20410408 
AL310  ELEMENTS OF ADVANCED ALGEBRA

Also available in another semester or year

20410407 
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.

9

MAT/03

48

24





Related or supplementary learning activities

ITA 
20410409 
AM310  ELEMENTS OF ADVANCED ANALYSIS

Also available in another semester or year

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

Also available in another semester or year

20410412 
MC310  Fundaments of Complementary Mathematics

Also available in another semester or year

20410445 
AL410  COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.

9

MAT/02

48

24





Related or supplementary learning activities

ITA 
20410413 
AN410  NUMERICAL ANALYSIS 1

Also available in another semester or year

20410446 
BL410Introduction to Biology

Also available in another semester or year

20410439 
CH410  ELEMENTS OF CHEMISTRY

Also available in another semester or year

20410447 
CP410  Theory of Probability

Also available in another semester or year

20410415 
CR410Public Key Criptography

Also available in another semester or year

20410416 
FM410Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.


204104161 
FM410Complements of Analytical Mechanics  MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.

3

MAT/07

30







Related or supplementary learning activities

ITA 
204104162 
FM410Complements of Analytical Mechanics  Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.

3

MAT/07

30







Related or supplementary learning activities

ITA 
20410448 
FS410  DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.

6

FIS/08

48

12





Related or supplementary learning activities

ITA 
20410449 
GE410  ALGEBRAIC GEOMETRY 1

Also available in another semester or year

20410450 
GL410Elements of Geology I

Also available in another semester or year

20410417 
IN410Computability and Complexity

Also available in another semester or year

20410451 
LM410 THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.


204104511 
LM410 THEOREMS IN LOGIC 1  Module A

Also available in another semester or year

204104512 
LM410 THEOREMS IN LOGIC 1  Module B

Also available in another semester or year

20410418 
MA410  APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.

9

MAT/08

48

24





Related or supplementary learning activities

ITA 
20410452 
ME410  ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics.

6

MAT/04

48

12





Related or supplementary learning activities

ITA 
20410438 
MF410  Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.

9

SECSS/06

60







Related or supplementary learning activities

ITA 
20410419 
MS410Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.

9

MAT/07

48

24





Related or supplementary learning activities

ITA 
20410440 
ST410Introduction to Statistics

Also available in another semester or year

20410453 
TN410  INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.

9

MAT/02

48

24





Related or supplementary learning activities

ITA 
20410420 
AN420  NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.

9

MAT/08

48

24





Related or supplementary learning activities

ITA 
20410441 
CP420Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.

6

MAT/06

48

12





Related or supplementary learning activities

ITA 
20410436 
FS420  QUANTUM MECHANICS

Also available in another semester or year

20410442 
IN420  Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.

9

INF/01

48

24





Related or supplementary learning activities

ITA 
20410454 
GL420Elements of Geology II
(objectives)
The course aims to provide an adequate overview of the scientific contents of Earth Sciences. The course deals with the modern aspects of Earth Sciences, framing geological phenomena in the framework of the most modern theories and illustrating the hazards and risks associated with natural phenomena such as, for example, seismic and volcanic phenomena, also referring to the geology of the Italian territory. The course also aims to provide the basis for understanding the rocks cycle and their rocks genetic processes through laboratory and field experiences. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.

6

GEO/03

48







Related or supplementary learning activities

ITA 
20410455 
LM420  THEOREMS IN LOGIC 2
(objectives)
To support the students into an indepth analysis of the main results of first order classical logic and to study some of their remarkable consequences.

6

MAT/01

36







Related or supplementary learning activities

ITA 
20410456 
MC420Dydactics of Mathematics
(objectives)
1. Critical analysis of the evolution of ideas and methodologies in teaching mathematics, with particular emphasis on the role of the teacher. 2. The mathematics curriculum in compulsory schooling and in the various secondary schools (high schools, technical schools and trade schools), in an international context. 3. Didactic planning and methodologies for teaching mathematics: programming and rhythm, principles and methods for the construction of activities, classroom management. 4. Problem solving. Logic, intuition and history in teaching mathematics.

6

MAT/04

48

12





Related or supplementary learning activities

ITA 
20410469 
AM430  ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS

Also available in another semester or year

20410421 
AN430 Finite Element Method

Also available in another semester or year

20410457 
CP430  STOCHASTIC CALCULUS

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 GaussBonnet and HopfRinow.

6

MAT/03

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 spacetime 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 
20410422 
IN430  ADVANCED COMPUTING TECHNIQUES
(objectives)
Acquire the conceptualskills in structuring problems according to the objectoriented programming paradigm. Acquire the ability to design algorithmic solutions based on the objectoriented paradigm. Acquire the basic concepts related to programming techniques based on the objectoriented paradigm. Introduce the fundamental notions of parallel and concurrent programming.

6

INF/01

48

12





Related or supplementary learning activities

ITA 
20410458 
LM430  LOGICAL THEORIES 2
(objectives)
To acquire the basic notions of ZermeloFraenkel's axiomatic set theory and present some problems related to that theory.

