Università Roma Tre

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.

TO OBTAIN A SOLID KNOWLEDGE OF HOLOMORPHIC AND MEROMORPHIC FUNCTIONS OF ONE COMPLEX VARIABLE AND OF THEIR MAIN PROPERTIES. TO DEVELOP PRACTICAL SKILLS IN THE USE OF COMPLEX FUNCTIONS, ESPECIALLY IN COMPLEX INTEGRATION AND IN COMPUTATION OF REAL DEFINITE INTEGRALS.

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.

To acquire deep understanding of the principal geometry arguments treated in high-school mathematics

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.

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.

Acquiring a good knowledge of basic concepts and tools in ODE’s.

INTRODUCTION TO THE ADVANCED THEORY OF MARKOV CHAINS, WITH SPECIAL EMPHASIS ON THE TOPIC OF CONVERGENCE TO EQUILIBRIUM AND ITS APPLICATIONS.

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.

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.

WE STUDY THE GEOMETRY OF SURFACES IN EUCLIDEAN THREE-SPACE. THIS GIVES THE STUDENT CONCRETE EXAMPLES FOR THE NOTION OF CURVATURE IN GEOMETRY. WE USE METHODS OF MULTIVARIABLE CALCULUS, LINEAR ALGEBRA AND TOPOLOGY THUS GIVING THE STUDENTS A GOOD VIEW OF SOME ASPECTS OF MATHEMATICS. THE SOFTWARE “MATHEMATICA” IS ALSO USED TO VISUALIZE AND COMPUTE GEOMETRIC FEATURES OF SURFACES IN SPACE.

Nowadays, information is often stored and transmitted electronically. Ensuring the security of the vast and complex infrastructure of computers, servers and networks is an immense challenge. In this scenario, this course aims at describing:
- The relationship between number theory and information security techniques;
- How to protect networks, secure electronic assets, prevent attacks, ensure the privacy of computer users, and build secure infrastructures.

Problem solving with examples from secondary school mathematical curricula, with the help of a computer and a direct use of numerical and symbolic calculus and dynamical geometry software (MATHEMATICA, introduction on CABRI and GEOGEBRA).
All examples, in an interactive and “laboratorial” lessons, point at experience limits and opportunities of using computers at school on selected arguments like numerical approximation or visualization in geometry as well as analysis.

To acquire deep understanding of some of the principal arguments treated in high-school mathematics

The purpose of this course is to introduce mathematical statistics and statistical inference to students with good backgrounds in mathematics. Starting from the basic of probability this course, develop the theory of statistical inference using techniques, definition and concepts that are statistical and natural extensions and consequences of previous concepts. Purpose of this course it’s also to introduce students to the use of statistical software.

TO PROVIDE THE BASIC KNOWLEDGE OF THEORETHICAL PHYSICS WITH RESPECT TO SPECIAL RELATIVITY, RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY AND QED.

TO KNOW – AT A GRADUATE LEVEL – RESULTS ON LOGIC, INDEED MATHEMATICAL THEOREMS ON LOGIC, WHICH ARE AT THE BASIS OF THE INTERACTION BETWEEN LOGIC, COMPUTER SCIENCES AND OTHER SCIENCES (IN PARTICUALR, COMMUNICATION SCIENCES).

Application of the compactness theorem, Löwenheim-Skolem’s theorem. Basic recursion theory, decidability. Completeness and decidability of a first order theory, examples. Peano’s arithmetic and Gödel’s incompleteness theorems.

GAIN KNOWLEDGE OF THE BASIC PRINCIPLES OF QUANTUM MECHANICS APPLIED TO SIMPLE PHYSICAL SYSTEMS

The course aims to improve the mathematical culture of the student and to give him further tools for preparing his specific final dissertation to obtain the degree.

The student is going to acquire the ability to read a scientific text in English, or , if he or she chooses, in any other European tongue.

The student will become familiar with the operation of computers: punched cards, magnetic tape data storage, ferrite core memory, etc.

An introduction to problems and methods of nonlinear analysis.

LEARNING THE BASICS OF SPECTRAL THEORY FOR LINEAR OPERATORS LIMITED, WITH APPLICATIONS TO DIFFERENTIAL PROBLEMS.

