Degree Course: Computational Sciences
A.Y. 2021/2022
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 capacita 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 attivita 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 attivita 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 familiarita 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 capacita di lavorare bene autonomamente.
Tutte le attivita 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.
Attivita 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 attivita di tipo seminariale o di preparazione alle prove scritte sono tipicamente svolte in piccoli gruppi, mentre in altre attivita 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 possibilita di formalizzare matematicamente problemi applicativi, in ambito industriale e/o finanziario, e formulando gli adeguati modelli matematici a supporto di attivita in svariati ambiti.
L'obiettivo (a) e 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 e esplicitamente prevista la possibilita che l'elaborato scritto finale sia redatto in lingua inglese.
L'obiettivo (b) e raggiunto principalmente tramite le attivita 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 mentalita 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 attivita 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 e 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).
- Modalita di verifica del possesso di tali conoscenze
Verra 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 e preparata con la supervisione di un relatore e si svolge di norma nel secondo anno del corso, occupando circa la meta del tempo complessivo.Orientamento in ingresso
Le azioni di orientamento in ingresso sono improntate alla realizzazione di processi di raccordo con la scuola media secondaria.
Si concretizzano in attivita di carattere informativo sui Corsi di Studio (CdS) dell'Ateneo ma anche come impegno condiviso da scuola e universita per favorire lo sviluppo di una maggiore consapevolezza da parte degli/delle studenti/esse nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attivita 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 attivita svolte in collaborazione con le scuole per lo sviluppo di una maggiore consapevolezza nella scelta, il progetto di autorientamento e un intervento che consente di promuovere un raccordo particolarmente qualificato con alcune scuole medie superiori.
Il progetto, infatti, e articolato in incontri svolti presso le scuole ed e finalizzato a sollecitare nelle future matricole una riflessione sui propri punti di forza e sui criteri di scelta.
La presentazione dell'offerta formativa agli/alle studenti/esse 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;
◦ Giornate di Vita Universitaria (GVU), si svolgono ogni anno da dicembre a marzo e sono rivolte agli/alle studenti/esse degli ultimi due anni della scuola secondaria superiore.
Si svolgono in tutti i Dipartimenti dell'Ateneo e costituiscono un'importante occasione per le future matricole per vivere la realta universitaria.
Gli incontri sono strutturati in modo tale che accanto alla presentazione dei Corsi di Laurea, gli/le studenti/esse possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attivita didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti/esse seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente circa 5.000 studenti;
◦ Orientarsi a Roma Tre, rappresenta la manifestazione che riassume le annuali attivita di orientamento in ingresso e si svolge in Ateneo a luglio di ogni anno.
L'evento accoglie, perlopiu, studenti/esse romani/e che partecipano per mettere definitivamente a fuoco la loro scelta universitaria.
Durante la manifestazione viene presentata l'offerta formativa e sono presenti, con un proprio spazio, tutti i principali servizi di Roma Tre, le segreterie didattiche e la segreteria studenti.
I servizi di orientamento online messi a disposizione dei/delle futuri/e studenti/esse universitari/rie sono nel tempo aumentati tenendo conto dello sviluppo delle nuove opportunita 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 etc.) che possono aiutare gli/le studenti/esse nella loro scelta.
Il Dipartimento di Matematica e Fisica attribuisce una particolare importanza a tutte le attivita volte a fornire informazioni necessarie per orientare gli/le studenti/esse nella scelta del corso di studio in linea con le politiche dell'Ateneo.
Infatti partecipa a tutte le principali iniziative d'Ateneo dedicate all'orientamento: il Salone dello Studente; le Giornata di Vita Universitaria e la manifestazione 'Orientarsi a Roma Tre'.
Per la realizzazione dei propri progetti di orientamento, il Dipartimento:
◦ aderisce al Piano Nazionale Lauree Scientifiche promosso dal MIUR, dalla Conferenza Nazionale dei Presidenti e dei direttori delle strutture Universitarie di Scienze (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 sia alle scuole (studenti/esse ed insegnanti) sia a tutti/e i/le cittadini/e, e corsi di formazione ed aggiornamento per insegnanti.
