Course

Credits

Scientific Disciplinary Sector Code

Contact Hours

Exercise Hours

Laboratory Hours

Personal Study Hours

Type of Activity

Language

20402082 
FS220 Physics 2
(objectives)
The course provides the fundamental theoretical knowledge in developing mathematical modeling for electromagnetism, optics and special relativity.

GALLO PAOLA
( syllabus)
Coulomb's law and electrostatic field. Electric work and electrostatic potential, Stokes' theorem, electric dipole. Electric field flux and Gauss' law, Maxwell equations for electrostatics. Conductors and capacitors. Dielectrics, electric displacement field and Maxwell equations for electrostatics with dielectrics. Electric current, Ohm's law, power grids. Magnetic field, Gauss' law, magnetic force. Field sources, Ampere's law, Maxwell's equations for magnetostatics in empty space. Magnetic properties of matter, general equations for magnetostatics and the field H. Time dependent electric and magnetic fields, Faraday's law, AmpereMaxwell's law, Maxwell's equations in vacuum and with matter with charges and currents. Oscillations and alternate currents, RLC circuits. Maxwell's equations and the vector and scalar potentials, Gauge fixing, plane waves, D'Alembert operator and wave equation, pure radiation field. Special relativity, Einstein's relativity principle and Lorentz transformations, Minkowski space, quadrivectors and relativistic invariance. Reflection and refraction of waves. Interference and diffraction, interference of several sources, diffraction from a slit, diffraction grating.
( reference books)
TEXT BOOK
MAZZOLDI P., NIGRO M., VOCI C. "FISICA" VOLUME II [EDISES]
NOTES, PRSENTATIONS AND EXERCISES published on the website of the course http://webusers.fis.uniroma3.it/~gallop/

9

FIS/01

48

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Related or supplementary learning activities

ITA 
Optional group:
SCEGLIERE 1 INSEGNAMENTO (9 cfu) NEL GRUPPO 1  (show)

9








20410426 
IN480  PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for highperformance 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.

Derived from
20410426 IN480  CALCOLO PARALLELO E DISTRIBUITO in Scienze Computazionali LM40 CAMISASCA GAIA
( syllabus)
The education consists of lectures and programming sessions. The main programming language is C.
• Introduction to C • Introduction to High Performance Computing • Key concepts: Hardware Architecture and Memory Hierarchy • Parallelizzation techniques • Measuring parallel performance: theory and benchmark • Version Control of your code: Git software • Parallel programming with MPI: Message Passing Interface • Parallel programming with OpenMP: Open Multiprocessing • Parallel Input/Output • Introduction to GPU computing and OpenCL Programming
( reference books)
Introduction to Parallel Computing: From Algorithms to Programming on StateoftheArt Platforms. Trobec, Slivnik, Bulić, Robič, Springer

9

INF/01

48

24





Related or supplementary learning activities

ITA 
20410427 
IN490  PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the objectoriented paradigm and another nonimperative paradigm.

Derived from
20410427 IN490  LINGUAGGI DI PROGRAMMAZIONE in Scienze Computazionali LM40 LOMBARDI FLAVIO
( syllabus)
The objective of Linguaggi di Programmazione course is to introduce main formal language theory concepts and results as well as their application for programming language classification. Most relevant approaches for syntactic analysis of programming languages are introduced. Learning how to recognize the structure of a programming language and the implementation techniques for the abrstract machine. Understanding the Object Oriented paradigm together with other non imperative approaches.
( reference books)
[1] Maurizio Gabbrielli, Simone Martini,Programming Languages  Principles and paradigms, 2/ed. McGrawHill, (2011). [2] Dean Wampler, Alex Payne, Programming Scala: Scalability = Functional Programming + Objects, 2 edizione. O’Reilly Media, (2014). [3] David Parsons, Foundational Java Key Elements and Practical Programming. Springer Verlag, (2012). Course Slides

9

INF/01

48

24





Related or supplementary learning activities

ITA 

Optional group:
CURRICULUM MODELLISTICO  APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (9 cfu) NEL GRUPPO 2  (show)

