28417 - ISTITUZIONI DI FISICA MATEMATICA 1

Academic Year 2024/2025

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Mathematics (cod. 8010)

    Also valid for First cycle degree programme (L) in Mathematics (cod. 6061)

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