Degree Course: Mathematics
A.Y. 2014/2015
Conoscenza e capacità di comprensione
I laureati in Matematica avranno:
* acquisito una conoscenza ampia e adeguata di tematiche avanzate in più settori della matematica, nonché in alcuni settori affini a questa disciplina;
* potuto acquisire una conoscenza adeguata di tecniche di formalizzazione e modellizzazione, anche complesse, tipiche delle applicazioni della matematica in vari ambiti scientifici e professionali;
* potuto acquisire un livello di comprensione del linguaggio, delle tecniche e dei contenuti dei principali settori della matematica, soprattutto relativi al campo di specializzazione prescelta, tale da metterli in grado di iniziare percorsi di avviamento alla ricerca.
Inoltre, i laureati in Matematica dovranno avere facilità di astrazione, incluso lo sviluppo logico di teorie formali e delle loro relazioni.
Lo strumento didattico privilegiato per il raggiungimento di tali obiettivi sono le lezioni, le esercitazioni, i seminari e le attività di laboratorio e tutorato.
La verifica avviene in forma classica attraverso la valutazione di un elaborato scritto e/o un colloquio orale.
Capacità di applicare conoscenza e comprensione
I laureati magistrali in Matematica dovranno essere in grado di elaborare o applicare idee, anche originali, e possedere sicure competenze sia per ideare e sostenere argomentazioni che per risolvere problemi nel proprio campo di studi.
In particolare, essi dovranno essere in grado di:
* comprendere approfonditamente problemi matematici anche di livello elevato;
* identificare gli elementi essenziali di un problema e saperlo modellizzare, in termini matematici, identificando metodologie idonee per la sua soluzione;
* produrre dimostrazioni originali e rigorose di semplici proposizioni in diversi campi della matematica;
Inoltre, con riferimento al campo di specializzazione prescelta, essi dovranno essere capaci di:
* estrarre informazioni qualitative da dati quantitativi;
* comprendere, utilizzare e progettare metodi teorici e/o computazionali adeguati alle tematiche affrontate;
* utilizzare in maniera efficace strumenti informatici di supporto.
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.
L'elevato rigore richiesto nella soluzione dei quesiti delle prove scritte, il lavoro individuale richiesto per superare gli esami, e soprattutto il lavoro di tesi finale, che comprende anche un autonomo lavoro di ricerca bibliografica e di raccolta di informazioni, consente il raggiungimento di questi obiettivi.
Autonomia di giudizio
I laureati magistrali in Matematica dovranno:
(a) sapere collegare tra loro i diversi concetti matematici, tenendo presente la struttura logica e gerarchica della matematica;
(b) essere in grado di analizzare criticamente una dimostrazione, e di produrne una standard ove occorra;
(c) essere in grado di valutare l'appropriatezza di un modello o di una teoria matematica nella descrizione di un fenomeno concreto;
(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 Matematica concorrono al raggiungimento degli obiettivi (a) e (b), che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Le attività affini e integrative previste dal Corso di Laurea Magistrale concorrono al raggiungimento dell'obiettivo (c) soprattutto per i percorsi con una maggiore attenzione verso gli aspetti computazionali e le applicazioni della matematica.
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 Matematica dovranno essere in grado di:
(a) comunicare problemi, idee e soluzioni riguardanti settori avanzati della Matematica, sia proprie sia di altri autori, 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 situazioni di interesse applicativo, industriale 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.
Capacità di apprendimento
I laureati magistrali in Matematica:
(a) sono in grado di accedere al dottorato di ricerca, sia in Matematica che in altre discipline, con un alto grado di autonomia;
(b) hanno una mentalità flessibile, e sono in grado di inserirsi prontamente negli ambienti di lavoro, a un livello di elevata qualificazione, adattandosi facilmente a nuove problematiche.
Tutte le attività formative del Corso di Laurea Magistrale in Matematica concorrono al raggiungimento di questi obiettivi, che caratterizzano in modo particolare la preparazione del laureato magistrale in Matematica.
Requisiti di ammissione
Per l'ammissione al Corso di Laurea Magistrale in Matematica è richiesto il possesso di laurea o di diploma universitario di durata almeno triennale, o di altro titolo di studio conseguito all'estero e riconosciuto idoneo, e degli specifici requisiti curriculari confermanti il possesso di sufficienti conoscenze di base di Matematica e della lingua inglese, e descritti nel Regolamento Didattico del Corso di Laurea Magistrale.