Tra quest'ultime particolare rilievo assumono le seguenti attivita:
◦ Masterclass in Astrofisica, Fisica delle Particelle, Fisica Terrestre e dell'Ambiente, Ottica e Fisica della Materia, Logica, Geometria, Algebra e Crittografia, che offrono la possibilita di trascorrere una giornata da ricercatore ad alcune centinaia di studenti/esse fra i/le piu motivati/e degli ultimi due anni della Scuola Secondaria;
◦ Gare di Matematica, che comprendono la selezione provinciale delle Olimpiadi di Matematica, con circa 500 partecipanti provenienti dalle scuole superiori di tutta la provincia di Roma, e il concorso 'Immatricolazione gratuita a Roma Tre', con la partecipazione di piu di 400 studenti/esse dell'ultimo anno della scuola secondaria;
◦ 'La Fisica incontra la Citta', ciclo di seminari serali aperti al pubblico in cui vengono trattate le principali tematiche e scoperte della Fisica Moderna;
◦ 'Notte dei Ricercatori' e 'Occhi su ......', serate aperte al pubblico (con alcune migliaia di presenze in totale) in cui studenti/esse e ricercatori/trici diffondono conoscenze ed esperienze attraverso esperimenti, laboratori, dimostrazioni scientifiche, spettacoli, conferenze e seminari divulgativi.
Per ciascun Corso di Laurea e di Laurea Magistrale sono predisposte Guide Informative e Opuscoli, tra cui il ' benvenuto@matematica', che vengono distribuiti in occasione degli eventi dedicati all'orientamento e in fase di iscrizione ai corsi stessi e resi disponibili sul sito d'Ateneo e del Dipartimento.Il Corso di Studio in breve
Il Corso di Laurea Magistrale in Scienze Computazionali e articolato in una serie di insegnamenti che danno grande rilievo alla matematica applicata e a tutti gli aspetti del calcolo scientifico.
L'obiettivo e formare laureati/e che siano in grado di esercitare attivita professionali di tipo modellistico, matematico, computazionale e informatico nel campo industriale, della finanza, dei servizi e della pubblica amministrazione, nonche nella diffusione della cultura scientifica.
I/Le laureati/e potranno esercitare funzioni di elevata responsabilita, con compiti sia di ricerca scientifica che manageriali; l'alto livello di specializzazione raggiunto permettera sia l'ingresso nel mondo del lavoro a livello internazionale sia l'ingresso ai dottorati di ricerca italiani ed esteri con un'ottima qualificazione.
In particolare, i/le laureati/e nel Corso di Laurea Magistrale in Scienze Computazionali avranno:
◦ ottime conoscenze nell'area della matematica applicata e dell'informatica;
◦ solida padronanza dei metodi propri del calcolo scientifico, sia per quanto riguarda lo sviluppo e l'uso dei modelli matematici che per le tecniche computazionali e informatiche;
◦ capacita 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;
◦ capacita di utilizzare almeno una lingua dell'Unione Europea oltre l'italiano, nell'ambito specifico di competenza e per lo scambio di informazioni generali;
◦ capacita di lavorare in gruppo e di inserirsi prontamente negli ambienti di lavoro.
Il corso di studio prevede tre curricula, due di stampo piu teorico (Gestione e protezione dei dati, Analisi dei dati e statistica) e uno di stampo piu applicativo (Modellistica fisica e simulazioni numeriche).
All'interno di ogni curriculum e proposto, rispettivamente, un percorso formativo denominato:
◦ Crittografia e sicurezza dell'informazione
◦ Data science & statistica
◦ Modelli e simulazioni.
Il piano di studio e molto flessibile e consente ampia possibilita di scelta da parte dello/a studente/essa.
