Degree Course: Computational Sciences
A.Y. 2024/2025
Conoscenza e capacità di comprensione
I laureati magistrali in Scienze Computazionali avranno ampie conoscenze nei settori della matematica applicata, dell'informatica e del calcolo scientifico in generale.
Inoltre, avranno ottime capacità nell'utilizzare le conoscenze acquisite per affrontare e risolvere problemi di varia natura in contesti applicativi, anche nell'ambito di altre scienze, quali l'ingegneria, la fisica e le scienze naturali.
Lo strumento didattico per il raggiungimento di tali obiettivi sono le lezioni, le esercitazioni, i seminari e le attività di laboratorio e tutorato.
La verifica avviene attraverso la valutazione di un elaborato scritto e/o un colloquio orale.Capacità di applicare conoscenza e comprensione
I laureati sapranno elaborare o applicare competenze sia per ideare argomentazioni che per risolvere problemi applicativi.
Essi saranno capaci di estrarre informazioni qualitative da dati quantitativi, comprendere, utilizzare e progettare metodi teorici e/o computazionali adeguati; utilizzare in maniera efficace strumenti informatici; gestire ambienti di calcolo ad alte prestazioni.
Lo strumento didattico per il raggiungimento di tali obiettivi sono le lezioni, le esercitazioni, i seminari e le attività di laboratorio e tutorato.
La verifica del raggiungimento degli obiettivi posti avviene di norma mediante:
· le varie prove svolte durante gli insegnamenti impartiti e alla loro conclusione;
· l'esposizione e la discussione dei risultati conseguiti durante la preparazione della prova finale.Autonomia di giudizio
I laureati magistrali in Scienze Computazionali dovranno:
(a) sapere collegare tra loro i diversi concetti matematici, tenendo presente la struttura logica e gerarchica della matematica;
(b) essere in grado di valutare l'appropriatezza di un modello o di una teoria matematica nella descrizione di un fenomeno concreto;
(c) essere in grado di utilizzare strumenti informatici, sia software che hardware, in contesti applicativi;
(d) essere in grado di fare ricerche bibliografiche autonome utilizzando pubblicazioni di contenuto matematico, sviluppando anche una familiarità con le riviste scientifiche di settore;
(e) essere in grado di utilizzare per la ricerca scientifica gli archivi elettronici disponibili sul web, operando la necessaria selezione dell'informazione disponibile;
(f) avere esperienza di lavoro di gruppo, ma anche capacità di lavorare bene autonomamente.
Tutte le attività formative del Corso di Laurea Magistrale in Scienze Computazionali concorrono al raggiungimento degli obiettivi (a) che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Attività specifiche di questo corso di laurea dedicano una grande attenzione verso gli aspetti computazionali e le applicazioni della matematica e dell'informatica, e concorrono al raggiungimento degli obiettivi (b, c).
Le attività di tipo seminariale o di preparazione alle prove scritte sono tipicamente svolte in piccoli gruppi, mentre in altre attività formative prevale il lavoro autonomo dello studente in modo da permettere il raggiungimento degli obiettivi (d), (e) ed (f).
Abilità comunicative
I laureati magistrali in Scienze Computazionali dovranno essere in grado di:
(a) comunicare problemi, idee e soluzioni riguardanti settori avanzati del calcolo scientifico, sia sul versante della matematica applicata che su quello dell'informatica, a un pubblico specializzato o generico, nella propria lingua e in inglese, sia in forma scritta che orale;
(b) dialogare con esperti di altri settori, riconoscendo la possibilità di formalizzare matematicamente problemi applicativi, in ambito industriale e/o finanziario, e formulando gli adeguati modelli matematici a supporto di attività in svariati ambiti.
L'obiettivo (a) è raggiunto sia mediante le prove d'esame di tipo seminariale previste in alcuni insegnamenti che soprattutto con la prova finale; in particolare, per quanto riguarda la lingua inglese, gli insegnamenti faranno uso abituale di testi in lingua inglese, ed è esplicitamente prevista la possibilità che l'elaborato scritto finale sia redatto in lingua inglese.
