COURSE - Università Roma Tre

Degree Course: Mathematics A.Y. 2016/2017

Expected learning outcomes Syllabus Italian version

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: comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20402086 - FM310 - MATHEMATICAL PHYSICS 2	Also available in another semester or year
20402088 - AN410 - NUMERICAL ANALYSIS 1 (objectives) Provide the basic elements (including implementation in a programming language) of basic numerical approximation techniques, in particular those related to the solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.	7	MAT/08	72	-	-	-	Core compulsory activities	ITA
20402092 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20402093 - CP410 - PROBABILITY 2 (objectives) To gain a solid knowledge of the basic aspects of probabilità theory: construction of probabilità measures on measurable spaces, 0-1 law, independence, conditional expectation, random variables, convergence of random variables, characteristic functions, central limit theorem, branching processes, discrete martingales.	7	MAT/06	60	-	-	-	Core compulsory activities	ITA
20402101 - CP430 - STOCHASTIC CALCULUS	Also available in another semester or year
20402103 - FM410 - MATHEMATICAL PHYSICS 3 (objectives) CONTINUING THE STUDY, BEGAN DURING FM210, OF DYNAMIC SYSTEMS OF PHYSICAL INTEREST WITH MOST STYLISH AND POWERFUL TECHNIQUES, SUCH AS THE LAGRANGIAN AND HAMITONIAN FORMALISM, THAT ARE IN THE VAST RANGE OF APPLICATIONS OF ANALYSIS AND MATHEMATICAL PHYSICS.	7	MAT/07	60	-	-	-	Core compulsory activities	ITA
20402123 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20402327 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS	Also available in another semester or year
20402100 - CP420 - STOCHASTIC PROCESSES	Also available in another semester or year
20402280 - AN430 – NUMERICAL ANALYSIS 3 (objectives) The purpose of this course is to bring together ideas and algorithms to solve quantitatively scientific problems. The course will give an overview about the numerical solutions of PDE, and will focus on some selected problems in mechanics and physics, covering the three main types of equations: elliptic, parabolic and hyperbolic. The course will cover the following topics: - Applied Linear Algebra. - Boundary Value Problems. - Initial Value Problems The students will be introduced to the use of scientific software for numerical simulations based on the Finite Element Method.	7	MAT/08	60	-	-	-	Core compulsory activities	ITA
20410160 - FM440 - FISICA MATEMATICA 6	Also available in another semester or year

Optional Group: comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

Optional Group: comune Orientamento unico SCEGLIERE DUE ATTIVITA' TRA LE SEGUENTI PER UN TOTALE DI 9 CFU - (show)

Optional Group: comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20402086 - FM310 - MATHEMATICAL PHYSICS 2 (objectives) The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations	7	MAT/07	72	-	-	-	Core compulsory activities	ITA
20402088 - AN410 - NUMERICAL ANALYSIS 1	Also available in another semester or year
20402092 - AN420 - NUMERICAL ANALYSIS 2 (objectives) THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.	7	MAT/08	60	-	-	-	Core compulsory activities	ITA
20402093 - CP410 - PROBABILITY 2	Also available in another semester or year
20402101 - CP430 - STOCHASTIC CALCULUS (objectives) Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.	7	MAT/06	10	-	-	-	Core compulsory activities	ITA
20402103 - FM410 - MATHEMATICAL PHYSICS 3	Also available in another semester or year
20402123 - 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.	7	MAT/08	60	12	-	-	Core compulsory activities	ITA
20402327 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS (objectives) To acquire a solid knowledge of some problems in the theory of quantum mechanics	7	MAT/07	60	-	-	-	Core compulsory activities	ITA
20402100 - CP420 - STOCHASTIC PROCESSES (objectives) Acquire a solid basic preparation in the aspects The main theories of stochastic processes with particular Regarding Markov's processes and their applications (Monte Carlo method and simulated annealing) of theory Of casual walks and of the simplest models of Interacting particle systems	7	MAT/06	60	-	-	-	Core compulsory activities	ITA
20402280 - AN430 – NUMERICAL ANALYSIS 3	Also available in another semester or year
20410160 - FM440 - FISICA MATEMATICA 6 (objectives) To acquire a solid knowledge of the mathematical theory of statistical mechanics, and of the methods for studying models of interacting particles	7	MAT/07	10	-	-	-	Core compulsory activities	ITA