Esso prevede sempre la conoscenza di una lingua straniera, conoscenze informatiche e computazionali, ulteriori conoscenze utili per l'inserimento nel mondo del lavoro e lo svolgimento di un tirocinio interno oppure esterno presso imprese, enti pubblici o privati, ordini professionali.
Inoltre, lo/la studente/essa interessato/a puo svolgere parte del proprio percorso formativo in mobilita internazionale.
Tutte le attivita proposte forniscono sia una base teorica, sia attivita 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 e aperto a tutti/e i/le laureati/e triennali delle classi di laurea scientifiche.
Sono previste borse di merito sia per gli/le studenti/esse immatricolati/e al primo anno sia per gli/le studenti/esse iscritti/e agli anni successivi.
Lo studente espliciterà le proprie scelte al momento della presentazione,
tramite il sistema informativo di ateneo, del piano di completamento o del piano di studio individuale,
secondo quanto stabilito dal regolamento didattico del corso di studio.
Gestione e protezione dei dati
FIRST YEAR
First semester
Course
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Credits
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Scientific Disciplinary Sector Code
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Contact Hours
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Exercise Hours
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Laboratory Hours
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Personal Study Hours
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Type of Activity
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Language
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Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
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24
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20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
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Also available in another semester or year
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20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
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9
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MAT/05
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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 |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
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9
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MAT/03
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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 |
20410445 -
AL410 - COMMUTATIVE ALGEBRA
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Also available in another semester or year
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20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces.
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9
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MAT/03
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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 |
20410417 -
IN410-Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.
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9
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MAT/01
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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 |
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
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20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
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6
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MAT/01
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32
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16
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-
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-
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Core compulsory activities
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ITA |
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
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3
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MAT/01
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16
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8
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-
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-
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Core compulsory activities
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ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
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Also available in another semester or year
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20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
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Also available in another semester or year
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20410425 -
GE460- GRAPH THEORY
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Also available in another semester or year
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20410444 -
GE430 - RIEMANNIAN GEOMETRY
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Also available in another semester or year
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20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.
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6
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MAT/05
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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 |
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
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Also available in another semester or year
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20410557 -
GE530-Linear algebra for Machine Learning
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Also available in another semester or year
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20410529 -
LM510 - LOGICAL THEORIES 1
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Also available in another semester or year
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20410625 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
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20410625-1 -
CR410 - Public Key Criptography - MODULE A
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
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6
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MAT/02
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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 |
20410625-2 -
CR410-Public Key Criptography - MODULE B
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
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3
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MAT/02
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-
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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 |
20410635 -
AM410 - PARTIAL DIFFERENTIAL EQUATIONS
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Also available in another semester or year
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20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
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6
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MAT/02
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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 |
20410613 -
LM430-Logic and mathematical foundations
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Also available in another semester or year
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20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
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Also available in another semester or year
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20410637 -
AM450 - FUNCTIONAL ANALYSIS
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Also available in another semester or year
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20410407 -
AC310 - Complex analysis
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Also available in another semester or year
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Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
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15
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20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
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9
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MAT/07
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48
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24
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-
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-
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Core compulsory activities
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ITA |
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
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9
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MAT/08
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48
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24
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-
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-
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Core compulsory activities
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ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
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20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
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Also available in another semester or year
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20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
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Also available in another semester or year
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20410419 -
MS410-Statistical Mechanics
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Also available in another semester or year
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20410420 -
AN420 - NUMERICAL ANALYSIS 2
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Also available in another semester or year
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20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
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6
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MAT/08
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48
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12
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-
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-
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Core compulsory activities
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ITA |
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.
