Degree Course: Computational Sciences
A.Y. 2022/2023
Conoscenza e capacità di comprensione
I laureati magistrali in Scienze Computazionali avranno ampie conoscenze nei settori della matematica applicata, dell'informatica e del calcolo scientifico in generale.
Inoltre, avranno ottime capacità nell'utilizzare le conoscenze acquisite per affrontare e risolvere problemi di varia natura in contesti applicativi, anche nell'ambito di altre scienze, quali l'ingegneria, la fisica e le scienze naturali.
Lo strumento didattico per il raggiungimento di tali obiettivi sono le lezioni, le esercitazioni, i seminari e le attività di laboratorio e tutorato.
La verifica avviene in forma classica attraverso la valutazione di un elaborato scritto e/o un colloquio orale.Capacità di applicare conoscenza e comprensione
I laureati sapranno elaborare o applicare competenze sia per ideare argomentazioni che per risolvere problemi applicativi.
Essi saranno capaci di estrarre informazioni qualitative da dati quantitativi, comprendere, utilizzare e progettare metodi teorici e/o computazionali adeguati; utilizzare in maniera efficace strumenti informatici; gestire ambienti di calcolo ad alte prestazioni.
Lo strumento didattico per il raggiungimento di tali obiettivi sono le lezioni, le esercitazioni, i seminari e le attività di laboratorio e tutorato.
La verifica del raggiungimento degli obiettivi posti avviene di norma mediante:
· le varie prove svolte durante gli insegnamenti impartiti e alla loro conclusione;
· l'esposizione e la discussione dei risultati conseguiti durante la preparazione della prova finale.Autonomia di giudizio
I laureati magistrali in Scienze Computazionali dovranno:
(a) sapere collegare tra loro i diversi concetti matematici, tenendo presente la struttura logica e gerarchica della matematica;
(b) essere in grado di valutare l'appropriatezza di un modello o di una teoria matematica nella descrizione di un fenomeno concreto;
(c) essere in grado di utilizzare strumenti informatici, sia software che hardware, in contesti applicativi;
(d) essere in grado di fare ricerche bibliografiche autonome utilizzando pubblicazioni di contenuto matematico, sviluppando anche una familiarità con le riviste scientifiche di settore;
(e) essere in grado di utilizzare per la ricerca scientifica gli archivi elettronici disponibili sul web, operando la necessaria selezione dell'informazione disponibile;
(f) avere esperienza di lavoro di gruppo, ma anche capacità di lavorare bene autonomamente.
Tutte le attività formative del Corso di Laurea Magistrale in Scienze Computazionali concorrono al raggiungimento degli obiettivi (a) che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Attività specifiche di questo corso di laurea dedicano una grande attenzione verso gli aspetti computazionali e le applicazioni della matematica e dell’informatica, e concorrono al raggiungimento degli obiettivi (b, c).
Le attività di tipo seminariale o di preparazione alle prove scritte sono tipicamente svolte in piccoli gruppi, mentre in altre attività formative prevale il lavoro autonomo dello studente in modo da permettere il raggiungimento degli obiettivi (d), (e) ed (f).
Abilità comunicative
I laureati magistrali in Scienze Computazionali dovranno essere in grado di:
(a) comunicare problemi, idee e soluzioni riguardanti settori avanzati del calcolo scientifico, sia sul versante della matematica applicata che su quello dell’informatica, a un pubblico specializzato o generico, nella propria lingua e in inglese, sia in forma scritta che orale;
(b) dialogare con esperti di altri settori, riconoscendo la possibilità di formalizzare matematicamente problemi applicativi, in ambito industriale e/o finanziario, e formulando gli adeguati modelli matematici a supporto di attività in svariati ambiti.
L'obiettivo (a) è raggiunto sia mediante le prove d'esame di tipo seminariale previste in alcuni insegnamenti che soprattutto con la prova finale; in particolare, per quanto riguarda la lingua inglese, gli insegnamenti faranno uso abituale di testi in lingua inglese, ed è esplicitamente prevista la possibilità che l'elaborato scritto finale sia redatto in lingua inglese.