Optional Group: comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

20402089 - IN410 - COMPUTER SCIENCE 2 (objectives) THE COURSE COMPUTER SCIENCE 2 (IN2 - MODELS OF COMPUTATION) IS DEVOTED TO THE INTRODUCTION OF MATHEMATICAL ASPECTS OF THE CONCEPT OF COMPUTATION, AND TO THE STUDY OF RELATIONS BETWEEN DIFFERENT MODELS OF COMPUTATION AND BETWEEN DIFFERENT PROGRAMMING STYLES. IN PARTICULAR, AN INTRODUCTION TO OBJECT ORIENTED IS GIVEN DURING THE COURSE.	7	INF/01	60	12	-	-	Related or supplementary learning activities	ITA
20402091 - TN410 - INTRODUCTION TO NUMBER THEORY (objectives) TO HAVE A GOOD KNOWLEDGE OF CONCEPTS AND METHODS OF ELEMENTARY NUMBER THEORY, WITH PARTICULAR RESPECT OF STUDY OF DIOPHANTINE EQUATIONS AND POLYNOMIAL CONGRUENCES. TO GIVE PREREQUISITES FOR ADVANCED COURSES OF ALGEBRAIC AND ANALYTIC NUMBER THEORY.	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402102 - CR410 - CRYPTOGRAPHY 1	Also available in another semester or year
20402107 - GE510 - ALGEBRAIC GEOMETRY 2 (objectives) Introduction and applications od the language of modern algebraic geometry through the theory of sheaves and the theory of schemes. In depth examination of the interactions of geometry and algebra. Description of research themes and open problems in modern algebra and geometry.	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402108 - IN430 - INFORMATICS 4: 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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20402111 - IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY (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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20402114 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20402115 - ST410 - STATISTICS 1	Also available in another semester or year
20402122 - FS420 - QUANTUM MECHANICS	Also available in another semester or year
20402297 - AL410 - COMMUTATIVE ALGEBRA - C	Also available in another semester or year
20402298 - AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C	Also available in another semester or year
20402299 - AN410 - NUMERICAL ANALYSIS 1 - C	Also available in another semester or year
20402300 - CP410 - PROBABILITY 2 - C	Also available in another semester or year
20402301 - FM410 - MATHEMATICAL PHYSICS 3 - C	Also available in another semester or year
20402302 - GE410 - ALGEBRAIC GEOMETRY 1 - C	Also available in another semester or year
20402304 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C (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	7	MAT/08	60	12	-	-	Related or supplementary learning activities	ITA
20402305 - MC410 - COMPLEMENTARY MATHEMATICS 1 - C	Also available in another semester or year
20402306 - AN420 - NUMERICAL ANALYSIS 2 - C (objectives) 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	7	MAT/08	60	-	-	-	Related or supplementary learning activities	ITA
20402309 - CP430 - STOCHASTIC CALCULUS - C (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations	7	MAT/06	10	-	-	-	Related or supplementary learning activities	ITA
20402313 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C (objectives) 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	7	MAT/04	60	-	-	-	Related or supplementary learning activities	ITA
20402335 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C (objectives) Form a broad, not only qualitative competence on the models, technologies and computer architectures adopted on modern corporate information systems	7	MAT/07	60	-	-	-	Related or supplementary learning activities	ITA
20410043 - FIRST-ORDER CLASSICAL LOGIC	Also available in another semester or year
20410044 - FS430 - FISICA 3, RELATIVITA' E TEORIE RELATIVISTICHE (objectives) Familiarize yourself with the notion of invariance, covariance for Lorentz's transformations, cronotope and formalism Three - dimensional and tensorial always taking into account the Phenomenology (constancy of light speed, equality Of the inertial and gravitational mass) on which the theory of relativity	7	FIS/02	60	-	-	-	Related or supplementary learning activities	ITA
20410073 - IN460 - INFORMATICA 7, GEOMETRIA COMPUTAZIONALE	Also available in another semester or year
20402290 - Information Theory	Also available in another semester or year