9








20410408 
AL310  ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.

Derived from
20410408 AL310  ISTITUZIONI DI ALGEBRA SUPERIORE in Matematica L35 PAPPALARDI FRANCESCO, TOLLI FILIPPO
( syllabus)
Cardano equations for the solvability of third degree equations, rings and fields, the characteristic of a field, reminders of polynomial rings, field extensions, construction of some field extensions, the subring generated by a subset, the subfield generated by a subset, algebraic and transcendental elements, algebraically closed fields.
Splitting fields. Simple extensions and maps between simple extensions, splitting fields, existence of the splitting field, uniqueness except for isomorphisms of the splitting field, multiple roots, formal derivatives, separable polynomials and perfect fields, minimal polynomials and their characterizations.
The fundamental theorem of Galois theory. Group of automorphisms of a field, normal, separable and Galois extensions, characterisations of separable extensions, fundamental theorem of Galois correspondence, examples, Galois group of polynomials, root extensions, solvable groups and the Galois theorem on solving equations, Theorem of the existence of the primitive element.
The calculation of the Galois group. Galois groups as subgroups of S_n, transitive subgroups of S_n, characterization of irreducibility in terms of transitivity, polynomials with Galois groups in A_n, Discriminant theory, Galois groups of polynomials of degree less than or equal to 4, examples of polynomials with Galois group S_p, Dedekind theorem (only statement). Applications of Dedekind's Theorem, how to construct a polynomial with Galois group S_n.
Cyclotomic fields. Definitions, Galois group, under maximal real fields, quadratic subfields, Galois groups, cyclotomic polynomials and their properties, Galois inverse theory for abelian groups.
Finite Fields. Existence and uniqueness of finite fields, Galois group of a finite field, subfields of a finite field, enumeration of irreducible polynomials on finite fields. Construction of the algebraic closure of a finite field with p elements.
Constructions with ruler and compass. Definition of constructible plane points, constructible real numbers, characterization of constructible points in terms of fields, constructible subfields and construction of constructible numbers, cube duplication, angle trisection, circle quadrature and Gauss theorem for constructing regular polygons with ruler and compass.
( reference books)
J. S. Milne,Fields and Galois Theory.Course Notes, (2015).

9

MAT/02

48

24





Core compulsory activities

ITA 
20410409 
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.

Derived from
20410409 AM310  ISTITUZIONI DI ANALISI SUPERIORE in Matematica LM40 BATTAGLIA LUCA, ESPOSITO PIERPAOLO
( syllabus)
Measure theory, outer measures, construction of Borel measures and the Lebesgue measure. Integration theory, limit theorems, convergence in mean and in measure, integration on product spaces, change of variables for the Lebesgue integral. Radon measures, regularity, positive linear functionals, Riesz representation theorem. Signed measures, decomposition theorems, differentiation, BV functions, fundamental theorem of calculus. Lp spaces, basic properties, dual spaces, density theorems.
( reference books)
G. Folland  "Real Analysis"  Wiley

9

MAT/05

48

24





Core compulsory activities

ITA 
20410411 
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.

9

MAT/03

48

24





Core compulsory activities

ITA 
20410412 
MC310  Fundaments of Complementary Mathematics
(objectives)
1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.

9

MAT/04

48

24





Core compulsory activities

ITA 
20410415 
CR410Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of publickey encryption theory, providing an overview of the models which are most widely used in this field.

9

MAT/02

48

24





Core compulsory activities

ITA 
20410449 
GE410  ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces

9

MAT/03

48

24





Core compulsory activities

ITA 
20410417 
IN410Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.