Inoltre sarà effettuata una verifica della personale preparazione dello studente, basata su un esame del curriculum pregresso e su un eventuale colloquio orale, con modalità descritte in dettaglio nel Regolamento Didattico del Corso di Laurea Magistrale.
Tenendo conto delle specificità della preparazione iniziale, secondo modalità previste nel Regolamento Didattico del Corso di Laurea Magistrale, l'ammissione potrà essere subordinata alla scelta da parte dello studente di un piano di studi individuale, concordato con il Consiglio del Corso, che comunque dovrà essere conforme all'Ordinamento Didattico.
Si prevede in particolare, per studenti provenienti da Corsi di Laurea Triennali di altre facoltà, la possibilità di concordare dei piani di studio adeguati che potrebbero richiedere l'acquisizione preventiva di competenze previste dalla Laurea Triennale in Matematica.
Prova finale
La prova finale del Corso di Laurea Magistrale in Matematica consiste nella stesura di una tesi (in italiano o in inglese) elaborata in modo originale dallo studente con l'assistenza di almeno un docente (relatore), eventualmente esterno al corso di studi, e in una esposizione orale di tipo seminariale conclusiva del lavoro svolto.
La prova finale verrà valutata in base all'originalità dei risultati, alla padronanza dell'argomento, all'autonomia e alle capacità espositive e di ricerca bibliografica mostrate dal candidato.
La redazione della tesi può eventualmente avvenire anche all'interno di un tirocinio formativo (stage) presso aziende o laboratori esterni, o durante soggiorni di studio presso altre università italiane ed estere, anche nel quadro di accordi internazionali.Sbocchi occupazionali e professionali previsti per i laureati
I laureati nel Corso di Laurea Magistrale in Matematica potranno:
• esercitare funzioni di elevata responsabilità nella costruzione e analisi di modelli matematici di varia natura e nella progettazione ed analisi di metodi per la loro risoluzione in ambiti applicativi, scientifici, industriali, aziendali, nei servizi e nella pubblica amministrazione, con vari ambiti di interesse, tra cui quello informatico, finanziario, ingegneristico, ambientale, sanitario;
• esercitare funzioni di elevata responsabilità nei settori dell'insegnamento e della comunicazione della Matematica e della scienza;
• inserirsi nella ricerca tramite la prosecuzione degli studi nei corsi di Dottorato di Ricerca, in Matematica o in altre discipline scientifiche.
I laureati nel Corso di Laurea Magistrale in Matematica hanno le competenze (o possono facilmente acquisire le eventuali conoscenze necessarie mancanti) per svolgere le professioni dei punti 2.1.1.3.1 (Matematici), 2.1.1.3.2 (Statistici) e 2.6.2.1.1 (Ricercatori e tecnici laureati nelle scienze matematiche e dell'informazione) della classificazione ISTAT delle professioni.
I laureati possono prevedere come occupazione anche attività di insegnamento, una volta completato il processo di abilitazione all'insegnamento e superati i concorsi previsti dalla normativa vigente.
Orientamento in ingresso
Le attività di orientamento, tirocinio, stage e placement, a livello di Ateneo, sono promosse e coordinate dal Gruppo di Lavoro per l’Orientamento di Ateneo (GLOA) costituito da delegati di ciascun Dipartimento dell'Ateneo, dalla Responsabile della Divisione Politiche per gli Studenti e coordinato dal delegato del Rettore per le politiche di orientamento.
Il GLOA promuove azioni relative all’orientamento in ingresso, all’orientamento in itinere (tutorato, tirocini e stage) e all’orientamento in uscita (politiche attive per il lavoro e placement).
Le azioni di orientamento in ingresso sono improntate alla realizzazione di processi di raccordo con la scuola media secondaria.
Si concretizzano in attività di carattere informativo sui Corsi di Studio (CdS) dell'Ateneo ma anche come impegno condiviso da Scuola e Università per favorire lo sviluppo di una maggiore consapevolezza da parte degli studenti nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attività promosse si articolano in:
a) seminari e attività formative realizzate in collaborazione con i docenti della scuola;
b) incontri e manifestazioni informative rivolte alle future matricole;
c) sviluppo di servizi on line per l'orientamento e l'auto-orientamento.
Tra le attività svolte in collaborazione con le scuole per lo sviluppo di una maggiore consapevolezza nella scelta, il “progetto di auto-orientamento” è un intervento significativo che consente di promuovere un raccordo particolarmente qualificato con alcune scuole medie superiori che insistono sul territorio limitrofo a Roma Tre.