L'obiettivo (b) è raggiunto principalmente tramite le attività formative affini e integrative, soprattutto per i percorsi con una maggiore attenzione verso gli aspetti computazionali e le applicazioni della matematica e dell’informatica.
Capacità di apprendimento
I laureati magistrali in Scienze Computazionali:
(a) sono in grado di accedere al dottorato di ricerca, sia in Matematica che in altre discipline, con un alto grado di autonomia;
(b) hanno una mentalità flessibile, e sono in grado di inserirsi prontamente negli ambienti di lavoro, a un livello di elevata qualificazione, adattandosi facilmente a differenti contesti.
Tutte le attività formative del Corso di Laurea Magistrale in Scienze Computazionali concorrono al raggiungimento di questi obiettivi, che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Requisiti di ammissione
- Conoscenze richieste per l'accesso
Sono ammessi al corso di laurea magistrale in Scienze Computazionali studenti in possesso di laurea triennale, ovvero di altro titolo di studio conseguito all'estero e ritenuto idoneo, previa verifica caso per caso da parte della Commissione Didattica di Matematica del possesso da parte dell'immatricolando dei requisiti curricolari specificati in dettaglio nel Regolamento Didattico del Corso di Studio.
Si richiede inoltre un'adeguata conoscenza della lingua inglese, sia in forma scritta che orale, per la comunicazione in ambito scientifico.
In ogni caso per accedere alla laurea magistrale è necessario che i laureati siano in possesso dei seguenti requisiti curricolari:
- 18 crediti nei settori di formazione matematica di base (MAT/02, MAT/03, MAT/05, MAT/06, MAT/07, MAT/08);
- 6 crediti nei settori di formazione informatica di base (INF/01, ING-INF/05);
- ulteriori 6 crediti nei settori MAT/01-09, FIS/01-08, INF/01, ING-INF/01-05, SECS-S/01-06;
- conoscenze di base della lingua inglese o di altra lingua straniera (livello almeno B1).
- Modalità di verifica del possesso di tali conoscenze
Verrà esaminato il Curriculum Studiorum del candidato; inoltre, saranno previsti colloqui integrativi per coloro che - in possesso dei requisiti curricolari - abbiano delle carenze nella preparazione personale.
Prova finale
La prova finale consiste nella preparazione e nella discussione, davanti ad apposita commissione, di una tesi costituita da un documento scritto (in lingua italiano o inglese), che presenti i risultati di una ricerca nel settore del calcolo scientifico, quali lo sviluppo e la soluzione di problemi matematici o informatici motivati dalle applicazioni.
La tesi è preparata con la supervisione di un relatore e si svolge di norma nel secondo anno del corso, occupando circa la metà del tempo complessivo.Orientamento in ingresso
Le azioni di orientamento in ingresso consistono sia in attività informative e di approfondimento dei caratteri formativi dei Corsi di Studio (CdS) dell’Ateneo, sia in un impegno che favorisca lo sviluppo di una maggiore consapevolezza da parte degli/delle studenti/esse nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attività promosse si articolano in:
- incontri e manifestazioni rivolte ai futuri studenti;
- sviluppo di servizi online e pubblicazione di guide sull’offerta formativa dei CdS.
L’orientamento in ingresso prevede le seguenti attività principali, distribuite nel corso dell’anno accademico, alle quali partecipano tutti i Dipartimenti e i CdS.
• Giornate di Vita Universitaria (GVU), si svolgono ogni anno nell’arco di circa 4 mesi e sono rivolte agli/alle studenti/esse degli ultimi due anni della scuola secondaria superiore.
Sono tenuti in tutti i Dipartimenti dell’Ateneo e costituiscono un’importante occasione per le future matricole per vivere la realtà universitaria.
