Degree Course: Computational Sciences
A.Y. 2020/2021
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 sono improntate alla realizzazione di processi di raccordo con la scuola secondaria di secondo grado.
Si concretizzano in attività di carattere informativo sui Corsi di Studio (CdS) dell'Ateneo ma anche come impegno condiviso da scuola e università per favorire lo sviluppo di una maggiore consapevolezza da parte degli studenti nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attività promosse si articolano in:
a) autorientamento;
b) incontri e manifestazioni informative rivolte alle future matricole;
c) sviluppo di servizi online e pubblicazione di guide sull'offerta formativa dei CdS.
Tra le attività svolte in collaborazione con le scuole per lo sviluppo di una maggiore consapevolezza nella scelta, il progetto di autorientamento è un intervento che consente di promuovere un raccordo particolarmente qualificato con alcune scuole superiori.
Il progetto, infatti, è articolato in incontri svolti presso le scuole ed è finalizzato a sollecitare nelle future matricole una riflessione sui propri punti di forza e sui criteri di scelta.
La presentazione dell'offerta formativa agli studenti delle scuole superiori prevede tre eventi principali distribuiti nel corso dell'anno accademico ai quali partecipano tutti i CdS:
- Salone dello studente, si svolge presso la fiera di Roma fra ottobre e novembre e coinvolge tradizionalmente tutti gli Atenei del Lazio e molti Atenei fuori Regione, Enti pubblici e privati che si occupano di Formazione e Lavoro.
Roma Tre partecipa a questo evento con un proprio spazio espositivo, con conferenze di presentazione dell'offerta formativa dell'Ateneo e promuove i propri Dipartimenti scientifici grazie all'iniziativa 1,2,3 Scienze!;
- Giornate di Vita Universitaria (GVU), si svolgono ogni anno da dicembre a marzo e sono rivolte agli studenti degli ultimi due anni della scuola superiore.
Si svolgono 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 studenti possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente circa 5.000 studenti;
- Orientarsi a Roma Tre, rappresenta la manifestazione che chiude le annuali attività di orientamento in ingresso e si svolge in Ateneo a luglio di ogni anno.
L'evento accoglie, perlopiù, studenti romani 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 online messi a disposizione dei futuri studenti universitari nel tempo sono 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 servizi online (siti web di Dipartimento, di Ateneo, Portale dello studente, ecc.) che possono aiutare gli studenti nella loro scelta.
Il Dipartimento di Matematica e Fisica attribuisce una particolare importanza a tutte le attività volte a fornire informazioni necessarie per orientare gli studenti nella scelta del corso di studio in linea con le politiche d'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!; le Giornate di Vita Universitaria e la manifestazione "Orientarsi a Roma Tre".
Oltre alle iniziative di orientamento ad ampio spettro, è organizzato annualmente un incontro con gli studenti della laurea triennale per presentare gli insegnamenti a scelta del successivo A.A.
e la loro importanza ai fini dei vari percorsi formativi magistrali, per orientare e supportare in scelte consapevoli lo studente interessato a proseguire gli studi nella laurea magistrale in Scienze Computazionali.
Per la realizzazione dei propri progetti di orientamento il Dipartimento inoltre:
- aderisce al Piano nazionale Lauree Scientifiche, promosso dal MIUR, dalla Conferenza Nazionale dei Presidenti e dei Direttori delle strutture Universitarie di Scienze e Tecnologie (Con.Scienze) e dalla Confindustria, offrendo alle scuole partner laboratori di matematica e di fisica;
- propone percorsi all'interno del progetto ministeriale Alternanza Scuola-Lavoro, come definito dalla legge 107 del 2015 (La Buona Scuola);
- promuove iniziative di divulgazione e comunicazione scientifica rivolte alle scuole (studenti ed insegnanti) e più in generale alla società.
Particolare rilievo assumono le seguenti attività:
- Masterclass in Astrofisica, Fisica delle Particelle, Fisica Terrestre e dell'Ambiente, Ottica e Fisica della Materia, e di prossima attivazione in Algebra e crittografia a chiave pubblica, Geometria: gruppi di simmetria del piano, Logica: dai sillogismi al computer, che offrono la possibilità di trascorrere una giornata da ricercatore ad alcune centinaia di studenti fra i più motivati degli ultimi due anni della scuola secondaria;
- Gare di Matematica, che comprendono la selezione provinciale delle Olimpiadi di Matematica, con circa 500 partecipanti studenti delle scuole superiori di tutta la provincia di Roma, e il concorso "Immatricolazione gratuita a Roma Tre", con più di 400 partecipanti studenti dell'ultimo anno della scuola secondaria;
- La Fisica incontra la Città, seminari serali aperti al pubblico in cui vengono trattate le principali tematiche e scoperte della Fisica Moderna;
- "Notte dei Ricercatori" e "Occhi su Luna/Marte/Giove/Saturno", serate aperte al pubblico con la presenza di migliaia di partecipanti, nelle quali studenti e ricercatori diffondono conoscenze ed esperienze attraverso esperimenti, laboratori, dimostrazioni scientifiche, spettacoli, conferenze e seminari divulgativi.