L'obiettivo (b) è raggiunto principalmente tramite le attività formative affini e integrative, soprattutto per i percorsi con una maggiore attenzione verso gli aspetti computazionali e le applicazioni della matematica e dell'informatica.
Capacità di apprendimento
I laureati magistrali in Scienze Computazionali hanno una mentalità flessibile e sono in grado di inserirsi prontamente negli ambienti di lavoro a un livello di elevata qualificazione, adattandosi facilmente a differenti contesti.
Tutte le attività formative del Corso di Laurea Magistrale in Scienze Computazionali concorrono al raggiungimento di questi obiettivi, che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Tale preparazione può consentire anche l'avvio di un percorso di ricerca in ambito accademico o aziendale.
Requisiti di ammissione
- Conoscenze richieste per l'accesso
Sono ammessi al corso di laurea magistrale in Scienze Computazionali studenti in possesso di laurea triennale, ovvero di altro titolo di studio conseguito all'estero e ritenuto idoneo, previa verifica caso per caso da parte della Commissione Didattica di Matematica del possesso da parte dell'immatricolando dei requisiti curricolari specificati in dettaglio nel Regolamento Didattico del Corso di Studio.
Si richiede inoltre un'adeguata conoscenza della lingua inglese, sia in forma scritta che orale, per la comunicazione in ambito scientifico.
In ogni caso per accedere alla laurea magistrale è necessario che i laureati siano in possesso dei seguenti requisiti curricolari:
- 18 crediti nei settori di formazione matematica di base (MAT/02, MAT/03, MAT/05, MAT/06, MAT/07, MAT/08);
- 6 crediti nei settori di formazione informatica di base (INF/01, ING-INF/05);
- ulteriori 6 crediti nei settori MAT/01-09, FIS/01-08, INF/01, ING-INF/01-05, SECS-S/01-06;
- conoscenze di base della lingua inglese o di altra lingua straniera (livello almeno B1).
- Modalità di verifica del possesso di tali conoscenze
Verrà esaminato il Curriculum Studiorum del candidato; inoltre, saranno previsti colloqui integrativi per coloro che - in possesso dei requisiti curricolari - abbiano delle carenze nella preparazione personale.
Prova finale
La prova finale consiste nella preparazione e nella discussione, davanti ad apposita commissione, di una tesi costituita da un documento scritto (in lingua italiano o inglese), che presenti i risultati di una ricerca nel settore del calcolo scientifico o in applicazioni della matematica.
La tesi è preparata sotto la supervisione di un relatore e si svolge di norma nel secondo anno del corso, occupando circa la metà del tempo complessivo.Orientamento in ingresso
Il Dipartimento di Matematica e Fisica attribuisce una particolare importanza a tutte le attività volte a fornire informazioni necessarie per orientare studenti/esse nella scelta del corso di studio in linea con le politiche dell'Ateneo.
Le azioni di orientamento in ingresso consistono in attività informative e di approfondimento dei caratteri formativi dei Corsi di Studio (CdS) dell'Ateneo, volti a 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 attività promosse si articolano in:
- incontri e manifestazioni rivolte ai futuri studenti;
- sviluppo di servizi online e pubblicazione di guide sull'offerta formativa dei CdS.
L'orientamento in ingresso prevede le seguenti attività principali, distribuite nel corso dell'anno accademico, alle quali partecipa il CdS.
• Giornate di Vita Universitaria (GVU), si svolgono ogni anno nell'arco di circa 4 mesi e sono rivolte agli/alle studenti/esse degli ultimi due anni della scuola secondaria superiore.
Sono tenuti in tutti i Dipartimenti dell'Ateneo e costituiscono un'importante occasione per le future matricole per vivere la realtà universitaria.