|
6
|
MAT/06
|
48
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
CP410 - Theory of Probability
(objectives)
Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
|
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 parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
|
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
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
|
Also available in another semester or year
|
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
|
Also available in another semester or year
|
20410417 -
IN410-Computability and Complexity
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
|
Also available in another semester or year
|
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
|
Also available in another semester or year
|
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 |
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
(objectives)
Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
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 |
20410529 -
LM510 - LOGICAL THEORIES 1
(objectives)
Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
|
Also available in another semester or year
|
20410625-2 -
CR410-Public Key Criptography - MODULE B
|
Also available in another semester or year
|
20410635 -
AM410 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410613 -
LM430-Logic and mathematical foundations
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410637 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410407 -
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/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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 |
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(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 |
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
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 |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Modellistica fisica e simulazioni numeriche
FIRST YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
15
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
|
Also available in another semester or year
|
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410445 -
AL410 - COMMUTATIVE ALGEBRA
|
Also available in another semester or year
|
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410417 -
IN410-Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.
|
9
|
MAT/01
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
6
|
MAT/01
|
32
|
16
|
-
|
-
|
Core compulsory activities
|
ITA |
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
3
|
MAT/01
|
16
|
8
|
-
|
-
|
Core compulsory activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
|
Also available in another semester or year
|
20410557 -
GE530-Linear algebra for Machine Learning
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
|
Also available in another semester or year
|
20410625 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625-2 -
CR410-Public Key Criptography - MODULE B
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
3
|
MAT/02
|
-
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410635 -
AM410 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410613 -
LM430-Logic and mathematical foundations
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20410637 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410407 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06, 1 Insegnamento (6 CFU) nel SSD MAT/07 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
CP410 - Theory of Probability
(objectives)
Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
|
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 parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
|
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
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
15
|
|
|
|
|
|
|
|
|
Optional Group:
CURRICULUM MODELLISTICA FISICA E SIMULAZIONI NUMERICHE: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06, 1 Insegnamento (6 CFU) nel SSD MAT/07 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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 |
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(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 |
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
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 |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Analisi dei dati e statistica
FIRST YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
|
Also available in another semester or year
|
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the abstract integration theory and of the functional spaces L^p.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410445 -
AL410 - COMMUTATIVE ALGEBRA
|
Also available in another semester or year
|
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410417 -
IN410-Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.
|
9
|
MAT/01
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
6
|
MAT/01
|
32
|
16
|
-
|
-
|
Core compulsory activities
|
ITA |
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
3
|
MAT/01
|
16
|
8
|
-
|
-
|
Core compulsory activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study of ordinary differential equations and their qualitative properties.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
|
Also available in another semester or year
|
20410557 -
GE530-Linear algebra for Machine Learning
|
Also available in another semester or year
|
20410529 -
LM510 - LOGICAL THEORIES 1
|
Also available in another semester or year
|
20410625 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625-2 -
CR410-Public Key Criptography - MODULE B
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
3
|
MAT/02
|
-
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410635 -
AM410 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410613 -
LM430-Logic and mathematical foundations
|
Also available in another semester or year
|
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20410637 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410407 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
Provide the basic elements (including implementation in a programming language) of elementary numerical approximation techniques, in particular those related to solution of linear systems and nonlinear scalar equations, interpolation and approximate integration.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410447 -
CP410 - Theory of Probability
(objectives)
Foundations of modern probability theory: measure theory, 0/1 laws, independence, conditional expectation with respect to sub sigma algebras, characteristic functions, the central limit theorem, branching processes, discrete parameter martingale theory.
|
9
|
MAT/06
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
|
Also available in another semester or year
|
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
|
Also available in another semester or year
|
20410419 -
MS410-Statistical Mechanics
|
Also available in another semester or year
|
20410420 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
|
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 parallel and distributed programming techniques, and know modern hardware and software architectures for high-performance scientific computing. Parallelization paradigms, parallelization on CPU and GPU, distributed memory systems. Data-intensive, Memory Intensive and Compute Intensive applications. Performance analysis in HPC systems.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410430 -
IN520-SECURITY IN TELECOMMUNICATIONS
|
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
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410571 -
FS520 – Complex networks
|
Also available in another semester or year
|
20410690 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
(objectives)
Discussion of theoretical and computational statistical models to the analysis of big datasets, and the introduction of more advanced methods for parametrical estimation.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410693 -
FM420 - Dynamic Systems
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
|
Also available in another semester or year
|
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
|
Also available in another semester or year
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
Acquire a good knowledge of some methods and fundamental results in the study of the commutative rings and their modules, with particular reference to the study of ring classes of interest for the algebraic theory of numbers and for algebraic geometry.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
|
Also available in another semester or year
|
20410417 -
IN410-Computability and Complexity
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems.