Per la diffusione e la consultazione di questi eventi il Dipartimento dedica sulla propria home page del sito una sezione ad hoc: "Il Dipartimento per la Città e per la Scuola".
Inoltre, in tale sezione è disponibile una piattaforma E-learning, che, tramite opportuni quesiti, aiuta gli studenti delle scuole superiori nell'autovalutazione della propria preparazione, evidenziando possibili lacune da colmare eventualmente con l'ausilio delle dispense sugli argomenti di base disponibili in rete a fianco dei quesiti.
Per entrambi i Corsi di Laurea e di Laurea Magistrale in Matematica sono predisposti opuscoli e guide informative, tra cui benvenuto@matematica è disponibile anche in formato pdf sul sito web del Dipartimento al link: http://dmf.matfis.uniroma3.it/matematica/orientamento/benvenuto.php, che vengono distribuiti in occasione degli eventi dedicati all'orientamento e in fase di iscrizione ai corsi stessi.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 che siano in grado si 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 laureati 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 laureati 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 due curricula, uno di stampo più teorico (Gestione e protezione dei dati) e uno di stampo più applicativo (Modellistica fisica e simulazioni numeriche).
All'interno del primo sono proposti tre percorsi formativi:
- Crittografia e sicurezza dell'informazione;
- Informatica;
- Data science & statistics.
All'interno del secondo sono consigliati i seguenti percorsi formativi:
- Modelli matematici e simulazioni numeriche;
- Algoritmi e modelli per sistemi complessi.
Il piano di studio è molto flessibile e consente ampia possibilità di scelta da parte dello studente.
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; i corrispondenti CFU possono alternativamente essere acquisiti frequentando le attività High Performance Computing (HPC) presso la Scuola Internazionale di Studi Superiori e Avanzati - SISSA di Trieste.
Inoltre, lo studente interessato 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 i laureati triennali delle classi di laurea scientifiche.
Sono previste borse di merito sia per gli studenti immatricolati al primo anno sia per gli studenti iscritti 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:
CURRICULUM GESTIONE E PROTEZIONE DEI DATI: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B) - (show)
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24
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Optional Group:
CURRICULUM GESTIONE E PROTEZIONE DEI DATI: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B) - (show)
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15
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20410410 -
FM310 - Equations of Mathematical Physics
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Also available in another semester or year
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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
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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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20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
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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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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.
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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 |
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
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ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
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Also available in another semester or year
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20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
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Also available in another semester or year
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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 |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
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6
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MAT/06
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48
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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 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) - (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
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MAT/08
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48
|
24
|
-
|
-
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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
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Also available in another semester or year
|
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
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Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
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Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
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Also available in another semester or year
|
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 |
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 |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
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Also available in another semester or year
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20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
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Also available in another semester or year
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20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
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Also available in another semester or year
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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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Related or supplementary learning activities
|
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
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Also available in another semester or year
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20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
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 |
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
|
Also available in another semester or year
|
20410431 -
IN540 - COMPUTATIONAL TOPOLOGY
|
Also available in another semester or year
|
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
|
Also available in another semester or year
|
20410412 -
MC310 - Fundaments of Complementary Mathematics
(objectives)
1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.
|
9
|
MAT/04
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
|
Also available in another semester or year
|
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 |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
|
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
|
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 on the onset of pathologies. Maintain the modeling aspect as well as that of numerical simulation, especially problems formulated by equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful for analyzing biological data.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente - (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 GESTIONE E PROTEZIONE DEI DATI: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B) - (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
|
Also available in another semester or year
|
20410415 -
CR410-Public Key Criptography
|
Also available in another semester or year
|
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
|
20410453 -
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.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
(objectives)
To support the students into an in-depth analysis of the main results of first order classical logic and to study some of their remarkable consequences.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410458 -
LM430 - LOGICAL THEORIES 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410460 -
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.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
(objectives)
Acquire a basic knowledge of the concepts and methods related to the theory of public key cryptography using the group of points of an elliptic curve on a finite field. Apply the theory of elliptic curves to classical problems of computational number theory such as factorization and primality testing.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410463 -
TN510 - NUMBER THEORY
|
Also available in another semester or year
|
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410559 -
TN520 - Irrationality, trascendence and Diophantine equations
(objectives)
Acquire good knowledge of the method of auxiliary polynomials and of its applications to problems of irrationality, transcendence and to the study of diophantine equations.