20402116 - TN510 - NUMBER THEORY	Also available in another semester or year
20410040 - COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY	Also available in another semester or year
20410068 - MATHEMATICS OF FINANCIAL MARKETS	Also available in another semester or year
20410069 - FS410 - LABORATORIO DI DIDATTICA DELLA FISICA (objectives) Learn statistical and laboratory techniques For the preparation of didactic experiences of physics Laboratory.	7	FIS/08	30	-	30	-	Related or supplementary learning activities	ITA
20410038 - GRAPH THEORY	Also available in another semester or year
20402249 - CH410 - ELEMENTS OF CHEMISTRY	Also available in another semester or year
20410037 - GE450 - TOPOLOGIA ALGEBRICA	Also available in another semester or year
20410034 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	Also available in another semester or year
20402120 - LM510 - LINEAR TYPES AND LOGIC (objectives) A DEEP AND CRITICAL INTRODUCTION TO A SPECIFIC LOGICAL THEORY WHICH CONCERNS THE THEME OF THE INTERACTION AND IS CENTRAL IN THE CONTEMPORARY RESEARCH ON INFROMATION AND COMMUNICATION: LINEAR LOGIC AND ITS DEVELOPMENTS.	7	MAT/01	60	-	-	-	Related or supplementary learning activities	ITA
20410074 - LM430 - TEORIA ASSIOMATICA DEGLI INSIEMI (objectives) Acquire the basics of theory Axiomatic of Zermelo-Fraenkel's and Get acquainted with the issues related to Such theory	7	MAT/01	60	-	-	-	Related or supplementary learning activities	ITA
20410070 - LOGIC AND ARITHMETIC	Also available in another semester or year
20402100 - CP420 - STOCHASTIC PROCESSES (objectives) Acquire a solid basic preparation in the aspects The main theories of stochastic processes with particular Regarding Markov's processes and their applications (Monte Carlo method and simulated annealing) of theory Of casual walks and of the simplest models of Interacting particle systems	7	MAT/06	60	-	-	-	Related or supplementary learning activities	ITA
20402095 - 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	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402106 - GE430 - DIFFERENTIAL GEOMETRY 2 (objectives) Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20410094 - GE470 - Riemann surfaces (objectives) Acquire a sufficiently broad knowledge of the topological, analytical and geometric aspects of the theory of Riemann surfaces	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402293 - 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	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402188 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402183 - AM550 - PROBLEMS OF SMALL DIVISORS IN INFINITE DIMENSIONS (objectives) To introduce to the study of small divisors problems in infinite dimension and relative applications to partial differential equations	7	MAT/05	60	-	-	-	Related or supplementary learning activities	ITA
20402291 - ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS	Also available in another semester or year
20402110 - IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20402280 - AN430 – NUMERICAL ANALYSIS 3	Also available in another semester or year
20402336 - IN530 - COMPUTER SCIENCE 9 - COMPUTER INFORMATION SYSTEMS (objectives) The course has the objective of providing an overview, mainly qualitative, on the modern enterprise information systems and their main components.	4	INF/01	40	-	-	-	Related or supplementary learning activities	ITA
20402098 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410107 - CR410 - CRITTOGRAFIA 1 (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.	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20410133 - IN480 - CALCOLO PARALLELO E DISTRIBUITO (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	7	INF/01	48	12	-	-	Related or supplementary learning activities	ITA
20410134 - IN540 - TOPOLOGIA ALGEBRICA E COMPUTAZIONALE (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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20410160 - FM440 - FISICA MATEMATICA 6 (objectives) To acquire a solid knowledge of the mathematical theory of statistical mechanics, and of the methods for studying models of interacting particles	7	MAT/07	10	-	-	-	Core compulsory activities	ITA

