COURSE - Università Roma Tre

Degree Course: Mathematics A.Y. 2019/2020

Expected learning outcomes Syllabus Italian version

Teorico

FIRST YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM TEORICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM TEORICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

SECOND YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM TEORICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM TEORICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

20410376 - UCL - FURTHER LANGUAGE STUDIES (objectives)

Other activities

ITA

20410377 - AIT - COMPUTER AND TELEMATIC SKILLS (objectives)

INF/01

Other activities

ITA

20410497 - TFO- EDUCATIONAL AND ORIENTATION INTERNSHIP (objectives)

Other activities

ITA

20410467 - FINAL EXAM (objectives)

Final examination and foreign language test

ITA

TOTAL

120

Modellistico-applicativo

FIRST YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM MODELLISTICO-APPLICATIVO SCEGLIERE TRE INSEGNAMENTI (24 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: CURRICULUM MODELLISTICO APPLICATIVO SCEGLIERE DUE INSEGNAMENTI (15 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM MODELLISTICO-APPLICATIVO SCEGLIERE TRE INSEGNAMENTI (24 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: CURRICULUM MODELLISTICO APPLICATIVO SCEGLIERE DUE INSEGNAMENTI (15 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	Also available in another semester or year
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 (objectives) To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.	3	MAT/07	30	-	-	-	Core compulsory activities	ITA
20410416-2 - FM410-Complements 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	-	-	-	Core compulsory activities	ITA
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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410441 - CP420-Introduction 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	-	-	Core compulsory activities	ITA
20410421 - AN430- Finite Element Method	Also available in another semester or year
20410457 - CP430 - STOCHASTIC CALCULUS	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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

SECOND YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM MODELLISTICO-APPLICATIVO SCEGLIERE TRE INSEGNAMENTI (24 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: CURRICULUM MODELLISTICO APPLICATIVO SCEGLIERE DUE INSEGNAMENTI (15 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM MODELLISTICO-APPLICATIVO SCEGLIERE TRE INSEGNAMENTI (24 CFU) NEI SEGUENTI SSD MAT/01,02,03,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: CURRICULUM MODELLISTICO APPLICATIVO SCEGLIERE DUE INSEGNAMENTI (15 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	Also available in another semester or year
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 (objectives) To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.	3	MAT/07	30	-	-	-	Core compulsory activities	ITA
20410416-2 - FM410-Complements 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	-	-	-	Core compulsory activities	ITA
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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410441 - CP420-Introduction 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	-	-	Core compulsory activities	ITA
20410421 - AN430- Finite Element Method	Also available in another semester or year
20410457 - CP430 - STOCHASTIC CALCULUS	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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

20410376 - UCL - FURTHER LANGUAGE STUDIES (objectives)

Other activities

ITA

20410377 - AIT - COMPUTER AND TELEMATIC SKILLS (objectives)

INF/01

Other activities

ITA

20410497 - TFO- EDUCATIONAL AND ORIENTATION INTERNSHIP (objectives)

Other activities

ITA

20410467 - FINAL EXAM (objectives)

Final examination and foreign language test

ITA

TOTAL

120

Didattico

FIRST YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM DIDATTICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	48	24	-	-	Core compulsory activities	ITA
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410445 - AL410 - COMMUTATIVE ALGEBRA	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	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Core compulsory activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Core compulsory activities	ITA
20410425 - GE460- GRAPH THEORY	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM DIDATTICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20410408 - AL310 - ELEMENTS OF ADVANCED ALGEBRA	Also available in another semester or year
20410412 - MC310 - Fundaments of Complementary Mathematics	Also available in another semester or year
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	-	-	Core compulsory activities	ITA
20410456 - MC420-Dydactics 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
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	-	-	Core compulsory activities	ITA
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS	Also available in another semester or year
20410411 - GE310 - ELEMENTS OF ADVANCED GEOMETRY	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	-	-	Core compulsory activities	ITA
20410449 - GE410 - ALGEBRAIC GEOMETRY 1	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - LM410 -THEOREMS IN LOGIC 1 - Module B	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2 (objectives) To support the students into an in-depth analysis of the main results of first order classical logic and to study some of their remarkable consequences.	6	MAT/01	36	-	-	-	Core compulsory activities	ITA
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	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	-	-	Core compulsory activities	ITA
20410458 - LM430 - LOGICAL THEORIES 2 (objectives) To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.	6	MAT/01	36	-	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410465 - GE450 - TOPOLOGIA ALGEBRICA	Also available in another semester or year
20410425 - GE460- GRAPH THEORY (objectives) Provide tools and methods for graph theory.	6	MAT/03	48	12	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

