Computer Science and Systems Engineering

Convex Optimization

The course covers the basics of convex optimization methods, with an emphasis on numerical algorithms that can solve a large variety of optimization problems arising in control engineering, machine learning, mechanical engineering, statistics, economics, and finance.

Computational Contact and Fracture Mechanics

This course provides an overview on the theories of contact and fracture mechanics relevant for a wide range of disciplines ranging from materials science to engineering. Introducing their theoretical foundations, the physical aspects of the resulting nonlinearities induced by such phenomena are emphasized. Numerical methods (FEM, BEM) for their approximate solution are also presented together with a series of applications to real case studies.

Banking and Finance (long seminar without exam)

One of the most challenging task in finance is the gap between theoretical models and the actual software implementation. Cross some different areas (derivatives evaluation, risk management, accounting issues) several problems arise: discretization, analytical approximation, montecarlo simulation vs. numerical probability, optmization and so on. After a short overview of the main financial areas, the course aims to give some insights on these topics, with a special focus on the risk management current hard problems and the related software algorithms.

Applied Econometrics I

This course covers some of the most important methodological issues arising in any field of applied economics when the main scope of the analysis is to estimate causal effects. A variety of methods will be illustrated using theory and papers drawn from the recent applied literature. The aim is to bridge the step from a technical econometrics course to doing applied research. The emphasis will be on the applications. The goal is to provide students with enough knowledge to understand when these techniques are useful and how to implement each method in their empirical research.

Applications of Stochastic Processes

This course offers an introduction to stochastic processes as a practical modelling tool for the quantitative analysis of systems. It covers the fundamentals of Markov chains, and presents algorithms and state-of-the-art software applications and libraries for their numerical solution and simulation. The class of Markov Population Processes is presented, with its most notable applications to as diverse disciplines as chemistry, ecology, systems biology, health care, computer networking, and electrical engineering.

Analytics and Data Science in Economics and Management I

A) Python Course for Data Science (A. Chessa):
1) Introduction to the language: basic statements (if, else, type casting), cycles and functions, examples and exercices;
2) Diving into the language: advanced types: sets and dictionaries, classes and modules, using PIP and ipython, examples and exercises;
3) Scraping the web: introduction to BeautifulSoup, the regular expressions module re, the request module, examples and exercises;
4) Introduction to Plotting: basic numpy, plotting overview, examples and exercises;

Advanced Topics of Control Systems

In this course we will venture to go through some of the most advanced control schemes whose development has been motivated by problems in process control and economics. The course's main objective will be to bring students in touch with the state of the art in MPC theory and explore various research opportunities that emerge. We will see how the mature concept of model predictive control (MPC) can be combined with process economics to yield a unifying framework -- known as economic model predictive control (EMPC) -- for simultaneous control and process optimization.

Advanced Topics of Computer Science

This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on System Modelling and Analisys (SysMA).

Advanced Topics of Computational Mechanics

The course is organized as a set of seminars and lectures delivered by IMT Professors and by invited recognized international experts. It covers advanced topics of computational mechanics.

Advanced Numerical Analysis

1. General considerations on matrices

Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)

2.a Direct methods for general linear systems

Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability

2.b Direct methods for sparse linear systems

Factorizations of banded matrices