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 2025
- Offered
- 2025/26
- Learning activities
- Caratterizzante
- Area
- Formazione matematica modellistico-computazionale avanzata
- Academic discipline
- MAT/07
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The course focuses on the study of complex systems composed of interacting living entities (e.g. biological, social or economic agents), using advanced mathematical tools. Starting from the modelling of such systems, the mathematical methods underlying machine learning and artificial intelligence are introduced, with a bridge to concrete applications. The reference theory for the modelling of biological/social systems is the kinetic theory of active particles (KTAP); the model of the kinetic theory of dilute gases and, in particular, the Boltzmann equation will be derived, highlighting similarities and differences to classical physical systems. The aim of the course is to provide a rigorous understanding of mathematical models for living systems by highlighting their non-linear and stochastic dynamics. Applications: Epidemiology; Models for opinion and information diffusion; Crowd dynamics; Machine Learning.
- Reference texts
- Bellomo Nicola, Abdelghani Bellouquid, Livio Gibelli, and Nisrine Outada. ''A quest towards a mathematical theory of living systems''. Cham, Switzerland: Springer International Publishing, 2017.
- Educational objectives
- The course aims to provide advanced mathematical tools for the modelling and analysis of complex systems, with a focus on kinetic theory and integral-differential equations; analytical techniques for the study of non-linear dynamical systems.
- Prerequisites
- Knowledge of differential and integral calculus in several variables; hints at partial derivative equations (classification and basic examples); distributions (Poisson and Gaussian); elementary stochastic processes; notions of classical mechanics.
- Teaching methods
- Classroom lectures on all course topics and related exercises. Students will find the detailed lecture programme and additional material on unistudium.
- Other information
- Class attendance: optional but recommended.
- Learning verification modality
- Oral examination with discussion of a project on a kinetic model. For information on support services for students with disabilities and/or DSA visit http://www.unipg.it/disabilita-e-dsa
- Extended program
- Study of complex systems composed of interacting living entities (e.g. biological, social or economic agents); Kinetic theory of active particles (KTAP); Derivation of the dilute gas kinetic theory model (Boltzmann equation). Applications: Epidemiology; Models for opinions and information dissemination; Crowd dynamics; Machine Learning.
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- quality education.