Gli incontri sono strutturati in modo tale che, accanto alla presentazione dei Corsi di Laurea, gli/le studenti/esse possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti/esse seniores che svolgono una significativa mediazione di tipo tutoriale.
Sono presentate anche le lauree magistrali attive nel Dipartimento, per rendere gli/le studenti/esse più consapevoli dell'intero percorso formativo loro offerto.
• Open Day Magistrali: da quest'anno si svolge una giornata di orientamento dedicata solo alle lauree magistrali.
Durante tale incontro si presentano i percorsi formativi del corso di studio e le prospettive lavorative dei laureati magistrali in Matematica (che sono molto allettanti e in grande crescita), anche grazie ad un confronto con alcuni portatori di interesse che parteciperanno all'incontro.
• Orientarsi a Roma Tre: manifestazione che riassume le attività di orientamento in ingresso e si svolge ogni anno a metà luglio presso la sede del Rettorato.
Durante la manifestazione viene presentata l'offerta formativa di tutto l'ateneo e sono presenti, con un proprio spazio, le segreterie didattiche e la segreteria studenti.
I servizi di orientamento online messi a disposizione dei/delle future studenti/esse universitari/rie sono nel tempo aumentati, tenendo conto dello sviluppo delle nuove opportunità di comunicazione tramite web.
Inoltre, durante tutte le manifestazioni di presentazione dell'offerta formativa, sono illustrati i siti web (di Dipartimento, di Ateneo, Portale dello studente, etc.), che possono aiutare gli/le studenti/esse nella loro scelta.
Infine, l'Ateneo valuta, di volta in volta, l'opportunità di partecipare ad ulteriori occasioni di orientamento in presenza/online (Salone dello studente ed altre iniziative).
Il Dipartimento di Matematica e Fisica organizza inoltre iniziative per la scuola e il territorio che permettono di entrare in contatto con professori/esse, studenti/esse e personale del Dipartimento.
In particolare, il Dipartimento di Matematica e Fisica è impegnato da vari anni in attività di comunicazione e formazione scientifica dedicate alle scuole:
• Percorsi per le Competenze Trasversali per l'Orientamento (PCTO)
• Corsi di formazione per Insegnanti
• Masterclass
• Orientamento
• Orientamento on-line
• Piano Lauree Scientifiche
• Gare di Matematica
• Seminari divulgativi
• Progetti per le scuole
• Laboratori
Il Corso di studio partecipa anche a numerose attività di comunicazione scientifica in collaborazione con altri Dipartimenti, enti e associazioni esterne (Notte Europea dei Ricercatori - Occhi sulla Luna - Occhi su Marte - Occhi su Giove - Occhi su Saturno).
Ogni anno è organizzato un incontro, rivolto agli studenti della nostra laurea triennale ed a tutti gli eventuali interessati, per presentare la laurea magistrale in Scienze Computazionali, i percorsi formativi disponibili e l'offerta didattica prevista per il successivo anno accademico.Il Corso di Studio in breve
Il Corso di Laurea Magistrale in Scienze Computazionali non è semplicemente un corso di laurea in matematica applicata ma rappresenta un'offerta formativa innovativa di cui il mondo produttivo ha una necessità impellente.
Le molteplici figure professionali che poggiano le proprie competenze sull'utilizzo della matematica e dell'informatica sono attualmente estremamente richieste e al tempo stesso rare.
Per questo abbiamo disegnato un corso di studio che coniuga le aree più profonde della formazione matematica con l'informatica.
Il corso di studio prevede tre curricula:
due di formazione più teorica
- Crittografia e sicurezza informatica;
- Analisi dei dati e statistica;
e uno di formazione più applicativa:
- Modellistica fisica e simulazioni numeriche.
All'interno di ciascun curriculum è proposto, rispettivamente, un percorso formativo denominato:
◦ Crittografia
◦ Data science & statistica
◦ Modelli e simulazioni.
