First Cycle (Undergraduate)
00686 · 8 CFU
Analytical Mechanics (A–L)
First cycle degree in Physics · Bologna campus · A.Y. 2026/27
From a recap of Newtonian mechanics to the Lagrangian and Hamiltonian formulations: the course covers the rigorous mathematical framework of classical physics, including phase space analysis, central fields and Kepler's problem, variational principles, Lagrangian mechanics with constraints, Noether's theorem, Poisson parentheses, canonical transformations, small oscillations, and the rigid body.
Second Cycle (Graduate)
C8544 · 6 CFU
Dynamical Systems and Ergodic Theory
Second cycle degree in Physics · Bologna campus · Sep–Dec 2026
An introduction to the mathematical theory of dynamical systems and the basic elements of ergodic theory, from both a theoretical and applied perspective: an introduction to chaotic dynamical systems, topological dynamics, ergodic theory, Kolmogorov-Sinai entropy, etc., with applications to physics and other sciences.
99512 · Module 1
Statistical Physics for Climate Science
Second cycle degree in Science of Climate · Bologna campus · Sep–Nov 2026
A two-module course covering the mathematical foundations of probability — probability spaces, random variables, limit theorems including the Central Limit Theorem, and Bayes' theorem — followed by an introduction to classical statistical mechanics: thermodynamics, kinetic theory of gases, microcanonical and canonical ensembles, and applications to paradigmatic models relevant to climate science.
Collegio Superiore (School of Excellence)
D0854 · 4 CFU
Proving Theorems with Computers: Lean, AI and the Future of Mathematics
Ordinary Programs of the Collegio Superiore · Bologna campus · Jan-Mar 2027
A three-module course on the rigorous computer verification of proofs and programs, centered on the interactive theorem prover Lean, and on how such tools can be combined with machine learning. The first module introduces the logical and computational foundations of formal verification and the limits of what algorithms can compute or prove; the second is a hands-on introduction to Lean and its ecosystem, including the mathlib library; the third places these ideas in the context of large language models, covering how they can support formal reasoning and the generation of verified Lean code.
Recently Taught · A.Y. 2025/26
Second Cycle (Graduate)
77802 · 6 CFU
Complex Systems
Second cycle degree in Science of Climate · Bologna campus · Sep–Dec 2025
An introduction to dynamical systems theory with a strong emphasis on deterministic chaos and predictability: stability analysis via linearization and Lyapunov functions, ergodic theory, hyperbolicity, attractors, bifurcations, and the statistical description of deterministic systems. A companion module addresses data assimilation and emergent self-organization in complex physical, biological, and social systems.
Collegio Superiore (School of Excellence)
C7690 · 1 CFU
Conterintuitive Results in Probability and Related Sciences
Ordinary Programs of the Collegio Superiore · Bologna campus · Mar 2026
A seminar exploring celebrated paradoxes and counterintuitive phenomena in probability, statistics, and related sciences. Starting from a rigorous introduction to the foundations of probability theory, the course examines striking examples that confound common sense — discussing their cognitive and social dimensions, and stressing the importance of a precise logical-mathematical framing of any problem.
Most Frequently Taught Courses · Bologna (before A.Y. 2022/23)
Graduate (MSc Mathematics)
76304 · 6 CFU
Information Theory and Complexity
Second cycle degree in Mathematics (cod. 8208 / 5827) · Bologna campus · Taught 6 times: 2015/16, 2017/18–2021/22
Foundations of information theory: entropy of partitions and random variables, joint and conditional entropies, relative entropy, mutual information, and the Shannon-McMillan-Breiman theorem for i.i.d. and stationary processes. Applications to data compression: Kraft inequality, optimal codes, Huffman and Shannon-Elias-Fano codes, universal codes, algorithms LZ78 and LZW. Introduction to Kolmogorov algorithmic complexity: Turing machines, universal computation, the halting problem, and Chaitin's numbers.
Undergraduate (BSc Mathematics)
28360 · 7 CFU
Mathematical Physics 1
First cycle degree in Mathematics (cod. 8010) · Bologna campus · Taught 5 times: 2010/11–2014/15
An introduction to the physical and mathematical foundations of classical mechanics for mathematics students. Using elementary physical phenomena as motivation, the course develops core analytical tools — limits, derivatives, integrals, and vector calculus — in a scientific context. Topics include one-dimensional kinematics, harmonic motion, Newtonian dynamics, and an introduction to the scientific method, with the dual goal of familiarizing students with classical physics and illuminating the original motivations behind fundamental mathematical definitions.
Architecture · Single-Cycle Degree (Cesena campus)
00674 · 8 CFU · Module 1
Mathematics — Module 1: Calculus I
Single-cycle degree in Architecture (cod. 0881) · Cesena campus · Taught 5 times: 2016/17–2020/21
First module of a two-semester integrated mathematics course for architecture students. Covers single-variable calculus: functions of a real variable, limits and continuity, differential calculus and its applications (relative and absolute extrema, graph sketching), and integral calculus. The second module (Linear Algebra and Geometry, taught by a colleague) covered first-order ODEs, linear algebra, and three-dimensional analytic geometry.
70463 · 4 CFU
Fundamentals of Mathematics II
Single-cycle degree in Architecture (cod. 0881) · Cesena campus · Taught 5 times: 2016/17–2020/21
A follow-up mathematics course for architecture students, extending calculus to several variables. Topics include differential calculus for vector-valued functions and arc length; differential and integral calculus for scalar functions of several real variables; free and constrained optimization; and elementary second-order linear ODEs, with applications to areas, volumes, and moments.
Chemistry (Bologna campus)
15578 / 16954 · Module 2
Mathematics II / Mathematics 2
First cycle degree in Chemistry · Bologna campus · Taught 4 times: 2006/07–2009/10
Second module of the integrated two-semester course "Mathematics (I.C.)" for Chemistry students. The course covered standard Calculus 2 topics: linear algebra (vectors, linear independence, matrices, determinants, and linear transformations) and multivariable calculus (functions of several real variables, limits and continuity, partial derivatives, optimization of functions of several variables, and multiple integrals).