Optional Group: comune Orientamento unico SCEGLIERE DUE ATTIVITA' TRA LE SEGUENTI PER UN TOTALE DI 9 CFU - (show)

Optional Group: comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (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: comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20402086 - FM310 - MATHEMATICAL PHYSICS 2	Also available in another semester or year
20402088 - AN410 - NUMERICAL ANALYSIS 1 (objectives) Provide the basic elements (including implementation in a programming language) of basic numerical approximation techniques, in particular those related to the solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.	7	MAT/08	72	-	-	-	Core compulsory activities	ITA
20402092 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20402093 - CP410 - PROBABILITY 2 (objectives) To gain a solid knowledge of the basic aspects of probabilità theory: construction of probabilità measures on measurable spaces, 0-1 law, independence, conditional expectation, random variables, convergence of random variables, characteristic functions, central limit theorem, branching processes, discrete martingales.	7	MAT/06	60	-	-	-	Core compulsory activities	ITA
20402101 - CP430 - STOCHASTIC CALCULUS	Also available in another semester or year
20402103 - FM410 - MATHEMATICAL PHYSICS 3 (objectives) CONTINUING THE STUDY, BEGAN DURING FM210, OF DYNAMIC SYSTEMS OF PHYSICAL INTEREST WITH MOST STYLISH AND POWERFUL TECHNIQUES, SUCH AS THE LAGRANGIAN AND HAMITONIAN FORMALISM, THAT ARE IN THE VAST RANGE OF APPLICATIONS OF ANALYSIS AND MATHEMATICAL PHYSICS.	7	MAT/07	60	-	-	-	Core compulsory activities	ITA
20402123 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20402327 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS	Also available in another semester or year
20402100 - CP420 - STOCHASTIC PROCESSES	Also available in another semester or year
20402280 - AN430 – NUMERICAL ANALYSIS 3 (objectives) The purpose of this course is to bring together ideas and algorithms to solve quantitatively scientific problems. The course will give an overview about the numerical solutions of PDE, and will focus on some selected problems in mechanics and physics, covering the three main types of equations: elliptic, parabolic and hyperbolic. The course will cover the following topics: - Applied Linear Algebra. - Boundary Value Problems. - Initial Value Problems The students will be introduced to the use of scientific software for numerical simulations based on the Finite Element Method.	7	MAT/08	60	-	-	-	Core compulsory activities	ITA
20410160 - FM440 - FISICA MATEMATICA 6	Also available in another semester or year

Optional Group: comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

Optional Group: comune Orientamento unico SCEGLIERE DUE ATTIVITA' TRA LE SEGUENTI PER UN TOTALE DI 9 CFU - (show)

Optional Group: comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

Optional Group: comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

Optional Group: comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)

20402086 - FM310 - MATHEMATICAL PHYSICS 2 (objectives) The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations	7	MAT/07	72	-	-	-	Core compulsory activities	ITA
20402088 - AN410 - NUMERICAL ANALYSIS 1	Also available in another semester or year
20402092 - AN420 - NUMERICAL ANALYSIS 2 (objectives) THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.	7	MAT/08	60	-	-	-	Core compulsory activities	ITA
20402093 - CP410 - PROBABILITY 2	Also available in another semester or year
20402101 - CP430 - STOCHASTIC CALCULUS (objectives) Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.	7	MAT/06	10	-	-	-	Core compulsory activities	ITA
20402103 - FM410 - MATHEMATICAL PHYSICS 3	Also available in another semester or year
20402123 - 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.	7	MAT/08	60	12	-	-	Core compulsory activities	ITA
20402327 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS (objectives) To acquire a solid knowledge of some problems in the theory of quantum mechanics	7	MAT/07	60	-	-	-	Core compulsory activities	ITA
20402100 - CP420 - STOCHASTIC PROCESSES (objectives) Acquire a solid basic preparation in the aspects The main theories of stochastic processes with particular Regarding Markov's processes and their applications (Monte Carlo method and simulated annealing) of theory Of casual walks and of the simplest models of Interacting particle systems	7	MAT/06	60	-	-	-	Core compulsory activities	ITA
20402280 - AN430 – NUMERICAL ANALYSIS 3	Also available in another semester or year
20410160 - FM440 - FISICA MATEMATICA 6 (objectives) To acquire a solid knowledge of the mathematical theory of statistical mechanics, and of the methods for studying models of interacting particles	7	MAT/07	10	-	-	-	Core compulsory activities	ITA

Optional Group: comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)