Detaled study of homology and Cohomology of topological spaces bia techniques of algebra and homological algebra.

TO ACQUIRE A SOLID KNOWLEDGE OF HOLOMORPHIC AND MEROMORPHIC FUNCTIONS OF ONE COMPLEX VARIABLE AND THEIR MAIN PROPERTIES. TO DEVELOP PRACTICAL SKILLS IN THE USE OF COMPLEX FUNCTIONS, ESPECIALLY IN COMPLEX INTEGRATION AND IN COMPUTATION OF REAL DEFINITE INTEGRALS.

Study of graphs by means of combinatorial, topological and algebraic techniques.

The student is going to learn the basics of the Lebesgue integration theory: measure spaces, measurability, Lebesgue integral, L^p spaces, differentiation.

The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations

A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.

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.

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.

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.

This course is an introduction to the methods and techniques of Algebraic Number Theory, with applications to the study of some classical problems.

This course is an introduction to Multiplicative Ideal Theory, with applications to the study of Dedekind, Prüfer and Krull domains.

To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations

Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.

ACQUIRE GOOD KNOWLEDGE OF THE CONCEPTS AND MATHEMATICAL METHODS OF PUBLIC KEY CRYPTOGRAPHY PROVIDING AN OVERVIEW OF THOSE WHICH ARE CURRENTLY IN USE.

We present an introduction to Riemannian Geometry based on the study of geodesics. We prove selected results showing some relations between curvature and topology.

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.

THE COURSE IN430 – COMPUTER SCIENCE 4, ADVANCED COMPUTATIONAL TECHNIQUES IS FOCUSED ON THE ACQUISITION OF OBJECT ORIENTED PROGRAMMING LANGUAGES AND APPLICATION OF CONCEPTUAL TOOLS FOR ANALYSIS AND DEVELOPMENT IN OBJECT ORIENTEND PROGRAMMING. THIS COURSE INCLUDES AN INTRODUCTION TO MODELING AND DESIGN OF CLASSES THROUGH UML DIAGRAMS, AND THE STUDY OF SPECIFICATION AND IMPLEMENTATION OF ALGORITHMS FOR GRAPH ANALYSIS.

The aim of the course is to acquire skills on resolution techniques for combinatorial optimization problems, deepening the skills on graph theory, advanced technical skills for design, analysis and computer implementation of algorithms for solving optimization problems on graphs, trees and networks.

The course of Algorithms in cryptography is devoted to the study of encryption systems and their properties. In particular, we will study methods and algorithms developed to verify security level of cryptosystems, both from the point of view of formal verification (in the context of protocols) and from the point of view of cryptanalysis. Required as prerequisites are a basic level of computer knowledge of a Unix-like operating system (eg Linux) and programming in C or Java.

This course enables the student to:
1) Reach an understanding of the origin and evolution of mathematical thought in different historical and cultural contexts.
2) Consider the development of mathematics as a discipline and the relationship with philosophical thought, with the natural sciences and with technology and praxis.
3) Develop a cultural view of the role of mathematics in the contemporary world, including its transmission and matematical education.

Acquire knowledge of the principles and methods of analytic number theory, with particular emphasis on the distribution of prime numbers, prime numbers in arithmetic progression and analytical properties of the Riemann zeta dela fiction. Possibly, we will illustrate some of the techniques used in the proof of Theorem of Bombieri Vinogradov

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.

The axioms of Zermelo-Fraenkel. Odinal numbers. The axiom of foundation. The axiom of choice. The cardinal numbers and the continuum hypothesis.

CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.

Acquiring technics and methods for studying and constructing periodic/quasi-periodic solutions for Hamiltonian systems (resonance analysis, small divisor problems, KAM theory, Nekhoroshev theory, etc.)

The course aims to improve the mathematical culture of the student and to give him further tools for preparing his specific final dissertation to obtain the degree.

The student is going to acquire the ability to read a scientific text in English, or , if he or she chooses, in any other European tongue.

The student will become familiar with the operation of computers: punched cards, magnetic tape data storage, ferrite core memory, etc.