Gli incontri sono strutturati in modo tale che, accanto alla presentazione dei Corsi di Laurea, gli/le studenti/esse possano anche fare un’esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti/esse seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente circa 4.000 studenti/esse e nel 2021 si sono svolte in modalità telematica.
Sono presentate anche le lauree magistrali attive nel Dipartimento, per rendere gli/le studenti/esse più consapevoli dell’intero percorso formativo loro offerto.
• Attività di orientamento sviluppate dai singoli Dipartimenti, mediante incontri in presenza e servizi online.
• Orientarsi a Roma Tre nel 2021 si è svolta in modalità mista e, dal 2020, è fruibile un portale per l’orientamento molto accattivante: https://orientamento.uniroma3.it/.
Rappresenta la manifestazione che riassume le annuali attività di orientamento in ingresso e si svolge ogni anno alla fine dell’anno accademico.
L’evento accoglie, perlopiù, studenti/esse romani/e che partecipano per mettere definitivamente a fuoco la loro scelta universitaria.
Durante la manifestazione viene presentata l’offerta formativa e sono presenti, con un proprio spazio, tutti i principali servizi di Roma Tre, le segreterie didattiche e la segreteria studenti.
I servizi di orientamento online messi a disposizione dei/delle future studenti/esse universitari/rie sono nel tempo aumentati, tenendo conto dello sviluppo delle nuove opportunità di comunicazione tramite web.
Inoltre, durante tutte le manifestazioni di presentazione dell’offerta formativa, sono illustrati quei siti web (di Dipartimento, di Ateneo, Portale dello studente, etc.), che possono aiutare gli/le studenti/esse nella loro scelta.
Infine, l’Ateneo valuta, di volta in volta, l’opportunità di partecipare ad ulteriori occasioni di orientamento in presenza ovvero online (Salone dello studente ed altre iniziative).
Il Dipartimento di Matematica e Fisica attribuisce una particolare importanza a tutte le attività volte a fornire informazioni necessarie per orientare studenti/esse nella scelta del corso di studio in linea con le politiche dell'Ateneo.
Infatti partecipa a tutte le principali iniziative d'Ateneo dedicate all'orientamento: il Salone dello Studente, in cui viene allestito lo stand con esperimenti e presentazioni 1, 2, 3… Scienze; la Giornata di Vita Universitaria e la manifestazione 'Orientarsi a Roma Tre'.
Il Dipartimento di Matematica e Fisica organizza inoltre iniziative per la scuola e il territorio che permettono di entrare in contatto con professori/esse, studenti/esse e personale del Dipartimento.
In particolare, il Dipartimento di Matematica e Fisica è impegnato da vari anni in attività di comunicazione e formazione scientifica dedicate alle scuole:
• Percorsi per le Competenze Trasversali per l’Orientamento (PCTO)
• Corsi di formazione per Insegnanti
• Masterclass
• Orientamento
• Orientamento on-line
• Piano Lauree Scientifiche
• Gare di Matematica
• La Fisica incontra la città
• Seminari divulgativi
• Progetti per le scuole
• Planetario e Astrogarden
• Laboratori
e in attività di comunicazione scientifica dedicate al pubblico, in collaborazione con altri Dipartimenti, enti e associazioni esterne (Notte Europea dei Ricercatori - Occhi sulla Luna - Occhi su Marte - Occhi su Giove - Occhi su Saturno) e eventi serali astronomici (Sotto un cielo pieno di stelle - Il cielo di Roma - Altri eventi serali).
Sono predisposti opuscoli e guide informative (Guida Breve; Benvenuto@Matematica; Matematica@RomaTre; Benvenuto@ScienzeComputazionali), disponibili anche in formato pdf sul sito web del Dipartimento e che vengono distribuiti in occasione degli eventi dedicati all'orientamento e in fase di iscrizione ai corsi stessi.
