material used during the course, including lecture notes, is made available to students through the Unistudium platform.
- Other information
- Class attendance is not mandatory, but it is strongly recommended. Given the presence of discussion and in-depth activities based on the scientific literature, active participation in class is particularly encouraged. All teaching materials used during the course are available on the Unistudium platform.
- Learning verification modality
- Learning assessment consists of an oral examination including the discussion of a scientific article covered during the course.
The examination is aimed at assessing the student's knowledge and understanding of the topics covered, the ability to interpret mathematical models developed in different application domains, and the ability to present concepts, methods and applications in a rigorous and appropriate manner. Assessment takes into account the command of the mathematical tools, the ability to establish connections among the different topics of the course, and the clarity of the presentation during the discussion.
For information on support services for students with disabilities and/or specific learning disorders (DSA), please visit http://www.unipg.it/disabilita-e-dsa. - Extended program
- Introduction to the mathematical modelling of real-world phenomena. The role of mathematical models in applied sciences and living systems. Descriptive scales and multiscale approaches: microscopic, macroscopic and kinetic models.
Review of the main mathematical tools used in modelling. Ordinary and partial differential equations as tools for the description of dynamical phenomena. Dimensionless analysis and interpretation of model parameters.
Mathematical models for collective phenomena. Examples and case studies from population dynamics, ecology, epidemiology and traffic flow. Comparison of different descriptive levels for the same phenomenon.
Introduction to kinetic theory and the Boltzmann equation. Probabilistic interpretation of kinetic models and their generalizations. Kinetic approaches to the description of systems composed of many interacting entities.
Mathematical modelling of living systems. Interactions, collective learning and emergent phenomena. Construction and analysis of mathematical models for biological and social systems.
Discussion of research articles and case studies concerning the modelling of living systems and collective phenomena, with particular attention to model interpretation and to the comparison of different modelling approaches. - Obiettivi Agenda 2030 per lo sviluppo sostenibile
- Goal 4 - Quality Education
The course contributes to the achievement of Sustainable Development Goal 4 by providing advanced skills in the mathematical modelling of living systems and collective phenomena. The development of quantitative tools for the analysis of complex problems fosters critical thinking, the ability to interpret data and models, and the acquisition of skills that are valuable for scientific research and lifelong learning.