- Docente: Pierluigi Contucci
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Mathematics (cod. 8010)
Also valid for First cycle degree programme (L) in Mathematics (cod. 6061)
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from Feb 17, 2025 to May 27, 2025
Learning outcomes
At the end of the course, the student was introduced to some essential topics in complexity theory, including thermodynamics and phase transition theory, information theory and statistical inference, the study of discrete dynamics through Markov chains, and finally, modern machine learning theory in both low and high dimensions. They are able to apply the knowledge acquired to complexity problems in both the hard sciences and the social sciences.
Course contents
Thermodynamic Systems
The First Law of Thermodynamics
The Second Law of Thermodynamics
The Lieb-Yngvason Axiomatic Approach
Entropy
Thermodynamic Potentials
Entropy and Information
Boltzmann Inference and Measurements
Error-Correcting Codes
Machine Learning Techniques
Readings/Bibliography
Lecture notes.
Thermodynamics, Enrico Fermi
The mathematical theory of communications, C.E. Shannon, W. Weaver.
Teaching methods
Frontal lectures that include theory, excercises and computer simulations.
Assessment methods
Oral exam
Teaching tools
Some of the lectures will be complemented with computer simulations
Office hours
See the website of Pierluigi Contucci