Derived from
20410417 IN410CALCOLABILITÀ E COMPLESSITÀ in Scienze Computazionali LM40 PEDICINI MARCO
( syllabus)
1) Computability, complexity and representability:
 Introduction to decision problems, algorithmic and nonalgorithmic procedures, deterministic computations, discrete procedures, the notion of alphabet, of speech. Decidability and semidecidability of a set. Deterministic, finitary and discrete computations. Formal algorithms: formal definition of algorithm, configurations of input, output, transition function. Example of formalization of an algorithm. Decidability for finished automata. Representation of the automata by matrices. Free Monoid of words. Formal semirings. Nondeterministic finite automata. Regular Languages. Equivalence between deterministic and nondeterministic automata.
 Turing machines: definition, decidability for Turing machine, stopping time, stopping space. Cost of computation. Complexity: worstcase and average case. Independence of decision time from a finite number of input configurations. Complexity functions, complexity classes DTIME and DSPACE (deterministic time and space). Inclusion DTIME (T (n)) ⊂ DSPACE (T (n)) ⊂ DTIME (2 ^ {cT (n)}). Pumping Lemma. Simulation of algorithms, simulation of the half tape Turing machine, simulation of a multitape machine. Special Turing machines. Linear Speedup theorem for Turing machines with an extended alphabet. Evaluation of acceleration coefficient in relation to alphabets. Decisions of natural number sets. Independence from representation. Considerations concerning complexity.
 Turing computability: definition of Turing computable function, characteristic functions of Turing decidable sets, the class of Turing computable functions is closed by composition, concatenation, primitive recursion and minimization. Examples of Turing computable functions. Recursive Functions: equivalence between Turing computability and recursive functions. Ackermann function ([1] chapter 1,2,3,4,5 and [4] chapter 1).
 Timeconstructible functions. The notion of Tclock. Examples of some time constructible function. Closure by composition.
 Nondeterministic Turing machines: characterization through the decidability of projection sets. Definition of the class of polynomial nondeterministic functions. NPcomplete problems.
2) Lambda calculus and functional programming:
 Declarative programming: a historical outline on the lambda calculus, basic definitions, the terms of the lambda calculus, the simple substitution. Relations on the lambda terms. Congruences, transition to the context. αequivalence. alphaequivalence passes to the context. The transitive closure of a relationship, owned by ChurchRosser. Listing of lambdaterms concerning alphaequivalence.
 Definition of betareduction and betaequivalence. ChurchRosser's theorem for betareduction. Normal forms for betareduction. Betareduction strategies. Normalizing strategy: left reduction (left mostouter most). Head reduction. Soluble Terms. Head Normal Forms. Solvability characterization theorem.
 Representation of the recursive functions: lambda definability theorem. Existence of the fixed point for the lambda terms. Church Fixed Point and Curry fixed point.  Representation of other data types in the lambdacalculus: pairs, lists, trees, the solution of recursive equations on lambdaterms ([2] chapters 1, 2, 5).
( reference books)
[1] DEHORNOY, P., COMPLEXITÈ ET DECIDABILITÈ. SPRINGERVERLAG, (1993). [2] KRIVINE, J.L., LAMBDA CALCULUS: TYPES AND MODELS. ELLIS HORWOOD, (1993). [3] SIPSER,M., INTRODUCTION TO THE THEORY OF COMPUTATION.THOMSON COURSE TECHNOLOGY, (2006).

9

MAT/01

48

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Core compulsory activities

ITA 
20410451 
LM410 THEOREMS IN LOGIC 1


204104511 
LM410 THEOREMS IN LOGIC 1  Module A

Derived from
204104511 LM410 TEOREMI SULLA LOGICA 1  MODULO A in Matematica LM40 MAIELI ROBERTO
( syllabus)
Part 1: Some preliminary notions. Order relations and trees, inductive definitions, proofs by induction, axiom of choice and Kőnig's lemma.
Part 2: Provability and satisyability. First order formal language: alphabet, terms, formulas, sequents. Structures for first order languages: structures, terms and formulas with parameters in a structure, value of terms, formulas and sequents. The calculus of sequents for first order logic: Gentzen's LK. Derivable sequents and derivations. Correctness of the rules of LK. Canonical analysis and fundamental theorem: construction of the canonical analysis (with and without cuts) and proof of the fundamental theorem of the canonical analysis. Consequences of the fundamental theorem: completeness theorem, compactness theorem, eliminability of cuts, L"owenheimSkolem's theorem.
Part 3: Towards prooftheory: the cutelimination theorem. The cutelimination procedure. Definition of the elementary steps of cutelimination. First proof strategy (big reduction steps). Second proof strategy (reversion of derivations). The complexity of the cutelimination procedure (sketch). Some immediate consequences of the cutelimination theorem.
( reference books)
Testi: V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014