Il progetto, infatti, è articolato in incontri svolti presso le scuole dagli esperti dell'Ufficio Orientamento con la collaborazione di studenti seniores ed è finalizzato a sollecitare nelle future matricole una riflessione sui propri punti di forza e sui criteri di scelta (gli incontri si svolgono nel periodo ottobre-dicembre).
La presentazione dell'offerta formativa agli studenti delle scuole superiori prevede tre eventi principali, distribuiti nel corso dell'anno accademico, ai quali partecipano tutti i CdS.
• Salone dello studente “Campus orienta”, si svolge presso la fiera di Roma fra ottobre e novembre e coinvolge tradizionalmente tutti gli Atenei del Lazio e molti Atenei fuori Regione, Enti pubblici e privati che si occupano di Formazione e Lavoro.
Roma Tre partecipa a questo evento con un proprio spazio espositivo e con conferenze di presentazione dell'offerta formativa dell'Ateneo.
• Le Giornate di Vita Universitaria (GVU) si svolgono ogni anno da gennaio a marzo e sono rivolte agli studenti degli ultimi due anni della scuola secondaria superiore.
Si svolgono in tutti i Dipartimenti dell'Ateneo e costituiscono una importante occasione per le future matricole per vivere la realtà universitaria.
Gli incontri sono strutturati in modo tale che accanto alla presentazione dei CdS, gli studenti possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente oltre 6.000 studenti delle secondarie.
• Orientarsi a Roma Tre rappresenta la manifestazione che chiude le annuali attività di orientamento in ingresso e si svolge in Ateneo a luglio di ogni anno.
L'evento accoglie mediamente circa 3.000 studenti romani e non solo, che partecipano per mettere definitivamente a fuoco la loro scelta universitaria.
Oltre all'offerta formativa sono presentati tutti i principali servizi di Roma Tre rivolti agli studenti e le segreterie didattiche sono a disposizione per tutte le informazioni relative alle pratiche di immatricolazione.
In tutte le manifestazioni di presentazione dell'offerta formativa, sono illustrati anche i vari servizi on line che possono aiutare gli studenti nella scelta: dai siti web dei Dipartimenti al sito del POS (Prove di Orientamento Simulate) che consente alle future matricole di autovalutarsi rispetto ai requisiti di accesso per tutti i CdS di Roma Tre.
Inoltre durante i suddetti incontri agli studenti viene presentato il sito web Orientarsi, un servizio pensato proprio in loro funzione, iscrivendosi al quale, possono ricevere sulla propria casella di posta elettronica, le informazioni relative ai CdS ai cui sono interessati e le informazioni di carattere pratico relative alle procedure amministrative di preiscrizione.
Infine, in tutte le manifestazioni che si svolgono in Ateneo sono somministrati ai partecipanti questionari di soddisfazione che vengono elaborati ed utilizzati per proporre miglioramenti all'organizzazione degli eventi.
Il Corso di Studio in breve
ALCUNE CARATTERISTICHE DEL CORSO DI LAUREA MAGISTRALE:
• ampia scelta dei piani di studio, sia dal punto di vista della Matematica di base che della Informatica teorica;
• un alto livello di specializzazione che permette sia l'ingresso nel mondo del lavoro
con competenze di tipo manageriale, sia l'ingresso ai dottorati di ricerca italiani ed
esteri con un'ottima qualificazione.
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.
comune
FIRST YEAR
First semester
Course
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Credits
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Scientific Disciplinary Sector Code
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Contact Hours
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Exercise Hours
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Laboratory Hours
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Personal Study Hours
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Type of Activity
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Language
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Optional Group:
comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
28
|
|
|
|
|
|
|
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20402083 -
AL4 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
OBTAIN GOOD KNOWLEDGE OF THE CONCEPTS AND METHODS OF THE THEORY OF EQUATIONS IN ONE VARIABLE. UNDERSTAND AND BE ABLE TO APPLY THE “FUNDAMENTAL THEOREM OF CORRESPONDENCE OF GALOIS” IN ORDER STUDY THE “COMPLEXITY” OF A POLYNOMIAL.
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7
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MAT/02
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72
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-
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-
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-
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Core compulsory activities
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ITA |
20402085 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
The student is going to learn the basics of the Lebesgue integration theory: measure spaces, measurability, Lebesgue integral, L^p spaces, differentiation.
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7
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MAT/05
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72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402087 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
A REFINED STUDY OF TOPOLOGY VIA ALGEBRAIC AND ANALYTIC TOOLS.