Sia grazie alla ridefinizione dei requisiti in ingresso che alla proposta formativa, gli studenti che si iscrivono a SC provengono non solo dalla Laurea in Matematica ma anche da Fisica, Ingegneria, Informatica ed Economia.
Inoltre, geograficamente provengono sia dai tre atenei romani che da fuori regione (ad esempio Toscana, Abruzzo, Molise, Campania).
Il Corso di Laurea Magistrale in Scienze Computazionali è articolato in una serie di insegnamenti che danno grande rilievo alla matematica applicata e a tutti gli aspetti del calcolo scientifico.
L'obiettivo è formare laureati/e che siano in grado di esercitare attività professionali di tipo modellistico, matematico, computazionale e informatico nel campo industriale, della finanza, dei servizi e della pubblica amministrazione, nonché nella diffusione della cultura scientifica.
I/Le laureati/e potranno esercitare funzioni di elevata responsabilità, con compiti sia di ricerca scientifica che manageriali; l'alto livello di specializzazione raggiunto permetterà sia l'ingresso nel mondo del lavoro a livello internazionale sia l'ingresso ai dottorati di ricerca italiani ed esteri con un'ottima qualificazione.
In particolare, i/le laureati/e nel Corso di Laurea Magistrale in Scienze Computazionali avranno:
◦ ottime conoscenze nell'area della matematica applicata e dell'informatica;
◦ solida padronanza dei metodi propri del calcolo scientifico, sia per quanto riguarda lo sviluppo e l'uso dei modelli matematici che per le tecniche computazionali e informatiche;
◦ capacità di comprendere e utilizzare descrizioni e modelli matematici di situazioni concrete di interesse scientifico, tecnologico e economico;
◦ ottime competenze per la gestione dei sistemi informatici per lo sviluppo e l'uso di software per il calcolo scientifico;
◦ capacità di utilizzare almeno una lingua dell'Unione Europea oltre l'italiano, nell'ambito specifico di competenza e per lo scambio di informazioni generali;
◦ capacità di lavorare in gruppo e di inserirsi prontamente negli ambienti di lavoro.
I piani di studio sono molto flessibili e consentono ampia possibilità di scelta da parte dello/a studente/essa.
Essi prevedono sempre la conoscenza di una lingua straniera, conoscenze informatiche e computazionali, ulteriori conoscenze utili per l'inserimento nel mondo del lavoro e lo svolgimento di un tirocinio interno oppure esterno presso imprese, enti pubblici o privati, ordini professionali.
Inoltre, lo/la studente/essa interessato/a può svolgere parte del proprio percorso formativo in mobilità internazionale.
Tutte le attività proposte forniscono sia una base teorica, sia attività di laboratorio computazionale e informatico dedicate alla modellazione matematica, allo sviluppo di applicazioni informatiche, al calcolo scientifico e ai linguaggi di programmazione.
L'accesso a questo Corso di Laurea Magistrale è aperto a tutti/e i/le laureati/e triennali delle classi di laurea scientifiche.
Sono previste borse di merito sia per gli/le studenti/esse immatricolati/e al primo anno sia per gli/le studenti/esse iscritti/e agli anni successivi.
Lo studente espliciterà le proprie scelte al momento della presentazione,
tramite il sistema informativo di ateneo, del piano di completamento o del piano di studio individuale,
secondo quanto stabilito dal regolamento didattico del corso di studio.
Crittografia e sicurezza informatica
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:
CRITTOGRAFIA E SICUREZZA INFORMATICA: 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
(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.
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9
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MAT/02
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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
(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.
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9
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MAT/02
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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 |
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 |
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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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 |
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.
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6
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MAT/01
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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 |
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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20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
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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 |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
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-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
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Also available in another semester or year
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-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
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Also available in another semester or year
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20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
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Also available in another semester or year
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20410882 -
AC310 - Complex analysis
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Also available in another semester or year
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20410876 -
AM400 - 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 |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
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Also available in another semester or year
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20410455 -
LM420 - THEOREMS IN LOGIC 2
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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 |
20410746 -
AL440 – GROUP THEORY
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Also available in another semester or year
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20410465 -
GE450 - ALGEBRAIC TOPOLOGY
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).
