Mathematical Sciences for Artificial Intelligence

General targets: To acquire basic knowledge in probability theory and in classical statistical mechanics. Knowledge and understanding: Students who have passed the exam will be able to construct mathematical models of systems with many degrees of freedom in the limit of non-interacting systems and in some instances of interacting systems with applications to selected problems. Applying knowledge and understanding: Students who have passed the exam will be able to: i) conduct a quantitative analysis of non-interacting systems with many degrees of freedom using different alternative methodologies [microcanonical, canonical and grancanonical ensembles]; ii) handle the equivalence of the different alternative methodologies; iii) identify the elements of a statistical mechanics approach for the description of interacting systems typically encountered in Physics but also Inference and Machine Learning. Critical skills: Students who have passed the exam will have developed the ability to think in probabilistic and statistical terms using the concepts of statistical mechanics as toolbox for “problem solving” in applications to problems of physical systems and more broadly in a number of disparate fields (inference, machine learning, AI in general, social-economic systems, biological systems, medical problems). Communication skills: Students who have passed the exam will have gained the ability to communicate concepts, ideas and methodologies of classical statistical mechanics and its application to systems with many degrees of freedom. Learning skills: The acquired knowledge will allow students who have passed the exam to face the study, at an individual level or in a master's degree course, of specialized aspects of classical statistical mechanics and, more generally, of the theory of complex systems.