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7
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MAT/03
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72
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-
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-
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-
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Core compulsory activities
|
ITA |
20402090 -
MC410 - COMPLEMENTARY MATHEMATICS 1
(objectives)
To acquire deep understanding of the principal geometry arguments treated in high-school mathematics
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7
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MAT/04
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60
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-
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-
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-
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Core compulsory activities
|
ITA |
20402094 -
AL410 - COMMUTATIVE ALGEBRA
(objectives)
THE PURPOSE OF THIS COURSE IS TO DEEPEN THE KNOWLEDGE OF SOME TOOLS AND FUNDAMENTAL PROPERTIES OF COMMUTATIVE RINGS AND THEIR MODULES, WITH PARTICULAR EMPHASIS TO THE CASE OF RINGS ARISING IN ALGEBRAIC NUMBER THEORY AND ALGEBRAIC GEOMETRY.
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7
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MAT/02
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60
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-
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-
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-
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Core compulsory activities
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ITA |
20402095 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
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Also available in another semester or year
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20402097 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations
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7
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MAT/05
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60
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-
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-
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-
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Core compulsory activities
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ITA |
20402104 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduction to the study of topological and geometrical structures defined using algebraic methods. Refinement of the algebraic knowledge using applications to the study of algebraic varieties in affine and projective spaces.
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7
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MAT/03
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60
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-
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-
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-
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Core compulsory activities
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ITA |
20402106 -
GE430 - DIFFERENTIAL GEOMETRY 2
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Also available in another semester or year
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20402113 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
Problem solving with examples from secondary school mathematical curricula, with the help of a computer and a direct use of numerical and symbolic calculus and dynamical geometry software (MATHEMATICA, introduction on CABRI and GEOGEBRA). All examples, in an interactive and “laboratorial” lessons, point at experience limits and opportunities of using computers at school on selected arguments like numerical approximation or visualization in geometry as well as analysis.
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7
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MAT/04
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60
|
-
|
-
|
-
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Core compulsory activities
|
ITA |
20402119 -
LM410 - MATHEMATICAL LOGIC 1
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7
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MAT/01
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60
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-
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-
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-
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Core compulsory activities
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ITA |
20402187 -
AL440 – GROUP THEORY
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Also available in another semester or year
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20402292 -
AM440 - SPECIAL TOPICS OF ORDINARY DIFFERENTIAL EQUATIONS
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Also available in another semester or year
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20402328 -
MC440 - FIRST ORDER CLASSICAL LOGIC
(objectives)
TO KNOW – AT A GRADUATE LEVEL – RESULTS ON LOGIC, INDEED MATHEMATICAL THEOREMS ON LOGIC, WHICH ARE AT THE BASIS OF THE INTERACTION BETWEEN LOGIC, COMPUTER SCIENCES AND OTHER SCIENCES (IN PARTICUALR, COMMUNICATION SCIENCES).
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7
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MAT/01
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60
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-
|
-
|
-
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Core compulsory activities
|
ITA |
20402338 -
AC310 – COMPLEX ANALYSIS 1
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7
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MAT/03
|
72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
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7
|
|
|
|
|
|
|
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20402086 -
FM310 - MATHEMATICAL PHYSICS 2
(objectives)
The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations
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7
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MAT/07
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72
|
-
|
-
|
-
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Core compulsory activities
|
ITA |
20402088 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.
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7
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MAT/08
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72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402092 -
AN420 - NUMERICAL ANALYSIS 2
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Also available in another semester or year
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20402093 -
CP410 - PROBABILITY 2
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Also available in another semester or year
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20402101 -
CP430 - STOCHASTIC CALCULUS
(objectives)
Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.
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7
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MAT/06
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60
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-
|
-
|
-
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Core compulsory activities
|
ITA |
20402103 -
FM410 - MATHEMATICAL PHYSICS 3
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Also available in another semester or year
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20402123 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.
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7
|
MAT/08
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402327 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS
(objectives)
The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).