20402089 - IN410 - COMPUTER SCIENCE 2 (objectives) THE COURSE COMPUTER SCIENCE 2 (IN2 - MODELS OF COMPUTATION) IS DEVOTED TO THE INTRODUCTION OF MATHEMATICAL ASPECTS OF THE CONCEPT OF COMPUTATION, AND TO THE STUDY OF RELATIONS BETWEEN DIFFERENT MODELS OF COMPUTATION AND BETWEEN DIFFERENT PROGRAMMING STYLES. IN PARTICULAR, AN INTRODUCTION TO OBJECT ORIENTED IS GIVEN DURING THE COURSE.	7	INF/01	60	12	-	-	Related or supplementary learning activities	ITA
20402091 - TN410 - INTRODUCTION TO NUMBER THEORY (objectives) TO HAVE A GOOD KNOWLEDGE OF CONCEPTS AND METHODS OF ELEMENTARY NUMBER THEORY, WITH PARTICULAR RESPECT OF STUDY OF DIOPHANTINE EQUATIONS AND POLYNOMIAL CONGRUENCES. TO GIVE PREREQUISITES FOR ADVANCED COURSES OF ALGEBRAIC AND ANALYTIC NUMBER THEORY.	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402102 - CR410 - CRYPTOGRAPHY 1	Also available in another semester or year
20402107 - GE510 - ALGEBRAIC GEOMETRY 2 (objectives) Introduction and applications od the language of modern algebraic geometry through the theory of sheaves and the theory of schemes. In depth examination of the interactions of geometry and algebra. Description of research themes and open problems in modern algebra and geometry.	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402108 - IN430 - INFORMATICS 4: 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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20402111 - IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY (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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20402114 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
20402115 - ST410 - STATISTICS 1	Also available in another semester or year
20402122 - FS420 - QUANTUM MECHANICS	Also available in another semester or year
20402297 - AL410 - COMMUTATIVE ALGEBRA - C	Also available in another semester or year
20402298 - AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C	Also available in another semester or year
20402299 - AN410 - NUMERICAL ANALYSIS 1 - C	Also available in another semester or year
20402300 - CP410 - PROBABILITY 2 - C	Also available in another semester or year
20402301 - FM410 - MATHEMATICAL PHYSICS 3 - C	Also available in another semester or year
20402302 - GE410 - ALGEBRAIC GEOMETRY 1 - C	Also available in another semester or year
20402304 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C (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	7	MAT/08	60	12	-	-	Related or supplementary learning activities	ITA
20402305 - MC410 - COMPLEMENTARY MATHEMATICS 1 - C	Also available in another semester or year
20402306 - AN420 - NUMERICAL ANALYSIS 2 - C (objectives) 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	7	MAT/08	60	-	-	-	Related or supplementary learning activities	ITA
20402309 - CP430 - STOCHASTIC CALCULUS - C (objectives) Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations	7	MAT/06	10	-	-	-	Related or supplementary learning activities	ITA
20402313 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C (objectives) 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	7	MAT/04	60	-	-	-	Related or supplementary learning activities	ITA
20402335 - FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C (objectives) Form a broad, not only qualitative competence on the models, technologies and computer architectures adopted on modern corporate information systems	7	MAT/07	60	-	-	-	Related or supplementary learning activities	ITA
20410043 - FIRST-ORDER CLASSICAL LOGIC	Also available in another semester or year
20410044 - FS430 - FISICA 3, RELATIVITA' E TEORIE RELATIVISTICHE (objectives) Familiarize yourself with the notion of invariance, covariance for Lorentz's transformations, cronotope and formalism Three - dimensional and tensorial always taking into account the Phenomenology (constancy of light speed, equality Of the inertial and gravitational mass) on which the theory of relativity	7	FIS/02	60	-	-	-	Related or supplementary learning activities	ITA
20410073 - IN460 - INFORMATICA 7, GEOMETRIA COMPUTAZIONALE	Also available in another semester or year
20402290 - Information Theory	Also available in another semester or year
20402116 - TN510 - NUMBER THEORY	Also available in another semester or year
20410040 - COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY	Also available in another semester or year
20410068 - MATHEMATICS OF FINANCIAL MARKETS	Also available in another semester or year