|
6
|
MAT/02
|
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
(objectives)
To acquire a broad knowledge of holomorphic and meromorphic functions of one complex variable and of their main properties. To acquire good dexterity in complex integration and in the calculation of real definite integrals.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
20410596 -
GE440 - DIFFERENTIAL TOPOLOGY
|
6
|
MAT/03
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
CURRICULUM GESTIONE E PROTEZIONE DEI DATI: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B) - (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
|
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 |
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
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 |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
(objectives)
To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti 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) - (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 |
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
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 |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
(objectives)
To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
(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 |
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
(objectives)
Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented paradigm. Introduce the fundamental notions of parallel and concurrent programming.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
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 |
20410423 -
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
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
(objectives)
Introduce the basic concepts of security and then show how to acquire autonomy in updating the understanding in the data and networks security domain. Provide the basic concepts for understanding and evaluating a security solution. Provide the basic knowledge to produce security solutions for small/medium-sized system
|
6
|
ING-INF/03
|
42
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410431 -
IN540 - COMPUTATIONAL TOPOLOGY
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
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 |
20410412 -
MC310 - Fundaments of Complementary Mathematics
|
Also available in another semester or year
|
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
1. Mathematics software, with particular attention to their use for teaching mathematics in school. 2. Analysis of the potential and criticality of the use of technological tools for teaching and learning mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
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 |
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
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 |
|
Optional Group:
12 CFU a scelta dello studente - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Second semester
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) - (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) - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
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
|
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
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
|
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 |
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 |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
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 |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
|
6
|
MAT/06
|
48
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti 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) - (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
|
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
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
|
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 |
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 |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
|
Also available in another semester or year
|
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
|
Also available in another semester or year
|
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
|
Also available in another semester or year
|
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
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 techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
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 |
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
|
Also available in another semester or year
|
20410431 -
IN540 - COMPUTATIONAL TOPOLOGY
|
Also available in another semester or year
|
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
|
Also available in another semester or year
|
20410412 -
MC310 - Fundaments of Complementary Mathematics
(objectives)
1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.
|
9
|
MAT/04
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
|
Also available in another semester or year
|
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 |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
|
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
|
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 on the onset of pathologies. Maintain the modeling aspect as well as that of numerical simulation, especially problems formulated by equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful for analyzing biological data.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente - (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) - (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
|
Also available in another semester or year
|
20410415 -
CR410-Public Key Criptography
|
Also available in another semester or year
|
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
|
20410453 -
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.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
(objectives)
To support the students into an in-depth analysis of the main results of first order classical logic and to study some of their remarkable consequences.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410458 -
LM430 - LOGICAL THEORIES 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410460 -
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.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
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
(objectives)
Acquire a basic knowledge of the concepts and methods related to the theory of public key cryptography using the group of points of an elliptic curve on a finite field. Apply the theory of elliptic curves to classical problems of computational number theory such as factorization and primality testing.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410463 -
TN510 - NUMBER THEORY
|
Also available in another semester or year
|
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410559 -
TN520 - Irrationality, trascendence and Diophantine equations
(objectives)
Acquire good knowledge of the method of auxiliary polynomials and of its applications to problems of irrationality, transcendence and to the study of diophantine equations.
|
6
|
MAT/02
|
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
(objectives)
To acquire a broad knowledge of holomorphic and meromorphic functions of one complex variable and of their main properties. To acquire good dexterity in complex integration and in the calculation of real definite integrals.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
20410596 -
GE440 - DIFFERENTIAL TOPOLOGY
|
6
|
MAT/03
|
-
|
-
|
-
|
-
|
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) - (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
|
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 |
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
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 |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
(objectives)
To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti 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) - (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 |
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
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 |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
(objectives)
To apply methods and tools of mathematical physics to some classes of models of dynamical systems and statistical mechanics, through both theoretical lectures and numerous practical exercises carried out in the computer lab.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
(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 |
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
(objectives)
Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented paradigm. Introduce the fundamental notions of parallel and concurrent programming.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
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 |
20410423 -
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
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
(objectives)
Introduce the basic concepts of security and then show how to acquire autonomy in updating the understanding in the data and networks security domain. Provide the basic concepts for understanding and evaluating a security solution. Provide the basic knowledge to produce security solutions for small/medium-sized system
|
6
|
ING-INF/03
|
42
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410431 -
IN540 - COMPUTATIONAL TOPOLOGY
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
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 |
20410412 -
MC310 - Fundaments of Complementary Mathematics
|
Also available in another semester or year
|
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
1. Mathematics software, with particular attention to their use for teaching mathematics in school. 2. Analysis of the potential and criticality of the use of technological tools for teaching and learning mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
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 |
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
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 |
|
Optional Group:
12 CFU a scelta dello studente - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Second semester