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7
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MAT/07
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60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402331 -
CP420 - STOCHASTIC PROCESSES (READING COURSE)
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)
|
28
|
|
|
|
|
|
|
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20402089 -
IN410 - COMPUTER SCIENCE 2
|
Also available in another semester or year
|
20402091 -
TN410 - INTRODUCTION TO NUMBER THEORY
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Also available in another semester or year
|
20402102 -
CR410 - CRYPTOGRAPHY 1
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Also available in another semester or year
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20402107 -
GE510 - ALGEBRAIC GEOMETRY 2
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Also available in another semester or year
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20402108 -
IN430 - INFORMATICS 4: ADVANCED COMPUTING TECHNIQUES
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Also available in another semester or year
|
20402110 -
IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY
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Also available in another semester or year
|
20402111 -
IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY
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Also available in another semester or year
|
20402114 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
To acquire deep understanding of some of the principal arguments treated in high-school mathematics
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402115 -
ST410 - STATISTICS 1
(objectives)
THE PURPOSE OF THIS COURSE IS TO INTRODUCE MATHEMATICAL STATISTICS, STATISTICAL INFERENCE AND THE USE OF STATISTICAL SOFTWARE TO STUDENTS WITH A GOOD BAKCGROUND IN MATHEMATICS.
|
7
|
SECS-S/01
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402117 -
FS410 - PHYSICS 3: RELATIVITY AND RELATIVISTIC THEORIES
|
Also available in another semester or year
|
20402120 -
LM510 - LINEAR TYPES AND LOGIC
|
Also available in another semester or year
|
20402122 -
FS420 - QUANTUM MECHANICS
(objectives)
GAIN KNOWLEDGE OF THE BASIC PRINCIPLES OF QUANTUM MECHANICS APPLIED TO SIMPLE PHYSICAL SYSTEMS
|
7
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402247 -
AM520 - OPERATOR THEORY 1
|
Also available in another semester or year
|
20402291 -
ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20402297 -
AL410 - COMMUTATIVE ALGEBRA - C
(objectives)
THE PURPOSE OF THIS COURSE IS TO DEEPEN THE KNOWLEDGE OF SOME TOOLS AND FUNDAMENTAL PROPERTIES OF COMMUTATIVE RINGS AND THEIR MODULES, WITH PARTICULAR EMPHASIS TO THE CASE OF RINGS ARISING IN ALGEBRAIC NUMBER THEORY AND ALGEBRAIC GEOMETRY.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402298 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C
(objectives)
To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations
|
7
|
MAT/05
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402299 -
AN410 - NUMERICAL ANALYSIS 1 - C
(objectives)
THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.
|
7
|
MAT/08
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402300 -
CP410 - PROBABILITY 2 - C
(objectives)
To gain a solid knowledge of the basic aspects of probabilità theory: construction of probabilità measures on measurable spaces, 0-1 law, independence, conditional expectation, random variables, convergence of random variables, characteristic functions, central limit theorem, branching processes, discrete martingales.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402301 -
FM410 - MATHEMATICAL PHYSICS 3 - C
(objectives)
CONTINUING THE STUDY, BEGAN DURING FM210, OF DYNAMIC SYSTEMS OF PHYSICAL INTEREST WITH MOST STYLISH AND POWERFUL TECHNIQUES, SUCH AS THE LAGRANGIAN AND HAMITONIAN FORMALISM, THAT ARE IN THE VAST RANGE OF APPLICATIONS OF ANALYSIS AND MATHEMATICAL PHYSICS.
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402302 -
GE410 - ALGEBRAIC GEOMETRY 1 - C
(objectives)
Introduction to the study of topological and geometrical structures defined using algebraic methods. Refinement of the algebraic knowledge using applications to the study of algebraic varieties in affine and projective spaces.
|
7
|
MAT/03
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402303 -
LM410 - MATHEMATICAL LOGIC 1 - C
|
7
|
MAT/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402304 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C
|
Also available in another semester or year
|
20402305 -
MC410 - COMPLEMENTARY MATHEMATICS 1 - C
(objectives)
To acquire deep understanding of the principal geometry arguments treated in high-school mathematics
|
7
|
MAT/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402306 -
AN420 - NUMERICAL ANALYSIS 2 - C
|
Also available in another semester or year
|
20402309 -
CP430 - STOCHASTIC CALCULUS - C
(objectives)
Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402312 -
GE430 - DIFFERENTIAL GEOMETRY 2 - C
|
Also available in another semester or year
|
20402313 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C
(objectives)
Problem solving with examples from secondary school mathematical curricula, with the help of a computer and a direct use of numerical and symbolic calculus and dynamical geometry software (MATHEMATICA, introduction on CABRI and GEOGEBRA). All examples, in an interactive and “laboratorial” lessons, point at experience limits and opportunities of using computers at school on selected arguments like numerical approximation or visualization in geometry as well as analysis.
