COURSE - Università Roma Tre

Degree Course: Mathematics A.Y. 2015/2016

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

20401885 - AL110 - ALGEBRA 1 (objectives)

MAT/02

Basic compulsory activities

ITA

20401886 - AM110 - MATHEMATICAL ANALYSIS 1 (objectives)

MAT/05

Basic compulsory activities

ITA

20401890 - IN110 - COMPUTER SCIENCE 1 (ALGORITHMS AND COMPUTER PROGRAMMING) (objectives)

INF/01

Basic compulsory activities

ITA

Optional Group: Gruppo idoneità di lingue - (show)

Second semester

Course	Credits	Scientific Disciplinary Sector Code	Contact Hours	Exercise Hours	Laboratory Hours	Personal Study Hours	Type of Activity	Language
20401887 - AM120 - MATHEMATICAL ANALYSIS 2 (objectives) To obtain the fundamental notions about derivation and integration of real functions of one real variable and to develop abilities in calculus methods. To develop the fundamentals of the theory of real and complex series.	10	MAT/05	60	36	-	-	Core compulsory activities	ITA
20401888 - GE110- GEOMETRY 1 (objectives) OBTAIN GOOD KNOWLEDGE OF THE CONCEPTS AND METHODS OF BASIC LINEAR ALGEBRA, WITH SPECIAL EMPHASIS ON THE STUDY OF LINEAR SYSTEMS, MATRICES AND DETERMINANTS, VECTOR SPACES AND LINEAR MAPS, AFFINE GEOMETRY.	10	MAT/03	60	36	-	-	Basic compulsory activities	ITA
20401889 - CP110 - PROBABILITY 1 (objectives) INTRODUCTION TO THE MAIN ASPECTS OF PROBABILITY THEORY: PROBABILITY SPACES, REPEATED TRIALS, RANDOM VARIABLES, PROBABILITY DISTRIBUTIONS, SOME LIMIT THEOREMS AND A FIRST LOOK AT FINITE MARKOV CHAINS	10	MAT/06	60	36	-	-	Core compulsory activities	ITA

SECOND YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

20402075 - AL210 - ALGEBRA 2 (objectives)

MAT/02

Core compulsory activities

ITA

20402076 - AM210 - MATHEMATICAL ANALYSIS 3 (objectives)

MAT/05

Core compulsory activities

ITA

20402079 - GE210 - GEOMETRY 2 (objectives)

MAT/03

Core compulsory activities

ITA

Optional Group: comune Orientamento unico UN INSEGNAMENTO A SCELTA NEL GRUPPO 1 - (show)

20402088 - 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	7	MAT/08	60	12	-	-	Related or supplementary learning activities	ITA
20402089 - IN410 - COMPUTER SCIENCE 2	Also available in another semester or year
20402090 - MC410 - COMPLEMENTARY MATHEMATICS 1 (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
20402091 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

20402077 - AM220 - MATHEMATICAL ANALYSIS 4 (objectives)

MAT/05

Core compulsory activities

ITA

20402078 - FS210 - PHYSICS 1 (objectives)

FIS/01

Basic compulsory activities

ITA

20402080 - GE220 - GEOMETRY 3 (objectives)

MAT/03

Core compulsory activities

ITA

Optional Group: comune Orientamento unico UN INSEGNAMENTO A SCELTA NEL GRUPPO 1 - (show)

20402088 - AN410 - NUMERICAL ANALYSIS 1	Also available in another semester or year
20402089 - IN410 - COMPUTER SCIENCE 2 (objectives) FUNCTIONAL MODELS OF LAMBDA-CALCULUS. OBJECT-ORIENTED PROGRAMMING: CLASSES, FUNCTIONAL CLASSES. CLASS INHERITANCE. ABSTRACT CLASS DECLARATION. PUBLIC AND PRIVATE METHODS. METHOD LATE-BINDING.	7	INF/01	60	12	-	-	Related or supplementary learning activities	ITA
20402090 - MC410 - COMPLEMENTARY MATHEMATICS 1	Also available in another semester or year
20402091 - TN410 - INTRODUCTION TO NUMBER THEORY (objectives) TO ACQUIRE 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

THIRD YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

20402081 - FM210 - MATHEMATICAL PHYSICS 1 (objectives)

MAT/07

Core compulsory activities

ITA

20402131 - SCIENTIFIC ENGLISH

Also available in another semester or year

Optional Group: comune Orientamento unico DUE INSEGNAMENTI A SCELTA NEL GRUPPO 2 - (show)