Ogni anno è organizzato un incontro, rivolto agli studenti della nostra laurea triennale ed a tutti gli eventuali interessati, per presentare la laurea magistrale in Scienze Computazionali, i percorsi formativi disponibili e l'offerta didattica prevista per il successivo anno accademico.Il Corso di Studio in breve
Il Corso di Laurea Magistrale in Scienze Computazionali è articolato in una serie di insegnamenti che danno grande rilievo alla matematica applicata e a tutti gli aspetti del calcolo scientifico.
L'obiettivo è formare laureati/e che siano in grado di esercitare attività professionali di tipo modellistico, matematico, computazionale e informatico nel campo industriale, della finanza, dei servizi e della pubblica amministrazione, nonché nella diffusione della cultura scientifica.
I/Le laureati/e potranno esercitare funzioni di elevata responsabilità, con compiti sia di ricerca scientifica che manageriali; l'alto livello di specializzazione raggiunto permetterà sia l'ingresso nel mondo del lavoro a livello internazionale sia l'ingresso ai dottorati di ricerca italiani ed esteri con un'ottima qualificazione.
In particolare, i/le laureati/e nel Corso di Laurea Magistrale in Scienze Computazionali avranno:
◦ ottime conoscenze nell'area della matematica applicata e dell'informatica;
◦ solida padronanza dei metodi propri del calcolo scientifico, sia per quanto riguarda lo sviluppo e l'uso dei modelli matematici che per le tecniche computazionali e informatiche;
◦ capacità di comprendere e utilizzare descrizioni e modelli matematici di situazioni concrete di interesse scientifico, tecnologico e economico;
◦ ottime competenze per la gestione dei sistemi informatici per lo sviluppo e l'uso di software per il calcolo scientifico;
◦ capacità di utilizzare almeno una lingua dell'Unione Europea oltre l'italiano, nell'ambito specifico di competenza e per lo scambio di informazioni generali;
◦ capacità di lavorare in gruppo e di inserirsi prontamente negli ambienti di lavoro.
Il corso di studio prevede tre curricula, due di stampo più teorico (Gestione e protezione dei dati, Analisi dei dati e statistica) e uno di stampo più applicativo (Modellistica fisica e simulazioni numeriche).
All'interno di ogni curriculum è proposto, rispettivamente, un percorso formativo denominato:
◦ Crittografia e sicurezza dell'informazione
◦ Data science & statistica
◦ Modelli e simulazioni.
Il piano di studio è molto flessibile e consente ampia possibilità di scelta da parte dello/a studente/essa.
Esso prevede sempre la conoscenza di una lingua straniera, conoscenze informatiche e computazionali, ulteriori conoscenze utili per l'inserimento nel mondo del lavoro e lo svolgimento di un tirocinio interno oppure esterno presso imprese, enti pubblici o privati, ordini professionali.
Inoltre, lo/la studente/essa interessato/a può svolgere parte del proprio percorso formativo in mobilità internazionale.
Tutte le attività proposte forniscono sia una base teorica, sia attività di laboratorio computazionale e informatico dedicate alla modellazione matematica, allo sviluppo di applicazioni informatiche, al calcolo scientifico e ai linguaggi di programmazione.
L'accesso a questo Corso di Laurea Magistrale è aperto a tutti/e i/le laureati/e triennali delle classi di laurea scientifiche.
Sono previste borse di merito sia per gli/le studenti/esse immatricolati/e al primo anno sia per gli/le studenti/esse iscritti/e agli anni successivi.
Lo studente espliciterà le proprie scelte al momento della presentazione,
tramite il sistema informativo di ateneo, del piano di completamento o del piano di studio individuale,
secondo quanto stabilito dal regolamento didattico del corso di studio.
Gestione e protezione dei dati
FIRST YEAR
First semester
Course
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Credits
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Scientific Disciplinary Sector Code
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Contact Hours
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Exercise Hours
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Laboratory Hours
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Personal Study Hours
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Type of Activity
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Language
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Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
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24
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Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
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15
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20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
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9
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MAT/07
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48
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24
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-
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-
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Core compulsory activities
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ITA |
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.