The course provides a rigorous introduction to financial economic problems using mathematical methods, including the portfolio decision of an investor and the determination of the no-arbitrage price of stocks in both discrete and continuous time. The pricing of derivative securities in continuous time including various stock and interest rate options will also be included. Specific topics include derivative strategies, financial risk management techniques. The course aims to deepen the students' understanding of important concepts of mathematics of finance, the valuation of financial securities, capital investment evaluation and the estimation of required rates of return.

THE COURSE IS INTENDED TO REVIEW THE BASIC CONCEPTS IN THE NUMERICAL APPROXIMATION OF PARTIAL DIFFERENTIAL EQUATIONS (PDES), WITH RESPECT TO BOTH THEIR CONSTRUCTION (FINITE DIFFERENCES, FINITE ELEMENTS, SPECTRAL) AND THEIR CONVERGENCE ANALYSIS.

DE RHAM COHOMOLOGY OF SMOOTH MANIFOLDS. STOKES’ THEOREM FOR MANIFOLDS WITH BOUNDARY.

ADVANCED COURSE IN GROUP THEORY. THE INTENT IS TO DEEPEN THE MAIN GROUP THEORY CONCEPTS STUDIED IN AL210, ALSO THROUGH SEMINARS GIVEN BY STUDENTS ABOUT TOPICS IN FINITE GROUP AND FREE GROUP THEORY.

OBTAIN KNOWLEDGE OF CLASSICAL ALGEBRAIC GEOMETRY TOPICS FROM A HIGHER POINT OF VIEW

THE COURSE IS INTENDED TO REVIEW THE BASIC CONCEPTS IN THE NUMERICAL APPROXIMATION OF PARTIAL DIFFERENTIAL EQUATIONS (PDES), WITH RESPECT TO BOTH THEIR CONSTRUCTION (FINITE DIFFERENCES, FINITE ELEMENTS, SPECTRAL) AND THEIR CONVERGENCE ANALYSIS.

Acquire knowledge of the principles and methods of analytic number theory, with particular emphasis on the distribution of prime numbers, prime numbers in arithmetic progression and analytical properties of the Riemann zeta dela fiction. Possibly, we will illustrate some of the techniques used in the proof of Theorem of Bombieri Vinogradov

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.

TO OBTAIN A SOLID KNOWLEDGE OF HOLOMORPHIC AND MEROMORPHIC FUNCTIONS OF ONE COMPLEX VARIABLE AND OF THEIR MAIN PROPERTIES. TO DEVELOP PRACTICAL SKILLS IN THE USE OF COMPLEX FUNCTIONS, ESPECIALLY IN COMPLEX INTEGRATION AND IN COMPUTATION OF REAL DEFINITE INTEGRALS.

A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.

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.

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.

To acquire deep understanding of the principal geometry arguments treated in high-school mathematics

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.

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.

To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations

Acquiring a good knowledge of basic concepts and tools in ODE’s.

INTRODUCTION TO THE ADVANCED THEORY OF MARKOV CHAINS, WITH SPECIAL EMPHASIS ON THE TOPIC OF CONVERGENCE TO EQUILIBRIUM AND ITS APPLICATIONS.

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.

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.

WE STUDY THE GEOMETRY OF SURFACES IN EUCLIDEAN THREE-SPACE. THIS GIVES THE STUDENT CONCRETE EXAMPLES FOR THE NOTION OF CURVATURE IN GEOMETRY. WE USE METHODS OF MULTIVARIABLE CALCULUS, LINEAR ALGEBRA AND TOPOLOGY THUS GIVING THE STUDENTS A GOOD VIEW OF SOME ASPECTS OF MATHEMATICS. THE SOFTWARE “MATHEMATICA” IS ALSO USED TO VISUALIZE AND COMPUTE GEOMETRIC FEATURES OF SURFACES IN SPACE.

Problem solving with examples from secondary school mathematical curricula, with the help of a computer and a direct use of numerical and symbolic calculus and dynamical geometry software (MATHEMATICA, introduction on CABRI and GEOGEBRA).
All examples, in an interactive and “laboratorial” lessons, point at experience limits and opportunities of using computers at school on selected arguments like numerical approximation or visualization in geometry as well as analysis.