20410069 - FS410 - LABORATORIO DI DIDATTICA DELLA FISICA (objectives) Learn statistical and laboratory techniques For the preparation of didactic experiences of physics Laboratory.	7	FIS/08	30	-	30	-	Related or supplementary learning activities	ITA
20410038 - GRAPH THEORY	Also available in another semester or year
20402249 - CH410 - ELEMENTS OF CHEMISTRY	Also available in another semester or year
20410037 - GE450 - TOPOLOGIA ALGEBRICA	Also available in another semester or year
20410034 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	Also available in another semester or year
20402120 - LM510 - LINEAR TYPES AND LOGIC (objectives) A DEEP AND CRITICAL INTRODUCTION TO A SPECIFIC LOGICAL THEORY WHICH CONCERNS THE THEME OF THE INTERACTION AND IS CENTRAL IN THE CONTEMPORARY RESEARCH ON INFROMATION AND COMMUNICATION: LINEAR LOGIC AND ITS DEVELOPMENTS.	7	MAT/01	60	-	-	-	Related or supplementary learning activities	ITA
20410074 - LM430 - TEORIA ASSIOMATICA DEGLI INSIEMI (objectives) Acquire the basics of theory Axiomatic of Zermelo-Fraenkel's and Get acquainted with the issues related to Such theory	7	MAT/01	60	-	-	-	Related or supplementary learning activities	ITA
20410070 - LOGIC AND ARITHMETIC	Also available in another semester or year
20402100 - CP420 - STOCHASTIC PROCESSES (objectives) Acquire a solid basic preparation in the aspects The main theories of stochastic processes with particular Regarding Markov's processes and their applications (Monte Carlo method and simulated annealing) of theory Of casual walks and of the simplest models of Interacting particle systems	7	MAT/06	60	-	-	-	Related or supplementary learning activities	ITA
20402095 - 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	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402106 - GE430 - DIFFERENTIAL GEOMETRY 2 (objectives) Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20410094 - GE470 - Riemann surfaces (objectives) Acquire a sufficiently broad knowledge of the topological, analytical and geometric aspects of the theory of Riemann surfaces	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402293 - 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	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20402188 - GE520 - ADVANCED GEOMETRY (objectives) Acquire up-to-date and advanced skills on topics chosen within the research themes of contemporary geometry	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20402183 - AM550 - PROBLEMS OF SMALL DIVISORS IN INFINITE DIMENSIONS (objectives) To introduce to the study of small divisors problems in infinite dimension and relative applications to partial differential equations	7	MAT/05	60	-	-	-	Related or supplementary learning activities	ITA
20402291 - ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS	Also available in another semester or year
20402110 - IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY	Also available in another semester or year
20402280 - AN430 – NUMERICAL ANALYSIS 3	Also available in another semester or year
20402336 - IN530 - COMPUTER SCIENCE 9 - COMPUTER INFORMATION SYSTEMS (objectives) The course has the objective of providing an overview, mainly qualitative, on the modern enterprise information systems and their main components.	4	INF/01	40	-	-	-	Related or supplementary learning activities	ITA
20402098 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20410107 - CR410 - CRITTOGRAFIA 1 (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.	7	MAT/03	60	-	-	-	Related or supplementary learning activities	ITA
20410133 - IN480 - CALCOLO PARALLELO E DISTRIBUITO (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	7	INF/01	48	12	-	-	Related or supplementary learning activities	ITA
20410134 - IN540 - TOPOLOGIA ALGEBRICA E COMPUTAZIONALE (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	7	INF/01	60	-	-	-	Related or supplementary learning activities	ITA
20410160 - FM440 - FISICA MATEMATICA 6 (objectives) To acquire a solid knowledge of the mathematical theory of statistical mechanics, and of the methods for studying models of interacting particles	7	MAT/07	10	-	-	-	Core compulsory activities	ITA

Optional Group: comune Orientamento unico SCEGLIERE DUE ATTIVITA' TRA LE SEGUENTI PER UN TOTALE DI 9 CFU - (show)

Optional Group: comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)

20410000 - Prova finale (objectives)

150

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. 2016/2017

Expected learning outcomes Syllabus Italian version

Autonomia di giudizio

Abilità comunicative

Capacità di apprendimento

Requisiti di ammissione

Prova finale

Il Corso di Studio in breve