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6
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MAT/03
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48
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12
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-
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-
|
Core compulsory activities
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ITA |
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Optional Group:
CRITTOGRAFIA E SICUREZZA INFORMATICA: 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 - (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
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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
|
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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Core compulsory activities
|
ITA |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
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Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods for Machine Learning
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (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
|
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 |
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20411003 -
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.
|
3
|
FIS/03
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
(objectives)
Present the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms.
|
3
|
ING-INF/05
|
27
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
-
IN510 – QUANTUM COMPUTING MODULE B
(objectives)
Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20411014 -
IN580- ETHICAL HACKING
|
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. 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:
CRITTOGRAFIA E SICUREZZA INFORMATICA: scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/01, MAT/02, MAT/03, MAT/05 tra le attività caratterizzanti (B), di cui almeno 1 Insegnamento (6 CFU) nel SSD MAT/01 - (show)
|
24
|
|
|
|
|
|
|
|
|
Optional Group:
CRITTOGRAFIA E SICUREZZA INFORMATICA: 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 - (show)
|
15
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods 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 statistics, image processing and optimization–and above all a full explanation of the structure of Neural Networks.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
(objectives)
Acquire the knowledge of the main encryption algorithms. Deepen the mathematical skills necessary for the description of the algorithms. Acquire the cryptanalysis techniques used in the assessment of the security level provided by the encryption systems.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
(objectives)
Acquire the basic knowledge of biological systems and problems related to their understanding also in relation to deviations from normal functioning and thus on the onset of pathologies. Maintain the modeling aspect as well as that of numerical simulation, especially problems formulated by equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful for analyzing biological data.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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 |
20411003 -
FS520 – Complex networks
|
Also available in another semester or year
|
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
|
Also available in another semester or year
|
-
IN510 – QUANTUM COMPUTING MODULE B
|
Also available in another semester or year
|
20411014 -
IN580- ETHICAL HACKING
|
6
|
ING-INF/03
|
72
|
-
|
-
|
-
|
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. 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:
COMUNE AI CURRICULA MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e ANALISI DATI E STATISTICA: 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
(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 |
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
(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
(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 |
20410425 -
GE460- GRAPH THEORY
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
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 |
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
|
Also available in another semester or year
|
20410637 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410882 -
AC310 - Complex analysis
|
Also available in another semester or year
|
20410876 -
AM400 - 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 |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
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 |
20410746 -
AL440 – GROUP THEORY
|
Also available in another semester or year
|
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA MODELLISTICA FISICA E SIMULAZIONI NUMERICHE (MFSN) e ANALISI DATI E STATISTICA (ADS): scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui per MFSN 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 mentre per ADS almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 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
|
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 |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods for Machine Learning
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (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
|
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 |
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20411003 -
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.
|
3
|
FIS/03
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
(objectives)
Present the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms.