To acquire deep understanding of some of the principal arguments treated in high-school mathematics

The purpose of this course is to introduce mathematical statistics and statistical inference to students with good backgrounds in mathematics. Starting from the basic of probability this course, develop the theory of statistical inference using techniques, definition and concepts that are statistical and natural extensions and consequences of previous concepts. Purpose of this course it’s also to introduce students to the use of statistical software.

TO PROVIDE THE BASIC KNOWLEDGE OF THEORETHICAL PHYSICS WITH RESPECT TO SPECIAL RELATIVITY, RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY AND QED.

TO KNOW – AT A GRADUATE LEVEL – RESULTS ON LOGIC, INDEED MATHEMATICAL THEOREMS ON LOGIC, WHICH ARE AT THE BASIS OF THE INTERACTION BETWEEN LOGIC, COMPUTER SCIENCES AND OTHER SCIENCES (IN PARTICUALR, COMMUNICATION SCIENCES).

Application of the compactness theorem, Löwenheim-Skolem’s theorem. Basic recursion theory, decidability. Completeness and decidability of a first order theory, examples. Peano’s arithmetic and Gödel’s incompleteness theorems.

GAIN KNOWLEDGE OF THE BASIC PRINCIPLES OF QUANTUM MECHANICS APPLIED TO SIMPLE PHYSICAL SYSTEMS

The course aims to improve the mathematical culture of the student and to give him further tools for preparing his specific final dissertation to obtain the degree.

The student is going to acquire the ability to read a scientific text in English, or , if he or she chooses, in any other European tongue.

The student will become familiar with the operation of computers: punched cards, magnetic tape data storage, ferrite core memory, etc.

An introduction to problems and methods of nonlinear analysis.

LEARNING THE BASICS OF SPECTRAL THEORY FOR LINEAR OPERATORS LIMITED, WITH APPLICATIONS TO DIFFERENTIAL PROBLEMS.

TO ACQUIRE A SOLID KNOWLEDGE OF HOLOMORPHIC AND MEROMORPHIC FUNCTIONS OF ONE COMPLEX VARIABLE AND THEIR MAIN PROPERTIES. TO DEVELOP PRACTICAL SKILLS IN THE USE OF COMPLEX FUNCTIONS, ESPECIALLY IN COMPLEX INTEGRATION AND IN COMPUTATION OF REAL DEFINITE INTEGRALS.

Study of graphs by means of combinatorial, topological and algebraic techniques.

The student is going to learn the basics of the Lebesgue integration theory: measure spaces, measurability, Lebesgue integral, L^p spaces, differentiation.

The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations

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.

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.

This course is an introduction to the methods and techniques of Algebraic Number Theory, with applications to the study of some classical problems.

This course is an introduction to Multiplicative Ideal Theory, with applications to the study of Dedekind, Prüfer and Krull domains.

Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.

ACQUIRE GOOD KNOWLEDGE OF THE CONCEPTS AND MATHEMATICAL METHODS OF PUBLIC KEY CRYPTOGRAPHY PROVIDING AN OVERVIEW OF THOSE WHICH ARE CURRENTLY IN USE.

We present an introduction to Riemannian Geometry based on the study of geodesics. We prove selected results showing some relations between curvature and topology.

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.

THE COURSE IN430 – COMPUTER SCIENCE 4, ADVANCED COMPUTATIONAL TECHNIQUES IS FOCUSED ON THE ACQUISITION OF OBJECT ORIENTED PROGRAMMING LANGUAGES AND APPLICATION OF CONCEPTUAL TOOLS FOR ANALYSIS AND DEVELOPMENT IN OBJECT ORIENTEND PROGRAMMING. THIS COURSE INCLUDES AN INTRODUCTION TO MODELING AND DESIGN OF CLASSES THROUGH UML DIAGRAMS, AND THE STUDY OF SPECIFICATION AND IMPLEMENTATION OF ALGORITHMS FOR GRAPH ANALYSIS.

The aim of the course is to acquire skills on resolution techniques for combinatorial optimization problems, deepening the skills on graph theory, advanced technical skills for design, analysis and computer implementation of algorithms for solving optimization problems on graphs, trees and networks.