SECOND YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM DIDATTICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	48	24	-	-	Core compulsory activities	ITA
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410445 - AL410 - COMMUTATIVE ALGEBRA	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	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Core compulsory activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Core compulsory activities	ITA
20410425 - GE460- GRAPH THEORY	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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
20410407 - AC310 - Complex analysis	Also available in another semester or year
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.	9	MAT/05	48	24	-	-	Related or supplementary learning activities	ITA
20410410 - FM310 - Equations of Mathematical Physics	Also available in another semester or year
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
20410412 - MC310 - Fundaments of Complementary Mathematics (objectives) 1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.	9	MAT/04	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
20410446 - BL410-Introduction to Biology (objectives) Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods.	6	BIO/13	48	-	-	-	Related or supplementary learning activities	ITA
20410439 - CH410 - ELEMENTS OF CHEMISTRY (objectives) Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.	6	CHIM/03	52	-	-	-	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
20410415 - 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.	9	MAT/02	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
20410448 - FS410 - DIDACTICS OF PHYSICS WORKSHOP	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
20410450 - GL410-Elements of Geology I (objectives) The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. 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
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
20410418 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20410452 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20410438 - MF410 - Computational Finance	Also available in another semester or year
20410419 - MS410-Statistical Mechanics	Also available in another semester or year
20410440 - ST410-Introduction to 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
20410453 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20410420 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20410441 - CP420-Introduction to Stochastic Processes	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
20410454 - GL420-Elements of Geology II	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2	Also available in another semester or year
20410456 - MC420-Dydactics of Mathematics	Also available in another semester or year
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.	6	MAT/05	48	12	-	-	Related or supplementary learning activities	ITA
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
20410457 - CP430 - STOCHASTIC CALCULUS (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.	6	MAT/06	48	12	-	-	Related or supplementary learning activities	ITA
20410444 - GE430 - RIEMANNIAN GEOMETRY	Also available in another semester or year
20410437 - FS430- Theory of Relativity	Also available in another semester or year
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20410458 - LM430 - LOGICAL THEORIES 2	Also available in another semester or year
20410459 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS	Also available in another semester or year
20410435 - FS440 - Data Acquisition and Experimental Control	Also available in another semester or year
20410423 - IN440 - COMBINATORIAL OPTIMISATION	Also available in another semester or year
20410460 - AM450 - FUNCTIONAL ANALYSIS	Also available in another semester or year
20410465 - GE450 - TOPOLOGIA ALGEBRICA (objectives) To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410424 - IN450 - ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20410461 - FS460 - Dydactics of Physics	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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.	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	Also available in another semester or year
20410470 - FM510 - MATHEMATICAL PHYSICS APPLICATIONS	Also available in another semester or year
20410429 - FS510 - MONTECARLO METHODS (objectives) Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.	6	FIS/01	48	12	-	-	Related or supplementary learning activities	ITA
20410462 - GE510 - ALGEBRAIC GEOMETRY 2	Also available in another semester or year
20410463 - TN510 - NUMBER THEORY	Also available in another semester or year
20410464 - IN530 - COMPUTER INFORMATION SYSTEMS	Also available in another semester or year
20410431 - IN540 - COMPUTATIONAL TOPOLOGY	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
20410443 - FS520 - Complex systems	Also available in another semester or year
20410518 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410520 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20410523 - MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES	Also available in another semester or year
20410522 - CP450 - DISCRETE PROBABILITY	Also available in another semester or year
20410524 - GE520 - ADVANCED GEOMETRY	Also available in another semester or year
20410529 - LM510 - LOGICAL THEORIES 1	Also available in another semester or year

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: CURRICULUM DIDATTICO SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) NEI SEGUENTI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20410408 - AL310 - ELEMENTS OF ADVANCED ALGEBRA	Also available in another semester or year
20410412 - MC310 - Fundaments of Complementary Mathematics	Also available in another semester or year
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	-	-	Core compulsory activities	ITA
20410456 - MC420-Dydactics 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
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	-	-	Core compulsory activities	ITA
20410409 - AM310 - ELEMENTS OF ADVANCED ANALYSIS	Also available in another semester or year
20410411 - GE310 - ELEMENTS OF ADVANCED GEOMETRY	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	-	-	Core compulsory activities	ITA
20410449 - GE410 - ALGEBRAIC GEOMETRY 1	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - LM410 -THEOREMS IN LOGIC 1 - Module B	Also available in another semester or year
20410455 - LM420 - THEOREMS IN LOGIC 2 (objectives) To support the students into an in-depth analysis of the main results of first order classical logic and to study some of their remarkable consequences.	6	MAT/01	36	-	-	-	Core compulsory activities	ITA
20410469 - AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	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	-	-	Core compulsory activities	ITA
20410458 - LM430 - LOGICAL THEORIES 2 (objectives) To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.	6	MAT/01	36	-	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410465 - GE450 - TOPOLOGIA ALGEBRICA	Also available in another semester or year
20410425 - GE460- GRAPH THEORY (objectives) Provide tools and methods for graph theory.	6	MAT/03	48	12	-	-	Core compulsory 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA

Optional Group: GRUPPO UNICO PER CURRICULA TEORICO e DIDATTICO: SCEGLIERE UN INSEGNAMENTO (9 CFU) NEI SEGUENTI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

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	-	-	Core compulsory activities	ITA
20410413 - AN410 - NUMERICAL ANALYSIS 1	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	-	-	Core compulsory activities	ITA
20410419 - MS410-Statistical 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	-	-	Core compulsory 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	-	-	Core compulsory activities	ITA
20410447 - CP410 - Theory of Probability	Also available in another semester or year

Optional Group: GRUPPO UNICO: SCEGLIERE QUATTRO INSEGNAMENTI (30 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

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 - BL410-Introduction 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 - CR410-Public Key Criptography	Also available in another semester or year
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 (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
20410416-2 - FM410-Complements 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 - GL410-Elements of Geology I	Also available in another semester or year
20410417 - IN410-Computability 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.
20410451-1 - LM410 -THEOREMS IN LOGIC 1 - Module A	Also available in another semester or year
20410451-2 - 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	SECS-S/06	60	-	-	-	Related or supplementary learning activities	ITA
20410419 - MS410-Statistical 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 - ST410-Introduction 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 - CP420-Introduction 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 - GL420-Elements 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 in-depth 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 - MC420-Dydactics 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 Gauss-Bonnet and Hopf-Rinow.	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 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
20410422 - IN430 - ADVANCED COMPUTING TECHNIQUES (objectives) Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented 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 Zermelo-Fraenkel'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 (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
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/medium-sized 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 large-sized 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 (objectives) The purpose of this Course is presenting a few typical topics of Mathematics especially useful for Physics and Engineering. These are the theory of analytic functions, Hilbert spaces, Fourier series, Fourier and Laplace transforms.	6	MAT/05	-	-	-	-	Related or supplementary learning activities	ITA
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
20410524 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	6	MAT/03	48	12	-	-	Related or supplementary learning activities	ITA
20410529 - LM510 - LOGICAL THEORIES 1 (objectives) Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research	6	MAT/01	36	-	-	-	Related or supplementary learning activities	ITA

Optional Group: Comune SCEGLIERE DUE INSEGNAMENTI PER UN TOTALE DI 12 CFU - (show)

20410376 - UCL - FURTHER LANGUAGE STUDIES (objectives)

Other activities

ITA

20410377 - AIT - COMPUTER AND TELEMATIC SKILLS (objectives)

INF/01

Other activities

ITA

20410497 - TFO- EDUCATIONAL AND ORIENTATION INTERNSHIP (objectives)

Other activities

ITA

20410467 - FINAL EXAM (objectives)

Final examination and foreign language test

ITA

TOTAL

120

LOGICA MATEMATICA E INFORMATICA TEORICA - CURRICULUM BINAZIONALE IN LOGICA

FIRST YEAR

First semester

Course	Credits	Scientific Disciplinary Sector Code	Contact Hours	Exercise Hours	Laboratory Hours	Personal Study Hours	Type of Activity	Language

Second semester

Course	Credits	Scientific Disciplinary Sector Code	Contact Hours	Exercise Hours	Laboratory Hours	Personal Study Hours	Type of Activity	Language

SECOND YEAR

First semester

Course	Credits	Scientific Disciplinary Sector Code	Contact Hours	Exercise Hours	Laboratory Hours	Personal Study Hours	Type of Activity	Language

Second semester

Course	Credits	Scientific Disciplinary Sector Code	Contact Hours	Exercise Hours	Laboratory Hours	Personal Study Hours	Type of Activity	Language

TOTAL

Università Roma Tre

Degree Course: Mathematics A.Y. 2019/2020

Expected learning outcomes Syllabus Italian version

Conoscenza e capacità di comprensione

Capacità di applicare conoscenza e comprensione

Autonomia di giudizio

Abilità comunicative

Capacità di apprendimento

Requisiti di ammissione

Prova finale

Orientamento in ingresso

Il Corso di Studio in breve