|
3
|
ING-INF/05
|
27
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
-
IN510 – QUANTUM COMPUTING MODULE B
(objectives)
Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20411014 -
IN580- ETHICAL HACKING
|
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. 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 MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e ANALISI DATI E STATISTICA: 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:
COMUNE AI CURRICULA MODELLISTICA FISICA E SIMULAZIONI NUMERICHE (MFSN) e ANALISI DATI E STATISTICA (ADS): scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui per MFSN 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 mentre per ADS almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods 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 statistics, image processing and optimization–and above all a full explanation of the structure of Neural Networks.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
(objectives)
Acquire the knowledge of the main encryption algorithms. Deepen the mathematical skills necessary for the description of the algorithms. Acquire the cryptanalysis techniques used in the assessment of the security level provided by the encryption systems.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
(objectives)
Acquire the basic knowledge of biological systems and problems related to their understanding also in relation to deviations from normal functioning and thus on the onset of pathologies. Maintain the modeling aspect as well as that of numerical simulation, especially problems formulated by equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful for analyzing biological data.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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 |
20411003 -
FS520 – Complex networks
|
Also available in another semester or year
|
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
|
Also available in another semester or year
|
-
IN510 – QUANTUM COMPUTING MODULE B
|
Also available in another semester or year
|
20411014 -
IN580- ETHICAL HACKING
|
6
|
ING-INF/03
|
72
|
-
|
-
|
-
|
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. 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 MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e ANALISI DATI E STATISTICA: 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
(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 |
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
(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
(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 |
20410425 -
GE460- GRAPH THEORY
|
Also available in another semester or year
|
20410428 -
CR510 – ELLIPTIC CRYPTOSYSTEMS
|
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 |
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
|
Also available in another semester or year
|
20410637 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410609 -
AM300 - Mathematical analysis 5
(objectives)
To acquire a good basic knowledge of Lebesgue integration theory in R^n, of Fourier theory and of the main results in the theory of ordinary differential equations.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410757 -
AM410 - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of general methods and basic techniques necessary to the study of classical and weak solutions for partial differential equations
|
|
-
AM410- MODULE A - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
-
AM410 - MODULE B - AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410756 -
AM420 - PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410882 -
AC310 - Complex analysis
|
Also available in another semester or year
|
20410876 -
AM400 - 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 |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
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 |
20410746 -
AL440 – GROUP THEORY
|
Also available in another semester or year
|
20410465 -
GE450 - ALGEBRAIC TOPOLOGY
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis).
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
COMUNE AI CURRICULA MODELLISTICA FISICA E SIMULAZIONI NUMERICHE (MFSN) e ANALISI DATI E STATISTICA (ADS): scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui per MFSN 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 mentre per ADS almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 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
|
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 |
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods for Machine Learning
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (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
|
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 |
20410437 -
FS430- Theory of Relativity
(objectives)
Make the student familiar with the theoretical underpinnings of General Relativity, both as a geometric theory of space-time and by stressing analogies and differences with the field theories based on local symmetries that describe the interactions among elementary particles. Illustrate the basic elements of differential geometry needed to correctly frame the various concepts. Introduce the student to extensions of the theory of interest for current research.
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410435 -
FS440 - Data Acquisition and Experimental Control
(objectives)
The lectures and laboratories allow the student to learn the basic concepts pinpointing the data acquisition of a high energy physics experiment with specific regard to the data collection, control of the experiment and monitoring.
|
6
|
FIS/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410429 -
FS510 - MONTECARLO METHODS
(objectives)
Acquire the basic elements for dealing with mathematics and physics problems using statistical methods based on random numbers.
|
6
|
FIS/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410432 -
IN550 – MACHINE LEARNING
(objectives)
Learn to instruct a computer to acquire concepts using data, without being explicitly programmed. Acquire knowledge of the main methods of supervised and non-supervised machine learning, and discuss the properties and criteria of applicability. Acquire the ability to formulate correctly the problem, to choose the appropriate algorithm, and to perform the experimental analysis in order to evaluate the results obtained. Take care of the practical aspect of the implementation of the introduced methods by presenting different examples of use in different application scenarios.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410410 -
FM310 - Equations of Mathematical Physics
(objectives)
To acquire a good knowledge of the elementary theory of partial differential equations and of the basic methods of solution, with particular focus on the equations describing problems in mathematical physics.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410555 -
ST410- Statistics
(objectives)
Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language Python . Understand the main constructs used in Python and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410560-2 -
MODULO B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLAB and its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20411003 -
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.
|
3
|
FIS/03
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
(objectives)
Present the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms.