6

MAT/01

32

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Core compulsory activities

ITA 
204104512 
LM410 THEOREMS IN LOGIC 1  Module B

Derived from
204104512 LM410 TEOREMI SULLA LOGICA 1  MODULO B in Matematica LM40 TORTORA DE FALCO LORENZO
( syllabus)
Proof of the compactness theorem for languages of any cardinality. Languages with equality. The compactness theorem for languages with equality. Correctness and completeness for languages with equality. L"owenheimSkolem's theorem for (denumerable) languages with equality. The limits of the expressive power of first order languages. Elementary equivalence, substructures, elementary substructures. Isomorphsims and elementary equivalence. The notion of substructure. Elementary substructures and diagrams. The preservation theorems. Generalisations of the L"owenheimSkolem's theorem. Completeness of a theory.
( reference books)
V. Michele Abrusci e Lorenzo Tortora de Falco, Logica. Vol. 1 Dimostrazioni e modelli al primo ordine, Springer, 2014

3

MAT/01

16

8





Core compulsory activities

ITA 

Optional group:
CURRICULUM MODELLISTICO  APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (6 cfu) NEL Gruppo 3  (show)

9








20410413 
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.

FERRETTI ROBERTO
( syllabus)
Linear Systems Direst methods: Gaussian elimination. Pivoting strategies. Gaussian elimination as a factorization. Doolittle and Choleshy factorizations. Iterative methods: Jacobi, GaussSeidel, SOR, Richardson, and related convergence results. Comparison of direct vs iterative solvers. Stability of algorithms for the solution of linear systems.
Iterative Methods for Scalar Nonlinear Equations The intermediate zero theorem. The algorithms of bisection, Newton, secants, chords, and related convergence results. (Reference: Chapter 1 excluding Section 1.2.3, and Appendices A.1, A.2)
Approximation of Functions General approximation strategies. Interpolating polynomial in Lagrange and Newton form. Representation of the interpolation error. Convergence of the interpolating polynomial for analytic functions. Refinement strategies in interpolation: Chebyshev nodes, composite approximations. Error estimates. Hermite polynomial, construction and representation of the error. Least Squares approximations. (Reference: Chapter 5 excluding Section 5.2, and Appendix A.4)
Numerical Integration General principles of numerical integration. Polya's Theorem on the convergence of interpolatory quadrature formulae. Closed and open NewtonCotes formulae. Stability results and error estimation. Generalized NewtonCotes formulae and their convergence. Gaussian quadratures and their convergence. (Reference: Chapter 6)
Laboratory Activity C language coding of some of the major algorithms, and in particular: Gaussian elimination, iterative methods for linear systems and scalar equations, Lagrange/Newton interpolation with a refinement strategy.
N.B.: References are provided with respect to the course notes.
( reference books)
Roberto Ferretti, "Appunti del corso di Analisi Numerica", available at the address: http://www.mat.uniroma3.it/users/ferretti/corso.pdf
Roberto Ferretti, "Esercizi d'esame di Analisi Numerica", available at the address: http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf
Slides of the lessons, available from the course page: http://www.mat.uniroma3.it/users/ferretti/bacheca.html

9

MAT/08

48

24





Core compulsory activities

ITA 
20410414 
CP410  Theory of Probability
(objectives)
Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.

CANDELLERO ELISABETTA
( syllabus)
Branching processes, introduction to Sigmaalgebras, measure spaces and probability spaces. Contruction of Lebesgue measure. Pisystems, Dynkin's lemma. Properties of measures, sup and inf limits of events, measurable functions and random variables. BorelCantelli lemmas. Law and distribution of a random variable. Concept of independence. Convergence in probability and almost sure convergence. Skorokhod's representation theorem. Kolmogorov's 01 law. Integrals, their properties and related theorems. Expectation of random variables. Markov, Jensen and Hoelder's inequalities. L^p spaces. Weierstrass' Theorem. Product measures, Fubini's theorem and joint laws. Conditional expectation and its properties. Martingales, predictable processes. Stopping times and stopped processes. Optional stopping theorem, applications to random walks. Theorems about convergence of martingales. Strong law of large numbers. Doob's inequalities for martingales and submartingales, applications. Characteristic functions and inversion theorem. Fourier transform in L^1. Equivalence between convergence in distribution and convergence of characteristic functions. Central limit theorem.
( reference books)
D. Williams, Probability with martingales R. Durrett, Probability: Theory and examples

9

MAT/06

48

24





Core compulsory activities

ITA 

Optional group:
SCEGLIERE 2 INSEGNAMENTI A SCELTA AMPIA (12 cfu)  (show)

12








20410446 
BL410Introduction to Biology
(objectives)
Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods

6

BIO/13

48







Elective activities

ITA 
20410439 
CH410  ELEMENTS OF CHEMISTRY
(objectives)
Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.