The course of Algorithms in cryptography is devoted to the study of encryption systems and their properties. In particular, we will study methods and algorithms developed to verify security level of cryptosystems, both from the point of view of formal verification (in the context of protocols) and from the point of view of cryptanalysis. Required as prerequisites are a basic level of computer knowledge of a Unix-like operating system (eg Linux) and programming in C or Java.

Nowadays, information is often stored and transmitted electronically. Ensuring the security of the vast and complex infrastructure of computers, servers and networks is an immense challenge. In this scenario, this course aims at describing:
- The relationship between number theory and information security techniques;
- How to protect networks, secure electronic assets, prevent attacks, ensure the privacy of computer users, and build secure infrastructures.

This course enables the student to:
1) Reach an understanding of the origin and evolution of mathematical thought in different historical and cultural contexts.
2) Consider the development of mathematics as a discipline and the relationship with philosophical thought, with the natural sciences and with technology and praxis.
3) Develop a cultural view of the role of mathematics in the contemporary world, including its transmission and matematical education.

Acquire knowledge of the principles and methods of analytic number theory, with particular emphasis on the distribution of prime numbers, prime numbers in arithmetic progression and analytical properties of the Riemann zeta dela fiction. Possibly, we will illustrate some of the techniques used in the proof of Theorem of Bombieri Vinogradov

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.

The axioms of Zermelo-Fraenkel. Odinal numbers. The axiom of foundation. The axiom of choice. The cardinal numbers and the continuum hypothesis.

CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.

Acquiring technics and methods for studying and constructing periodic/quasi-periodic solutions for Hamiltonian systems (resonance analysis, small divisor problems, KAM theory, Nekhoroshev theory, etc.)

The course aims to improve the mathematical culture of the student and to give him further tools for preparing his specific final dissertation to obtain the degree.

The student is going to acquire the ability to read a scientific text in English, or , if he or she chooses, in any other European tongue.

The student will become familiar with the operation of computers: punched cards, magnetic tape data storage, ferrite core memory, etc.

The course provides a rigorous introduction to financial economic problems using mathematical methods, including the portfolio decision of an investor and the determination of the no-arbitrage price of stocks in both discrete and continuous time. The pricing of derivative securities in continuous time including various stock and interest rate options will also be included. Specific topics include derivative strategies, financial risk management techniques. The course aims to deepen the students' understanding of important concepts of mathematics of finance, the valuation of financial securities, capital investment evaluation and the estimation of required rates of return.

THE COURSE IS INTENDED TO REVIEW THE BASIC CONCEPTS IN THE NUMERICAL APPROXIMATION OF PARTIAL DIFFERENTIAL EQUATIONS (PDES), WITH RESPECT TO BOTH THEIR CONSTRUCTION (FINITE DIFFERENCES, FINITE ELEMENTS, SPECTRAL) AND THEIR CONVERGENCE ANALYSIS.

DE RHAM COHOMOLOGY OF SMOOTH MANIFOLDS. STOKES’ THEOREM FOR MANIFOLDS WITH BOUNDARY.

ADVANCED COURSE IN GROUP THEORY. THE INTENT IS TO DEEPEN THE MAIN GROUP THEORY CONCEPTS STUDIED IN AL210, ALSO THROUGH SEMINARS GIVEN BY STUDENTS ABOUT TOPICS IN FINITE GROUP AND FREE GROUP THEORY.

OBTAIN KNOWLEDGE OF CLASSICAL ALGEBRAIC GEOMETRY TOPICS FROM A HIGHER POINT OF VIEW

Detaled study of homology and Cohomology of topological spaces bia techniques of algebra and homological algebra.

THE COURSE IS INTENDED TO REVIEW THE BASIC CONCEPTS IN THE NUMERICAL APPROXIMATION OF PARTIAL DIFFERENTIAL EQUATIONS (PDES), WITH RESPECT TO BOTH THEIR CONSTRUCTION (FINITE DIFFERENCES, FINITE ELEMENTS, SPECTRAL) AND THEIR CONVERGENCE ANALYSIS.

Acquire knowledge of the principles and methods of analytic number theory, with particular emphasis on the distribution of prime numbers, prime numbers in arithmetic progression and analytical properties of the Riemann zeta dela fiction. Possibly, we will illustrate some of the techniques used in the proof of Theorem of Bombieri Vinogradov