Ogni modulo equivale a 3 crediti ECTS. È possibile scegliere un totale di 10 moduli/30 ECTS nelle seguenti categorie:
- 12-15 crediti ECTS in moduli tecnico-scientifici (TSM)
I moduli TSM trasmettono competenze tecniche specifiche del profilo e si integrano ai moduli di approfondimento decentralizzati. - 9-12 crediti ECTS in basi teoriche ampliate (FTP)
I moduli FTP trattano principalmente basi teoriche come la matematica, la fisica, la teoria dell’informazione, la chimica ecc. I moduli ampliano la competenza scientifica dello studente e contribuiscono a creare un importante sinergia tra i concetti astratti e l’applicazione fondamentale per l’innovazione - 6-9 crediti ECTS in moduli di contesto (CM)
I moduli CM trasmettono competenze supplementari in settori quali gestione delle tecnologie, economia aziendale, comunicazione, gestione dei progetti, diritto dei brevetti, diritto contrattuale ecc.
La descrizione del modulo (scarica il pdf) riporta le informazioni linguistiche per ogni modulo, suddivise nelle seguenti categorie:
- Insegnamento
- Documentazione
- Esame
The ubiquitous presence of uncertainty and noise in the engineering sciences and the importance of randomized algorithms in computer and data science make it mandatory to understand and quantify random phenomena. To achieve this goal the course will provide a solid review of probability theory and an introduction to the theory of stochastic processes. Special attention is given to applications, including examples from various fields such as communications and vision, signal processing and control, queuing theory or physics of small systems (Brownian motion).
Requisiti
- Basis calculus (integration, differentiation, ordinary differential equations, complex numbers, Fourier transform)
- Basic probability theory (probability, conditional probability, Bayes' theorem, expectation, variance, random variables)
- Linear algebra (matrix algebra, system of linear equations, eigenvectors, eigenvalues)
Obiettivi di apprendimento
The student is familiar with the main working tools and concepts of stochastic modeling (expectation, variance, covariance, autocorrelation, power spectral density). He/She is able to explain properties and limitations of stochastic processes as a modeling tool for noisy systems. He/She will be able to model and analyze simple random phenomena through adaptation of proposed stochastic models.
Contenuti del modulo
- Probability review: random variables, conditional probabilities, theorem of large numbers, central limit theorem.
- General introduction to discrete and continuous stochastic processes. Applications, e.g., communications, Kalman filtering.
- Discrete, continuous and hidden Markov chains. Applications, e.g., page rank algorithm, queuing systems, pattern recognition, speech recognition.
- Bernoulli, Poisson, Gaussian processes, Brownian motion, white and colored noise.
Metodologie di insegnamento e apprendimento
Ex cathedra teaching
Presentation of simulation results and case studies
Bibliografia
The script is, in principle, sufficient. Further readings are:
- Sheldon M. Ross, Probability Models, Elsevier.
- John A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press.
- Mario Lefebvre, Applied Stochastic Processes, Springer.
- Bassel Solaiman, Processus stochastiques pour l’ingénieur, PPUR.
Scarica il descrittivo completo del modulo
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