6

MAT/01

36







Related or supplementary learning activities

ITA 
20410459 
MC430  LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
1. Mathematics software, with particular attention to their use for teaching mathematics in school. 2. Analysis of the potential and criticality of the use of technological tools for teaching and learning mathematics.

6

MAT/04

48

12





Related or supplementary learning activities

ITA 
20410435 
FS440  Data Acquisition and Experimental Control

Also available in another semester or year

20410423 
IN440  COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.

9

INF/01

48

24





Related or supplementary learning activities

ITA 
20410460 
AM450  FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.

6

MAT/05

48

12





Related or supplementary learning activities

ITA 
20410465 
GE450  TOPOLOGIA ALGEBRICA

Also available in another semester or year

20410424 
IN450  ALGORITHMS FOR CRYPTOGRAPHY
(objectives)
Acquire the knowledge of the main encryption algorithms. Deepen the mathematical skills necessary for the description of the algorithms. Acquire the cryptanalysis techniques used in the assessment of the security level provided by the encryption systems.

6

INF/01

48

12





Related or supplementary learning activities

ITA 
20410461 
FS460  Dydactics of Physics
(objectives)
The objectives of the course are to enable the students to acquire the necessary skills to practice an affective teaching of Physics in the secondary school, with particular attention to: a) knowledgeÿof literature research on Physic teaching; the Italian educational system and school regulations; b) the design of culturally significant educational paths for Physics teaching; c) the production of materials for the measurement and verification of learning through the exercise of formative evaluation; d) the role of the "laboratory" as a way of working that involves students in an active and participated way, which encourages experimentation and planning.

6

FIS/08

48







Related or supplementary learning activities

ITA 
20410425 
GE460 GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.

6

MAT/03

48

12





Related or supplementary learning activities

ITA 
20410426 
IN480  PARALLEL AND DISTRIBUTED COMPUTING

Also available in another semester or year

20410427 
IN490  PROGRAMMING LANGUAGES

Also available in another semester or year

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 
20410470 
FM510  MATHEMATICAL PHYSICS APPLICATIONS
(objectives)
To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.

9

MAT/07

48

24





Related or supplementary learning activities

ITA 
20410429 
FS510  MONTECARLO METHODS

Also available in another semester or year

20410462 
GE510  ALGEBRAIC GEOMETRY 2
(objectives)
Introduce to the study of algebraic geometry, with particular emphasis on beams, schemes and cohomology.

6

MAT/03

48

12





Related or supplementary learning activities

ITA 
20410463 
TN510  NUMBER THEORY
(objectives)
Provide a good knowledge of concepts and methods of analytical theory of numbers, with particular concern to the theory of prime numbers and prime numbers in arithmetic progression.ÿIntroduce to Riemann's zeta function theory.

6

MAT/02

48

12





Related or supplementary learning activities

ITA 
20410464 
IN530  COMPUTER INFORMATION SYSTEMS
(objectives)
Introduce the basic concepts of security and then show how to acquire autonomy in updating the understanding in the data and networks security domain. Provide the basic concepts for understanding and evaluating a security solution. Provide the basic knowledge to produce security solutions for small/mediumsized system.

6

INF/01

48

12





Related or supplementary learning activities

ITA 
20410431 
IN540  COMPUTATIONAL TOPOLOGY
(objectives)
Introduce the study of computational topology and in particular the concepts, representations and algorithms for topological and geometric structures to support geometric modeling, construction of simulations meshes, and scientific visualization. Acquire techniques for parallel implementation in the representation and processing of largesized graphs and complexes. Application of sparse matrices, for the implementation of algorithms on graphs and complexes with linear algebraic methods.

6

INF/01

48

12





Related or supplementary learning activities

ITA 
20410432 
IN550 – MACHINE LEARNING

Also available in another semester or year

20410434 
FS450  Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.

6

FIS/02

60







Related or supplementary learning activities

ITA 
20410443 
FS520  Complex systems
(objectives)
To understand algorithms related to complex systems, writing, executing and optimising simulation programs of such systems (Montecarlo and molecular dynamics programs) and analysing the data produced by simulations.

6

FIS/03

48

12





Related or supplementary learning activities

ITA 
20410518 
AM420  SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.

6

MAT/05

48

12





Related or supplementary learning activities

ITA 
20410520 
AL420  ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.

6

MAT/02

48

12





Related or supplementary learning activities

ITA 
20410523 
MA430  MATHEMATICAL METHODS FOR APPLIED SCIENCES

Also available in another semester or year

20410522 
CP450  DISCRETE PROBABILITY
(objectives)
Development of probabilistic techniques and advanced methods for the study of stochastic processes on graphs, randomized algorithms and random graphs, random walks and interacting particle systems.

6

MAT/06

48

12





Related or supplementary learning activities

ITA 