Derived from
20401116 ELEMENTI DI CHIMICA in Fisica L30 N0 IUCCI GIOVANNA
( syllabus)
1. ATOMIC THEORY AND ATOMIC STRUCTURE. Atoms, molecules, moles; atomic and molecular weight. Atomic models: Rutheford, Bohr. Quantum theory, quantum numbers and energy levels. Polyelectronic atoms; periodic system. 2. CHEMICAL BONDS. Ionic bond. Covalent bond: and bonds. Polyatomic molecules: molecular structure. Hybridization and resonance. Molecular orbital. Metallic bond. Intermolecular forces. 3. NOMENCLATURE AND CHEMICAL REACTIONS. Oxides, hydroxides, acids, salts, ions. Balancing chemical reactions: redox reactions. 4. STATES OF AGGREGATION. Gas state, ideal gas law. Solid state: ionic, covalent, molecular and metallic solids. Conductors, semiconductors, insulators. Liquid and amorphous states. Phase transitions and phase diagrams. 5. SOLUTIONS. Concentration, colligative properties; electrolyte solutions. 6. THERMODYNAMICS. Matter, energy, heat, first and second principles; enthalpy, entropy, free energy. 7. CHEMICAL EQUILIBRIUM. Equilibrium constant and free energy. Gasphase and heterogeneous equilibria. Le Chatelier’s principle. Van’t Hoff equation. 8. EQUILIBRIA IN SOLUTION. Acidbase equilibria: acids and bases, pH, dissociation constant, polyprotic acids, hydrolysis, buffers. Acidbase titrations and pH indicators. Solubility equilibria: solubility product, common ion effect. 9. ELECTROCHEMISTRY. Batteries, electrode potentials, Nernst’s equation. Electrolysis. 10. CHEMICAL KINETICS. Reaction speed, speed constant. Influence of the temperature on the reaction speed: Arrhenius equation. Catalysts. Numerical exercises on all the listed subjects.
( reference books)
P.W.Atkins, L. Jones; CHEMISTRY: MOLECULES, MATTER, AND CHANGE

6

CHIM/03

52







Elective activities

ITA 
20410416 
FM410Complements of Analytical Mechanics


20410450 
GL410Elements of Geology I
(objectives)
The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.

Derived from
20410384 ELEMENTI DI GEOLOGIA I in Geologia del Territorio e delle Risorse LM74 CIFELLI FRANCESCA
( syllabus)
The environment of celestial bodies; the Solar System; the shape and size of the Earth; the main motions of the Earth (rotation and revolution); the longterm movements of the Earth; the EarthMoon system.
Orientation; time and its measure; the representation of the earth's surface; the geographical coordinates (latitude and longitude), the reading of topographic maps. The shapes of the relief and the modeling of the terrestrial relief; the marine hydrosphere, the continental hydrosphere, the cryosphere; the atmosphere; the climate. The materials of the Earth: the minerals, the lithogenetic processes, the lithogenetic cycle. The evolution of the Earth.
( reference books)
Capire la Terra J.P. Grotzinger, TH Jordan (Terza edizione italiana condotta sulla settima edizione americana)
Il Globo Terrestre e la sua evoluzione E. L. Palmieri e M. Parotto Sesta Edizione (2008)
Educational material distributed during the course

6

GEO/03

48







Elective activities

ITA 
20410440 
ST410Introduction to Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.

6

MAT/06

48

12





Elective activities

ITA 
20410441 
CP420Introduction to 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.

6

MAT/06

48

12





Elective activities

ITA 
20410436 
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, waveparticle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.