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9
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MAT/08
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48
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24
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-
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-
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Core compulsory activities
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ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
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20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
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Also available in another semester or year
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20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
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Also available in another semester or year
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20410419 -
MS410-Statistical Mechanics
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Also available in another semester or year
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20410420 -
AN420 - NUMERICAL ANALYSIS 2
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Also available in another semester or year
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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.
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6
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MAT/08
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48
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12
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-
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-
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Core compulsory activities
|
ITA |
20410447 -
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.
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9
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MAT/06
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48
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24
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-
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-
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Core compulsory activities
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ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
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6
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MAT/06
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48
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12
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-
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-
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Core compulsory activities
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ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
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Also available in another semester or year
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20410441 -
CP420-Introduction to Stochastic Processes
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Also available in another semester or year
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20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
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9
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MAT/09
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48
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24
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-
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-
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Core compulsory activities
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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.
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6
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MAT/06
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-
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-
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-
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-
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Core compulsory activities
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ITA |
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Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
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30
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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.
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9
|
MAT/08
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48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
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.
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9
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MAT/06
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48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
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.
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6
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MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
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ITA |
20410438 -
MF410 - Computational Finance
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Also available in another semester or year
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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, wave-particle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.
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6
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FIS/02
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60
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-
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-
|
-
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Related or supplementary learning activities
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ITA |
20410442 -
IN420 - Information Theory
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Also available in another semester or year
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20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
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6
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FIS/02
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48
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-
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-
|
-
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Related or supplementary learning activities
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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.
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6
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FIS/04
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60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
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20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
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Also available in another semester or year
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20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
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9
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INF/01
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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 object-oriented paradigm and another non-imperative paradigm.
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9
|
INF/01
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48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
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6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410779 -
IN560 - Cybersecurity For Telecommunications
|
Also available in another semester or year
|
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
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
|
Also available in another semester or year
|
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
|
Also available in another semester or year
|
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
|
Also available in another semester or year
|
20410417 -
IN410-Computability and Complexity
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
|
Also available in another semester or year
|
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410557 -
GE530-Linear algebra for Machine Learning
(objectives)
Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410593 -
AC310 - Complex analysis
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
(objectives)
Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625 -
CR410-Public Key Criptography
(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.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
|
Also available in another semester or year
|
20410625-2 -
CR410-Public Key Criptography - MODULE B
|
Also available in another semester or year
|
20410613 -
LM430-Logic and mathematical foundations
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410637 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410746 -
AL440 – GROUP THEORY
(objectives)
Become familiar with the fundamental notions of group theory, particularly finite groups, so as to be able to study and classify some important classes of finite groups.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410766 -
TN520 - Heights and diophantine equations
(objectives)
Get familiar with the concept of height of an algebraic number as a tool for studying solutions of some diophantine equations
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Core compulsory activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - 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.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- 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
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410779 -
IN560 - Cybersecurity For Telecommunications
(objectives)
This course is designed to introduce students to the main aspects of cyber-physical security that are associated with telecommunications networks. It provides an introduction to the fundamentals of network security, including compliance and operational security; threats and vulnerabilities; application, data, and host security; access control and identity management; and encryption. The course also covers new topics in network security, including psychological approaches to social engineering attacks, multimedia information protection, and digital information forensics. Students will be engaged in lab activities.