|
7
|
MAT/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402314 -
AL440 – GROUP THEORY - C
|
Also available in another semester or year
|
20402315 -
AM440 - SPECIAL TOPICS OF ORDINARY DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402329 -
MC440 - FIRST ORDER CLASSICAL LOGIC - C
(objectives)
TO KNOW – AT A GRADUATE LEVEL – RESULTS ON LOGIC, INDEED MATHEMATICAL THEOREMS ON LOGIC, WHICH ARE AT THE BASIS OF THE INTERACTION BETWEEN LOGIC, COMPUTER SCIENCES AND OTHER SCIENCES (IN PARTICUALR, COMMUNICATION SCIENCES).
|
7
|
MAT/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402330 -
AL420 - ALGEBRAIC NUMBER THEORY - C
|
Also available in another semester or year
|
20402332 -
CP420 - STOCHASTIC PROCESSES (READING COURSE) - C
|
Also available in another semester or year
|
20402334 -
MC520 - AXIOMATIC SET THEORY
|
Also available in another semester or year
|
20402335 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C
|
Also available in another semester or year
|
20402337 -
IN460 - COMPUTER SCIENCE 10, COMPUTATIONAL GRAPHICS
|
Also available in another semester or year
|
20402339 -
MA420 - GEOMETRIC AND PHYSICAL MODELLING
|
Also available in another semester or year
|
|
20402127 -
UCL - FURTHER LANGUAGE STUDIES
(objectives)
The student is going to acquire the ability to read a scientific text in English, or , if he or she chooses, in any other European tongue.
|
5
|
|
40
|
-
|
-
|
-
|
Other activities
|
ITA |
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA AIT E IN530 - (show)
|
4
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)
|
10
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
28
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
7
|
|
|
|
|
|
|
|
20402086 -
FM310 - MATHEMATICAL PHYSICS 2
(objectives)
The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations
|
7
|
MAT/07
|
72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402088 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20402092 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402093 -
CP410 - PROBABILITY 2
|
Also available in another semester or year
|
20402101 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20402103 -
FM410 - MATHEMATICAL PHYSICS 3
|
Also available in another semester or year
|
20402123 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402327 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS
(objectives)
The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402331 -
CP420 - STOCHASTIC PROCESSES (READING COURSE)
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)
|
28
|
|
|
|
|
|
|
|
20402089 -
IN410 - COMPUTER SCIENCE 2
(objectives)
The course Theory of Computation and Interaction provides a in-deep view of theoretical aspects related to the concept of computation and the study of relations between different models of computation. The basic knowledge on information technology is here extended with new concepts and theoretical viewpoints. The course is divided into two units of 6 CFU. At choice, the student can decide to pass the first unit or both (12 CFU). More specifically, the course provides a formal presentation of the concepts of algorithm and computability. After the introduction of the classical concept of computability as formalized by Alan M. Turing, we address the basic concepts of algorithmic complexity and problem decidability, functional models and functional programming. In the second unit, we focus on interactive paradigms in the theory of computation which allow the description of additional complexity classes and their use in the semantics of programming languages.
|
7
|
INF/01
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402091 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
TO ACQUIRE A GOOD KNOWLEDGE OF CONCEPTS AND METHODS OF ELEMENTARY NUMBER THEORY, WITH PARTICULAR RESPECT OF STUDY OF DIOPHANTINE EQUATIONS AND POLYNOMIAL CONGRUENCES. TO GIVE PREREQUISITES FOR ADVANCED COURSES OF ALGEBRAIC AND ANALYTIC NUMBER THEORY.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402102 -
CR410 - CRYPTOGRAPHY 1
(objectives)
ACQUIRE GOOD KNOWLEDGE OF THE CONCEPTS AND MATHEMATICAL METHODS OF PUBLIC KEY CRYPTOGRAPHY PROVIDING AN OVERVIEW OF THOSE WHICH ARE CURRENTLY IN USE.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402107 -
GE510 - ALGEBRAIC GEOMETRY 2
(objectives)
Introduction and applications od the language of modern algebraic geometry through the theory of sheaves and the theory of schemes. In depth examination of the interactions of geometry and algebra. Description of research themes and open problems in modern algebra and geometry.
