Module 1: Nonlinear Physics and dynamical systems (C. Nore, 3 ECTS) Nonlinear systems are ubiquitous in real world. In this case the superposition principle is no more valid meaning that the response of the system is not proportional to the input it receives; the sum of different solutions is not a solution anymore. After a brief introduction, we study systems with increasing complexity starting from one dimensional systems to multiple dimension ones. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations using linearization about a basic state. Multiple solutions can exist that are visited through bifurcations when a parameter of the system is varied and can lead to interesting phenomena such as chaos. Module 2: Computational Science (F. Krzakala, 3 ECTS) This lecture introduces the students to the use of computing tools, with applications ranging from statistical physics to complex systems and modern subjects such as machine learning. The course is accompanied by tutorials, and students are given homework to program by themselves. We also attempt to introduce the students to modern applied mathematics and statistics (frequentist and Bayesian) and neural networks, and seek a fined-tune balance between mathematics, physics, algorithms and programming.

.

.

.

.

.

Module 1: Nonlinear Physics and dynamical systems Nonlinear dynamics and chaos, S. Strogatz, Westview Press. Structures dissipatives, chaos et turbulence, P. Manneville, Aléa Saclay. Course Notes for Nonlinear Dynamics, L. Tuckerman, https://www.pmmh.espci.fr/~laurette/explanatory Module 2: Computational Science Statistical Mechanics: Algorithms and Computations, W. Krauth, Oxford University Press. The Elements of Statistical Learning, T. Hastie, ‎R. Tibshirani & ‎J. Friedman, Springer. All of statistics a concise course in statistical inference, L. Wasserman, Springer.

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... .

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.