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
|
Also available in another semester or year
|
20410451-2 -
LM410 -THEOREMS IN LOGIC 1 - Module B
|
Also available in another semester or year
|
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 |
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
(objectives)
Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
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 |
20410529 -
LM510 - LOGICAL THEORIES 1
(objectives)
Address some questions of the theory of the proof of the twentieth century, in connection with the themes of contemporary research
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410625 -
CR410-Public Key Criptography
(objectives)
Acquire a basic understanding of the notions and methods of public-key encryption theory, providing an overview of the models which are most widely used in this field.
|
|
20410625-1 -
CR410 - Public Key Criptography - MODULE A
|
Also available in another semester or year
|
20410625-2 -
CR410-Public Key Criptography - MODULE B
|
Also available in another semester or year
|
20410635 -
AM410 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410613 -
LM430-Logic and mathematical foundations
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410627 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
Acquire a good knowledge of the concepts and methods of the elementary number theory, with particular reference to the study of the Diophantine equations and congruence equations. Provide prerequisites for more advanced courses of algebraic and analytical number theory.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410637 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410407 -
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/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA GESTIONE E PROTEZIONE DEI DATI E ANALISI DEI DATI E STATISTICA: scegliere 2 Insegnamenti (15 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/09 nel curriculum GESTIONE E PROTEZIONE DEI DATI e almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 nel curriculum ANALISI DEI DATI E STATISTICA - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
GRUPPO UNICO: Scegliere 4 insegnamenti (30 CFU) nei seguenti SSD FIS, INF/01, ING-INF/03, ING-INF/04, ING-INF/05, MAT/04,06,07,08,09, SECS-S/01,SECS-S/06 TRA LE ATTIVITA’ AFFINI INTEGRATIVE (C), di cui almeno 1 Insegnamento (6 CFU) nel SSD INF/01 nei curricula MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e almeno 2 Insegnamenti (12 CFU) nel SSD INF/01 nei curricula GESTIONE E PROTEZIONE DEI DATI e ANALISI DEI DATI E STATISTICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
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 |
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
(objectives)
Introduce key questions in the theory of signal transmission and quantitative analysis of signals, such as the notions of entropy and mutual information. Show the underlying algebraic structure. Apply the fundamental concepts to code theory, data compression and cryptography.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(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 |
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
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 |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410571 -
FS520 – Complex networks
(objectives)
This course introduces students to the fascinating network science, both from a theoretical and a computational point of view through practical examples. Networks with complex topological properties are a new discipline rapidly expanding due to its multidisciplinary nature: it has found in fact applications in many fields, including finance, social sciences and biology. The first part of the course is devoted to the characterization of the topological structure of complex networks and to the study of the most used network models. The second part is focused on growth and dynamical processes in these systems and to the study of specific networks of this kind.
|
6
|
FIS/03
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410690 -
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.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410692 -
ST420 – STATISTICS 2, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20410693 -
FM420 - Dynamic Systems
(objectives)
To acquire a solid knowledge on some advanced problems of interest in the theory of Dynamical Systems
|
6
|
MAT/07
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
-
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
12 CFU a scelta dello studente: Nei percorsi formativi proposti scegliere gli insegnamenti in base a precise esigenze formative nel seguente modo: 2 insegnamenti oppure 1 insegnamento e QLM. Si rinvia al regolamento per suggerimenti. - (show)
|
12
|
|
|
|
|
|
|
|
|
SECOND YEAR
First semester
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|