|
7
|
MAT/03
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402108 -
IN430 - INFORMATICS 4: ADVANCED COMPUTING TECHNIQUES
(objectives)
THE COURSE IN430 – COMPUTER SCIENCE 4, ADVANCED COMPUTATIONAL TECHNIQUES IS FOCUSED ON THE ACQUISITION OF OBJECT ORIENTED PROGRAMMING LANGUAGES AND APPLICATION OF CONCEPTUAL TOOLS FOR ANALYSIS AND DEVELOPMENT IN OBJECT ORIENTEND PROGRAMMING. THIS COURSE INCLUDES AN INTRODUCTION TO MODELING AND DESIGN OF CLASSES THROUGH UML DIAGRAMS, AND THE STUDY OF SPECIFICATION AND IMPLEMENTATION OF ALGORITHMS ON GRAPHS. THREAD CONCORRENCY OPPORTUNITIES AND CAVEATS ARE DISCUSSED. DISTRIBUTED (MOBILE) COMPUTING OVER THE NETWORK AND IN THE CLOUD IS INTRODUCED AND DISCUSSED.
|
7
|
INF/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402110 -
IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20402111 -
IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY
(objectives)
Nowadays, information is often stored and transmitted electronically. Ensuring the security of the vast and complex infrastructure of computers, servers and networks is an immense challenge. In this scenario, this course aims at describing: - The relationship between number theory and information security techniques; - How to protect networks, secure electronic assets, prevent attacks, ensure the privacy of computer users, and build secure infrastructures.
|
7
|
INF/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402114 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
|
Also available in another semester or year
|
20402115 -
ST410 - STATISTICS 1
|
Also available in another semester or year
|
20402117 -
FS410 - PHYSICS 3: RELATIVITY AND RELATIVISTIC THEORIES
|
7
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402120 -
LM510 - LINEAR TYPES AND LOGIC
(objectives)
A DEEP AND CRITICAL INTRODUCTION TO A SPECIFIC LOGICAL THEORY WHICH CONCERNS THE THEME OF THE INTERACTION AND IS CENTRAL IN THE CONTEMPORARY RESEARCH ON INFROMATION AND COMMUNICATION: LINEAR LOGIC AND ITS DEVELOPMENTS.
|
7
|
MAT/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402122 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20402247 -
AM520 - OPERATOR THEORY 1
|
Also available in another semester or year
|
20402291 -
ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20402297 -
AL410 - COMMUTATIVE ALGEBRA - C
|
Also available in another semester or year
|
20402298 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402299 -
AN410 - NUMERICAL ANALYSIS 1 - C
|
Also available in another semester or year
|
20402300 -
CP410 - PROBABILITY 2 - C
|
Also available in another semester or year
|
20402301 -
FM410 - MATHEMATICAL PHYSICS 3 - C
|
Also available in another semester or year
|
20402302 -
GE410 - ALGEBRAIC GEOMETRY 1 - C
|
Also available in another semester or year
|
20402303 -
LM410 - MATHEMATICAL LOGIC 1 - C
|
Also available in another semester or year
|
20402304 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C
(objectives)
CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402305 -
MC410 - COMPLEMENTARY MATHEMATICS 1 - C
|
Also available in another semester or year
|
20402306 -
AN420 - NUMERICAL ANALYSIS 2 - C
(objectives)
THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402309 -
CP430 - STOCHASTIC CALCULUS - C
|
Also available in another semester or year
|
20402312 -
GE430 - DIFFERENTIAL GEOMETRY 2 - C
|
Also available in another semester or year
|
20402313 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C
|
Also available in another semester or year
|
20402314 -
AL440 – GROUP THEORY - C
|
Also available in another semester or year
|
20402315 -
AM440 - SPECIAL TOPICS OF ORDINARY DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402329 -
MC440 - FIRST ORDER CLASSICAL LOGIC - C
|
Also available in another semester or year
|
20402330 -
AL420 - ALGEBRAIC NUMBER THEORY - C
|
Also available in another semester or year
|
20402332 -
CP420 - STOCHASTIC PROCESSES (READING COURSE) - C
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402334 -
MC520 - AXIOMATIC SET THEORY
|
7
|
MAT/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402335 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C
(objectives)
The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402337 -
IN460 - COMPUTER SCIENCE 10, COMPUTATIONAL GRAPHICS
(objectives)
The course aims to develop the skill needed to (a) produce geometric models of highly complex components and structures, both natural and man-made, and (b) understand the design and development of computer-aided modeling and simulation. The lectures offer some background about the geometric and mathematical techniques required, and provide insight into some main topics of computer graphics techniques, including computer rendering, geometric computing and scientific visualization. The theory is carefully linked to practice by implementing programming projects in a cutting edge graphics environment based on Javascript and webGL.
|
7
|
ING-INF/05
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402339 -
MA420 - GEOMETRIC AND PHYSICAL MODELLING
(objectives)
This course aims at highlighting the role of the association between physical quantities and geometrical objects in the mathematical models of physical reality. Exterior algebra and exterior calculus (differential and discrete) are introduced from this perspective.
