Università Roma Tre

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 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.

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.

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 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

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.

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 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

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.

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.

A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.

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 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

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 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.

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.

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.

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

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.

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.

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

Acquiring knowledge of the basic principles of General Chemistry and the ability to apply the acquired knowledge to simple problems of Chemistry.

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

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.

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