|
6
|
ING-INF/03
|
42
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Modellistica fisica e simulazioni numeriche
FIRST YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
15
|
|
|
|
|
|
|
|
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06, 1 Insegnamento (6 CFU) nel SSD MAT/07 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410447 -
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.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410555 -
ST410- 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
|
-
|
-
|
Core compulsory activities
|
ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory 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
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
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.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
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.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410438 -
MF410 - Computational Finance
|
Also available in another semester or year
|
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, wave-particle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning 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.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - 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.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
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 object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410779 -
IN560 - Cybersecurity For Telecommunications
|
Also available in another semester or year
|
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
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
15
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
|
Also available in another semester or year
|
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
|
Also available in another semester or year
|
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
|
Also available in another semester or year
|
20410417 -
IN410-Computability and Complexity
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
|
Also available in another semester or year
|
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
Also available in another semester or year
|
20410557 -
GE530-Linear algebra for Machine Learning
(objectives)
Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410593 -
AC310 - Complex analysis
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
(objectives)
Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625 -
CR410-Public Key Criptography
(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.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
|
Also available in another semester or year
|
20410625-2 -
CR410-Public Key Criptography - MODULE B
|
Also available in another semester or year
|
20410613 -
LM430-Logic and mathematical foundations
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410637 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410746 -
AL440 – GROUP THEORY
(objectives)
Become familiar with the fundamental notions of group theory, particularly finite groups, so as to be able to study and classify some important classes of finite groups.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410766 -
TN520 - Heights and diophantine equations
(objectives)
Get familiar with the concept of height of an algebraic number as a tool for studying solutions of some diophantine equations
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06, 1 Insegnamento (6 CFU) nel SSD MAT/07 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Core compulsory activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- 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
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410779 -
IN560 - Cybersecurity For Telecommunications
(objectives)
This course is designed to introduce students to the main aspects of cyber-physical security that are associated with telecommunications networks. It provides an introduction to the fundamentals of network security, including compliance and operational security; threats and vulnerabilities; application, data, and host security; access control and identity management; and encryption. The course also covers new topics in network security, including psychological approaches to social engineering attacks, multimedia information protection, and digital information forensics. Students will be engaged in lab activities.
|
6
|
ING-INF/03
|
42
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Analisi dei dati e statistica
FIRST YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410447 -
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.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410555 -
ST410- 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
|
-
|
-
|
Core compulsory activities
|
ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory 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
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
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.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
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.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410438 -
MF410 - Computational Finance
|
Also available in another semester or year
|
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, wave-particle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning 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.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
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 object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410773 -
IN570 – Quantum Computing
(objectives)
This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one. The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis, and the introduction of quantum programming languages and software platforms for the specification of quantum computations.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410779 -
IN560 - Cybersecurity For Telecommunications
|
Also available in another semester or year
|
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
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
|
Also available in another semester or year
|
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
|
Also available in another semester or year
|
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
|
Also available in another semester or year
|
20410417 -
IN410-Computability and Complexity
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
|
Also available in another semester or year
|
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410557 -
GE530-Linear algebra for Machine Learning
(objectives)
Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410593 -
AC310 - Complex analysis
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
(objectives)
Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625 -
CR410-Public Key Criptography
(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.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
|
Also available in another semester or year
|
20410625-2 -
CR410-Public Key Criptography - MODULE B
|
Also available in another semester or year
|
20410613 -
LM430-Logic and mathematical foundations
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410637 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410746 -
AL440 – GROUP THEORY
(objectives)
Become familiar with the fundamental notions of group theory, particularly finite groups, so as to be able to study and classify some important classes of finite groups.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410766 -
TN520 - Heights and diophantine equations
(objectives)
Get familiar with the concept of height of an algebraic number as a tool for studying solutions of some diophantine equations
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Core compulsory activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - 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.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction 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
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- 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
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410773 -
IN570 – Quantum Computing
|
Also available in another semester or year
|
20410779 -
IN560 - Cybersecurity For Telecommunications
(objectives)
This course is designed to introduce students to the main aspects of cyber-physical security that are associated with telecommunications networks. It provides an introduction to the fundamentals of network security, including compliance and operational security; threats and vulnerabilities; application, data, and host security; access control and identity management; and encryption. The course also covers new topics in network security, including psychological approaches to social engineering attacks, multimedia information protection, and digital information forensics. Students will be engaged in lab activities.
|
6
|
ING-INF/03
|
42
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|