20402083 - AL4 - ELEMENTS OF ADVANCED ALGEBRA (objectives) OBTAIN GOOD KNOWLEDGE OF THE CONCEPTS AND METHODS OF THE THEORY OF EQUATIONS IN ONE VARIABLE. UNDERSTAND AND BE ABLE TO APPLY THE “FUNDAMENTAL THEOREM OF CORRESPONDENCE OF GALOIS” IN ORDER STUDY THE “COMPLEXITY” OF A POLYNOMIAL.	7	MAT/02	60	12	-	-	Related or supplementary learning activities	ITA
20402085 - 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	7	MAT/05	60	12	-	-	Related or supplementary learning activities	ITA
20402086 - FM310 - MATHEMATICAL PHYSICS 2	Also available in another semester or year
20402087 - 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	7	MAT/03	60	12	-	-	Related or supplementary learning 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	-	-	-	Related or supplementary learning activities	ITA
20402279 - AC310 – COMPLEX ANALYSIS 1 (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	7	MAT/03	60	12	-	-	Related or supplementary learning activities	ITA
20410072 - CR410 - CRITTOGRAFIA 1	Also available in another semester or year
20410100 - AC310 - Complex analysis 1 (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	7	MAT/05	60	12	-	-	Related or supplementary learning activities	ITA
20410107 - CR410 - CRITTOGRAFIA 1	Also available in another semester or year

Optional Group: comune Orientamento unico DUE INSEGNAMENTI A SCELTA AMPIA - (show)

20402083 - AL4 - ELEMENTS OF ADVANCED ALGEBRA (objectives) OBTAIN GOOD KNOWLEDGE OF THE CONCEPTS AND METHODS OF THE THEORY OF EQUATIONS IN ONE VARIABLE. UNDERSTAND AND BE ABLE TO APPLY THE “FUNDAMENTAL THEOREM OF CORRESPONDENCE OF GALOIS” IN ORDER STUDY THE “COMPLEXITY” OF A POLYNOMIAL.	7	MAT/02	60	12	-	-	Elective activities	ITA
20402085 - 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	7	MAT/05	60	12	-	-	Elective activities	ITA
20402086 - FM310 - MATHEMATICAL PHYSICS 2	Also available in another semester or year
20402087 - 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	7	MAT/03	60	12	-	-	Elective activities	ITA
20402088 - 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	7	MAT/08	60	12	-	-	Elective activities	ITA
20402089 - IN410 - COMPUTER SCIENCE 2	Also available in another semester or year
20402090 - MC410 - COMPLEMENTARY MATHEMATICS 1 (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	-	-	-	Elective activities	ITA
20402091 - TN410 - INTRODUCTION TO NUMBER THEORY	Also available in another semester or year
20402092 - AN420 - NUMERICAL ANALYSIS 2	Also available in another semester or year
20402093 - CP410 - PROBABILITY 2	Also available in another semester or year
20402094 - AL410 - COMMUTATIVE ALGEBRA (objectives) THE PURPOSE OF THIS COURSE IS TO DEEPEN THE KNOWLEDGE OF SOME TOOLS AND FUNDAMENTAL PROPERTIES OF COMMUTATIVE RINGS AND THEIR MODULES, WITH PARTICULAR EMPHASIS TO THE CASE OF RINGS ARISING IN ALGEBRAIC NUMBER THEORY AND ALGEBRAIC GEOMETRY.	7	MAT/02	60	-	-	-	Elective activities	ITA
20402097 - AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS (objectives) To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations	7	MAT/05	60	-	-	-	Elective activities	ITA
20402101 - CP430 - STOCHASTIC CALCULUS	Also available in another semester or year
20402103 - FM410 - MATHEMATICAL PHYSICS 3 (objectives) To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory	7	MAT/07	60	-	-	-	Elective activities	ITA
20402104 - GE410 - ALGEBRAIC GEOMETRY 1 (objectives) Introduction to the study of topological and geometrical structures defined using algebraic methods. Refinement of the algebraic knowledge using applications to the study of algebraic varieties in affine and projective spaces.	7	MAT/03	60	-	-	-	Elective activities	ITA
20402108 - IN430 - INFORMATICS 4: ADVANCED COMPUTING TECHNIQUES	Also available in another semester or year
20402113 - MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS (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	-	-	-	Elective activities	ITA
20402114 - 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	7	MAT/02	60	-	-	-	Elective activities	ITA
20402115 - ST410 - STATISTICS 1 (objectives) Acquire a good understanding of the basic statistical mathematical methodologies for inference problems and statistical modeling. Develop a knowledge of some specific statistical packages for the practical application of acquired theoretical tools	7	SECS-S/01	60	12	-	-	Elective activities	ITA
20402122 - 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	7	FIS/02	60	-	-	-	Elective activities	ITA
20402123 - MA410 - APPLIED AND INDUSTRIAL MATHEMATICS	Also available in another semester or year
20402249 - CH410 - ELEMENTS OF CHEMISTRY	Also available in another semester or year
20402290 - IN420 - COMPUTER SCIENCE 3, INFORMATION THEORY (objectives) The course of Information Theory is devoted to the study of Shannon's Theory of coding and compressing for reliable communication. The quantitative study of information carried by data communications involves an interest area including statistical inference, natural language processing, cryptography, neurobiology, molecular codes, quantum computing. We will start with basic notions on random variables, and we will prove basic theorems such as channel coding and source coding. We will consider applications to lossless data compression, lossy data compression and channel coding. Several links to cryptography will be provided as well.	7	INF/01	60	-	-	-	Elective activities	ITA
20410031 - MF410 - MATEMATICA FINANZIARIA (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	7	SECS-S/06	60	-	-	-	Elective activities	ITA
20410032 - LM420 - COMPLEMENTI DI LOGICA CLASSICA (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	7	MAT/01	60	-	-	-	Elective activities	ITA
20410034 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	Also available in another semester or year
20410035 - LM430 - TEORIA ASSIOMATICA DEGLI INSIEMI	Also available in another semester or year
20410036 - FM450 - ASPETTI MATEMATICI DELLA MECCANICA QUANTISTICA	Also available in another semester or year
20410037 - GE450 - TOPOLOGIA ALGEBRICA	Also available in another semester or year
20410038 - GRAPH THEORY (objectives) Provide tools and methods for graph theory	7	MAT/03	60	-	-	-	Elective activities	ITA
20410040 - COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY (objectives) Acquire the basic knowledge of biological systems and problems related to their understanding, also in relation to deviations from normal functioning and thus to the insurgence of pathologies. Take care of the modeling aspect as well as of numerical simulation, especially for problems formulated by means of equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful to analyze biological data	7	INF/01	60	-	-	-	Elective activities	ITA
20410044 - FS430 - FISICA 3, RELATIVITA' E TEORIE RELATIVISTICHE	Also available in another semester or year
20410056 - FS410 - LABORATORIO DI DIDATTICA DELLA FISICA	Also available in another semester or year
20410043 - FIRST-ORDER CLASSICAL LOGIC (objectives) To acquire a good knowledge of first order classical logic and its fundamental theorems	7	MAT/01	60	-	-	-	Elective activities	ITA
20410072 - CR410 - CRITTOGRAFIA 1	Also available in another semester or year
20402279 - AC310 – COMPLEX ANALYSIS 1 (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	7	MAT/03	60	12	-	-	Elective activities	ITA
20402100 - CP420 - 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	7	MAT/06	60	-	-	-	Elective activities	ITA
20410073 - IN460 - INFORMATICA 7, GEOMETRIA COMPUTAZIONALE	Also available in another semester or year