|
3
|
ING-INF/05
|
27
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
-
IN510 – QUANTUM COMPUTING MODULE B
(objectives)
Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20411014 -
IN580- ETHICAL HACKING
|
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. 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 MODELLISTICA FISICA E SIMULAZIONI NUMERICHE e ANALISI DATI E STATISTICA: 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:
COMUNE AI CURRICULA MODELLISTICA FISICA E SIMULAZIONI NUMERICHE (MFSN) e ANALISI DATI E STATISTICA (ADS): scegliere 3 Insegnamenti (24 CFU) nei seguenti SSD MAT/06, MAT/07, MAT/08, MAT/09 tra le attività caratterizzanti (B), di cui per MFSN 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 mentre per ADS almeno 1 Insegnamento (6 CFU) nel SSD MAT/06 e 1 Insegnamento (6 CFU) nel SSD MAT/08 - (show)
|
24
|
|
|
|
|
|
|
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Core compulsory activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
Also available in another semester or year
|
20410875 -
FM530 - Mathematical Methods 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 statistics, image processing and optimization–and above all a full explanation of the structure of Neural Networks.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
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 ANALISI DATI E STATISTICA e CRITTOGRAFIA E SICUREZZA INFORMATICA - (show)
|
30
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410447 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410416 -
FM410-Complements of Analytical Mechanics
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
|
20410416-1 -
FM410-Complements of Analytical Mechanics - MODULE A
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410416-2 -
FM410-Complements of Analytical Mechanics - Module B
(objectives)
To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
|
3
|
MAT/07
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
(objectives)
Acquire the knowledge of the main encryption algorithms. Deepen the mathematical skills necessary for the description of the algorithms. Acquire the cryptanalysis techniques used in the assessment of the security level provided by the encryption systems.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410429 -
FS510 - MONTECARLO METHODS
|
Also available in another semester or year
|
20410432 -
IN550 – MACHINE LEARNING
|
Also available in another semester or year
|
20410410 -
FM310 - Equations of Mathematical Physics
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410560 -
IN400- Python and MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted languages Python and MATLAB. Understand the main constructs used in Python and MATLAB and their application to scientific computing and data processing scenarios.
|
|
20410560-1 -
MODULO A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULO B - MATLAB programming
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
(objectives)
Provide the student with a first view of some of the fundamental topics of Astrophysics and Cosmology using the mathematical and physical knowledge acquired in the first two years
|
6
|
FIS/05
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410626 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
MAT/09
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
(objectives)
Introduction to the theory of stochastic processes. Markov chains: ergodic theory, coupling, mixing times, with applications to random walks, card shuffling, and the Monte Carlo method. The Poisson process, continuous time Markov chains, convergence to equilibrium for some simple interacting particle systems.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
(objectives)
Acquire the basic knowledge of biological systems and problems related to their understanding also in relation to deviations from normal functioning and thus on the onset of pathologies. Maintain the modeling aspect as well as that of numerical simulation, especially problems formulated by equations and discrete systems. Acquire the knowledge of the major bio-informatics algorithms useful for analyzing biological data.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410470 -
FM510 - MATHEMATICAL PHYSICS APPLICATIONS
|
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 |
20411003 -
FS520 – Complex networks
|
Also available in another semester or year
|
20411002 -
IN510 – QUANTUM COMPUTING
(objectives)
Module A PPresent the computational paradigm of Quantum Computing. By the end of the course, students should be able to understand even complex Quantum algorithms and to analyze and write simple quantum algorithms. Module B Study of the quantum circuit model and its universality, in-depth exploration of key quantum techniques for algorithm design and analysis, and the introduction to some quantum programming languages and software platforms for the specification of quantum computations.
|
|
-
IN510 – QUANTUM COMPUTING MODULE A
|
Also available in another semester or year
|
-
IN510 – QUANTUM COMPUTING MODULE B
|
Also available in another semester or year
|
20411014 -
IN580- ETHICAL HACKING
|
6
|
ING-INF/03
|
72
|
-
|
-
|
-
|
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. 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
|