20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410445 -
AL410 - COMMUTATIVE ALGEBRA
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
CP410 - Theory of Probability
(objectives)
Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410417 -
IN410-Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.
|
9
|
MAT/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
6
|
MAT/01
|
32
|
16
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
3
|
MAT/01
|
16
|
8
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410438 -
MF410 - Computational Finance
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410436 -
FS420 - QUANTUM MECHANICS
(objectives)
Provide a basic knowledge of quantum mechanics, discussing the main experimental evidence and the resulting theoretical interpretations that led to the crisis of classical physics, and illustrating its basic principles: notion of probability, wave-particle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
(objectives)
Acquire a basic knowledge of the concepts and methods related to the theory of public key cryptography using the group of points of an elliptic curve on a finite field. Apply the theory of elliptic curves to classical problems of computational number theory such as factorization and primality testing.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410462 -
GE510 - ALGEBRAIC GEOMETRY 2
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410524 -
GE520 - ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20410623 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410621 -
MC410 - DIDACTICS OF MATHEMATICS
(objectives)
The course aims to deepen and to put in perspective, also from the historical-cultural point of view, theories and techniques of didactics of mathematics, communication, docimology and planning of teaching units.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410613 -
LM430-Logic and mathematical foundations
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410637 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of advanced techniques necessary for the study of partial differential equations
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410746 -
AL440 – GROUP THEORY
|
Also available in another semester or year
|
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410758 -
AM410 - MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410759 -
AM410 - MODULO B - - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410766 -
TN520 - Heights and diophantine equations
|
Also available in another semester or year
|
20410768 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410595 -
AM550 - PROBLEMS OF SMALL DIVISORS IN INFINITE DIMENSIONS
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410876 -
AM400 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410877 -
IN500 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
6
|
INF/01
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
(objectives)
Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
Also available in another semester or year
|
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410878 -
FM440 - Mathematical Physics
(objectives)
To acquire a solid knowledge of some advanced problems in mathematical physics
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410875 -
FM530 - Mathematical Methods for Machine Learning
|
Also available in another semester or year
|
20410882 -
AC310 - Complex analysis
(objectives)
To acquire a broad knowledge of holomorphic and meromorphic functions of one complex variable and of their main properties. To acquire good dexterity in complex integration and in the calculation of real definite integrals.
|
4
|
MAT/03
|
22
|
10
|
-
|
-
|
Attività formative affini ed integrative
|
5
|
MAT/05
|
26
|
14
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410952 -
AM560 - Geometric analysis
|
Also available in another semester or year
|