Second semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

20402082 - FS220 - PHYSICS 2 (objectives)

FIS/01

Related or supplementary learning activities

ITA

20402131 - SCIENTIFIC ENGLISH (objectives)

Other activities

ITA

Optional Group: comune Orientamento unico DUE INSEGNAMENTI A SCELTA NEL GRUPPO 2 - (show)

20402083 - AL4 - ELEMENTS OF ADVANCED ALGEBRA	Also available in another semester or year
20402085 - AM310 - ELEMENTS OF ADVANCED ANALYSIS	Also available in another semester or year
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	60	12	-	-	Related or supplementary learning activities	ITA
20402087 - GE310 - ELEMENTS OF ADVANCED GEOMETRY	Also available in another semester or year
20402092 - 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	7	MAT/08	60	-	-	-	Related or supplementary learning activities	ITA
20402093 - CP410 - PROBABILITY 2	Also available in another semester or year
20402279 - AC310 – COMPLEX ANALYSIS 1	Also available in another semester or year
20410072 - CR410 - CRITTOGRAFIA 1 (objectives) ACQUIRE GOOD KNOWLEDGE OF THE CONCEPTS AND MATHEMATICAL METHODS OF PUBLIC KEY CRYPTOGRAPHY PROVIDING AN OVERVIEW OF THOSE WHICH ARE CURRENTLY IN USE.	7	MAT/02	60	-	-	-	Related or supplementary learning activities	ITA
20410100 - AC310 - Complex analysis 1	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

Optional Group: comune Orientamento unico DUE INSEGNAMENTI A SCELTA AMPIA - (show)

20401599 - FINAL EXAM (objectives)

225

Final examination and foreign language test

ITA

TOTAL

180

Università Roma Tre

Degree Course: Mathematics A.Y. 2015/2016

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