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

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) THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.	7	MAT/08	60	12	-	-	Related or supplementary learning activities	ITA
20402089 - IN410 - COMPUTER SCIENCE 2 (objectives) The course Theory of Computation and Interaction provides a in-deep view of theoretical aspects related to the concept of computation and the study of relations between different models of computation. The basic knowledge on information technology is here extended with new concepts and theoretical viewpoints. The course is divided into two units of 6 CFU. At choice, the student can decide to pass the first unit or both (12 CFU). More specifically, the course provides a formal presentation of the concepts of algorithm and computability. After the introduction of the classical concept of computability as formalized by Alan M. Turing, we address the basic concepts of algorithmic complexity and problem decidability, functional models and functional programming. In the second unit, we focus on interactive paradigms in the theory of computation which allow the description of additional complexity classes and their use in the semantics of programming languages.	7	INF/01	60	12	-	-	Related or supplementary learning activities	ITA
20402090 - MC410 - COMPLEMENTARY MATHEMATICS 1 (objectives) To acquire deep understanding of the principal geometry arguments treated in high-school 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

20402081 - FM210 - MATHEMATICAL PHYSICS 1 (objectives)

MAT/07

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)

THIRD YEAR

First semester

Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

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) The student is going to learn the basics of the Lebesgue integration theory: measure spaces, measurability, Lebesgue integral, L^p spaces, differentiation.	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) A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.	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
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)

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	72	-	-	-	Elective activities	ITA
20402085 - AM310 - ELEMENTS OF ADVANCED ANALYSIS (objectives) The student is going to learn the basics of the Lebesgue integration theory: measure spaces, measurability, Lebesgue integral, L^p spaces, differentiation.	7	MAT/05	72	-	-	-	Elective activities	ITA
20402086 - FM310 - MATHEMATICAL PHYSICS 2	Also available in another semester or year
20402087 - GE310 - ELEMENTS OF ADVANCED GEOMETRY (objectives) A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.	7	MAT/03	72	-	-	-	Elective activities	ITA
20402088 - AN410 - NUMERICAL ANALYSIS 1 (objectives) THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.	7	MAT/08	72	-	-	-	Elective activities	ITA
20402089 - IN410 - COMPUTER SCIENCE 2 (objectives) The course Theory of Computation and Interaction provides a in-deep view of theoretical aspects related to the concept of computation and the study of relations between different models of computation. The basic knowledge on information technology is here extended with new concepts and theoretical viewpoints. The course is divided into two units of 6 CFU. At choice, the student can decide to pass the first unit or both (12 CFU). More specifically, the course provides a formal presentation of the concepts of algorithm and computability. After the introduction of the classical concept of computability as formalized by Alan M. Turing, we address the basic concepts of algorithmic complexity and problem decidability, functional models and functional programming. In the second unit, we focus on interactive paradigms in the theory of computation which allow the description of additional complexity classes and their use in the semantics of programming languages.	7	INF/01	60	12	-	-	Elective activities	ITA
20402090 - MC410 - COMPLEMENTARY MATHEMATICS 1 (objectives) To acquire deep understanding of the principal geometry arguments treated in high-school 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 (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	-	-	-	Elective activities	ITA
20402094 - AL410 - COMMUTATIVE ALGEBRA	Also available in another semester or year
20402097 - AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS	Also available in another semester or year
20402101 - CP430 - STOCHASTIC CALCULUS	Also available in another semester or year
20402103 - FM410 - MATHEMATICAL PHYSICS 3	Also available in another semester or year
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	Also available in another semester or year
20402114 - ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW	Also available in another semester or year
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) THE COURSE AIMS TO PROVIDE A BASIC KNOWLEDGE OF QUANTUM MECHANICS, DISCUSSING THE MAIN EXPERIMENTAL EVIDENCES AND THE FOLLOWING THEORETICAL INTERPRETATIONS WHICH LED TO THE CRISIS OF CLASSICAL PHYSICS AND ILLUSTRATING ITS FUNDAMENTAL PRINCIPLES: THE CONCEPT OF PROBABILITY, THE WAVE-PARTICLE DUALITY, THE UNCERTAINTY PRINCIPLE. THE QUANTUM DYNAMICS, THE SCHRODINGER EQUATION AND ITS RESOLUTION FOR SOME PHYSICAL RELEVANT SYSTEMS WILL BE 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 (objectives) Acquiring knowledge of the basic principles of General Chemistry and the ability to apply the acquired knowledge to simple problems of Chemistry.	7	CHIM/03	60	-	-	-	Elective activities	ITA
20402290 - IN420 - COMPUTER SCIENCE 3, INFORMATION THEORY	Also available in another semester or year
20410031 - MF410 - MATEMATICA FINANZIARIA	Also available in another semester or year
20410032 - LM420 - COMPLEMENTI DI LOGICA CLASSICA	Also available in another semester or year
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 of 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) Obtain a good understanding of the principles of the classical logic of the first order and the sequencing of sequences for it, as well as of the main results that concern it.	7	MAT/01	60	-	-	-	Elective activities	ITA
20402095 - AL420 - ALGEBRAIC THEORY OF NUMBERS	Also available in another semester or year
20402098 - AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS	Also available in another semester or year
20402100 - CP420 - STOCHASTIC PROCESSES	Also available in another semester or year
20402106 - GE430 - DIFFERENTIAL GEOMETRY 2	Also available in another semester or year
20402110 - IN450 - INFORMATICS 6: 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	7	INF/01	60	-	-	-	Elective activities	ITA
20410073 - IN460 - INFORMATICA 7, GEOMETRIA COMPUTAZIONALE	Also available in another semester or year
20402291 - ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS	Also available in another semester or year
20410100 - AC310 - Complex analysis 1	Also available in another semester or year
20410094 - GE470 - Riemann surfaces	Also available in another semester or year
20402280 - AN430 – NUMERICAL ANALYSIS 3 (objectives) Introduce to the main techniques used for Numerical Analysis applications to partial differential equations, such as the finite difference and variational methods	7	MAT/08	60	-	-	-	Elective activities	ITA
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	-	-	-	Elective activities	ITA
20410068 - MATHEMATICS OF FINANCIAL MARKETS (objectives) Acquire knowledge of the basic notions of financial mathematics. Deepen the valuation of financial assets and bonds, the forward rate structure of interest rates. Studying CAPM and APT Templates for portfolio choices, utility functions, stock price dynamics in discrete and continuous time, valuation of derivatives	7	SECS-S/06	60	-	-	-	Elective activities	ITA
20410069 - FS410 - LABORATORIO DI DIDATTICA DELLA FISICA	Also available in another semester or year
20410074 - LM430 - TEORIA ASSIOMATICA DEGLI INSIEMI	Also available in another semester or year
20410070 - LOGIC AND ARITHMETIC (objectives) To deepen the knowledge of the main results of the classical logic of the first order and study some of their significant consequences.	7	MAT/01	60	-	-	-	Elective 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	-	-	Elective activities	ITA

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) 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	-	-	-	Related or supplementary learning activities	ITA
20402093 - CP410 - PROBABILITY 2	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)

20401599 - FINAL EXAM (objectives)

225

Final examination and foreign language test

ITA

TOTAL

180

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