Derived from
20410015 MECCANICA QUANTISTICA in Fisica L30 LUBICZ VITTORIO, TARANTINO CECILIA
( syllabus)
Quantum mechanics: The crisis of classical physics. Waves and particles. State vectors and operators. Measurements and observables. The position operator. Translations and momentum. Time evolution and the schrodinger equation. Parity. Onedimensional problems. Harmonic oscillator. Symmetries and conservation laws. Time independent perturbation theory. Time dependent perturbation theory.
( reference books)
Lecture notes available on the course website
J.J. Sakurai, Jim Napolitano  Meccanica Quantistica Moderna  Seconda Edizione [Zanichelli, Bologna, 2014] An english version of the book is also available: Sakurai J.J., Modern Quantum Mechanics (Revised Edition) [AddisonWesley, 1994]

6

FIS/02

60







Elective activities

ITA 
20410421 
AN430 Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.

Derived from
20410421 AN430  METODO DEGLI ELEMENTI FINITI in Scienze Computazionali LM40 TERESI LUCIANO
( syllabus)
The purpose of this course is to give a brief introduction to the Finite Elements Method (FEM), a gold standard for the numerical solution of PDEs systems. Oddly enough, the widespread use of the FEM is not accompanied by an adequate knowledge of the mathematical framework underlying the method. This course, starting from the weak formulation of balance equations, will give an overview of the techniques used to reduce a differential problem into an algebraic one. During the course, some selected problems in mechanics and physics will be solved, 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 Moreover, the students will be introduced to the use COMSOL Multiphysics, a scientific software for numerical simulations based on the Finite Element Method.
( reference books)
1) Integral Form at a Glance, note a cura del docente
2) When functions have no value(s): Delta functions and distributions Steven G. Johnson, MIT course 18.303 notes, 2011
3) Understanding and Implementing the Finite Elements Method Mark S. Gockenbach, SIAM, 2006 Cap. 1 Some model PDE’s Cap. 2 The weak form of a BVP Cap. 3 The Galerkin method Cap. 4 Piecewise polynomials and the finite element method (sections 4.1, 4.2) Cap. 5 Convergence of the finite element method (sections 5.1 ~ 5.4)

6

MAT/08

48

12





Elective activities

ITA 
20410457 
CP430  STOCHASTIC CALCULUS
(objectives)
Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.

6

MAT/06

48

12





Elective activities

ITA 
20410435 
FS440  Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.

Derived from
20401070 ACQUISIZIONE DATI E CONTROLLO DI ESPERIMENTI in Fisica LM17 N0 RUGGIERI FEDERICO
( syllabus)
The aim of the course is to provide the student with the general cognitive elements underlying the acquisition, control and monitoring systems of Nuclear and Subnuclear Physics experiments. The course is divided into the following topics: Introduction to DAQParallelism and Pipelining systems DerandomizationDAQ and TriggerData Transmission Front End ElectronicsTriggerArchitecture Computing SystemsReal Time SystemsReal Time Operating Systems C LanguageTCP / IP Network ProtocolsDAQArchitecture Building VME BusRun ControlFarmingData Archiving During the course, laboratory exercises will take place with the execution of simple examples of:  reading and data transfer systems through pipe mechanisms with concurrent processes;  signalbased trigger simulation programs;  Run Control program for activation and termination of processes;  configuration and reading of data from board on VME bus.
( reference books)
Lecture notes prepared by the teacher on the basis of the slides presented and available on the Moodle server: https://matematicafisica.el.uniroma3.it

6

FIS/04

60







Elective activities

ITA 
20410469 
AM430  ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.

Derived from
20410469 AM430  EQUAZIONI DIFFERENZIALI ORDINARIE in Matematica LM40 PROCESI MICHELA
( syllabus)
Local existence and uniqueness theorems, existence times and extensions. Escape from compact sets. Comparison theorems. Behavior of linear systems with constant coefficients. Jordan canonical form. Differentiable functions on a Banach space. The Implicit Function Theorem. Applications to the search of periodic solutions. Lyapunov Schmidt decomposition. Hopf theorem. Dependence on initial data. The flow box theorem. Coordinate changes generated by the flow of a vector field. The Lie exponential. Poincare normal form.
( reference books)
Note del docente. Chierchia Analisi Matematica 2

6

MAT/05

48

12





Elective activities

ITA 
20410465 
GE450  TOPOLOGIA ALGEBRICA
(objectives)
To explain ideas and methods of algebraic topology, among which cohomology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis)

6

MAT/03

48

12





Elective activities

ITA 