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA AIT E IN530 - (show)
|
4
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)
|
10
|
|
|
|
|
|
|
|
|
SECOND 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 Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
28
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
7
|
|
|
|
|
|
|
|
20402086 -
FM310 - MATHEMATICAL PHYSICS 2
|
Also available in another semester or year
|
20402088 -
AN410 - NUMERICAL ANALYSIS 1
(objectives)
THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.
|
7
|
MAT/08
|
72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402092 -
AN420 - NUMERICAL ANALYSIS 2
|
Also available in another semester or year
|
20402093 -
CP410 - PROBABILITY 2
(objectives)
To gain a solid knowledge of the basic aspects of probabilità theory: construction of probabilità measures on measurable spaces, 0-1 law, independence, conditional expectation, random variables, convergence of random variables, characteristic functions, central limit theorem, branching processes, discrete martingales.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402101 -
CP430 - STOCHASTIC CALCULUS
(objectives)
Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402103 -
FM410 - MATHEMATICAL PHYSICS 3
(objectives)
CONTINUING THE STUDY, BEGAN DURING FM210, OF DYNAMIC SYSTEMS OF PHYSICAL INTEREST WITH MOST STYLISH AND POWERFUL TECHNIQUES, SUCH AS THE LAGRANGIAN AND HAMITONIAN FORMALISM, THAT ARE IN THE VAST RANGE OF APPLICATIONS OF ANALYSIS AND MATHEMATICAL PHYSICS.
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402123 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
|
Also available in another semester or year
|
20402327 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS
|
Also available in another semester or year
|
20402331 -
CP420 - STOCHASTIC PROCESSES (READING COURSE)
|
Also available in another semester or year
|
|
Optional Group:
comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)
|
28
|
|
|
|
|
|
|
|
20402089 -
IN410 - COMPUTER SCIENCE 2
|
Also available in another semester or year
|
20402091 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20402102 -
CR410 - CRYPTOGRAPHY 1
|
Also available in another semester or year
|
20402107 -
GE510 - ALGEBRAIC GEOMETRY 2
|
Also available in another semester or year
|
20402108 -
IN430 - INFORMATICS 4: ADVANCED COMPUTING TECHNIQUES
|
Also available in another semester or year
|
20402110 -
IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20402111 -
IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY
|
Also available in another semester or year
|
20402114 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
To acquire deep understanding of some of the principal arguments treated in high-school mathematics
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402115 -
ST410 - STATISTICS 1
(objectives)
THE PURPOSE OF THIS COURSE IS TO INTRODUCE MATHEMATICAL STATISTICS, STATISTICAL INFERENCE AND THE USE OF STATISTICAL SOFTWARE TO STUDENTS WITH A GOOD BAKCGROUND IN MATHEMATICS.
|
7
|
SECS-S/01
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402117 -
FS410 - PHYSICS 3: RELATIVITY AND RELATIVISTIC THEORIES
|
Also available in another semester or year
|
20402120 -
LM510 - LINEAR TYPES AND LOGIC
|
Also available in another semester or year
|
20402122 -
FS420 - QUANTUM MECHANICS
(objectives)
GAIN KNOWLEDGE OF THE BASIC PRINCIPLES OF QUANTUM MECHANICS APPLIED TO SIMPLE PHYSICAL SYSTEMS
|
7
|
FIS/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402247 -
AM520 - OPERATOR THEORY 1
|
Also available in another semester or year
|
20402291 -
ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20402297 -
AL410 - COMMUTATIVE ALGEBRA - C
(objectives)
THE PURPOSE OF THIS COURSE IS TO DEEPEN THE KNOWLEDGE OF SOME TOOLS AND FUNDAMENTAL PROPERTIES OF COMMUTATIVE RINGS AND THEIR MODULES, WITH PARTICULAR EMPHASIS TO THE CASE OF RINGS ARISING IN ALGEBRAIC NUMBER THEORY AND ALGEBRAIC GEOMETRY.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402298 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C
(objectives)
To develop a good knowledge of the general methods and the classical techniques useful in the study of partial differential equations
|
7
|
MAT/05
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402299 -
AN410 - NUMERICAL ANALYSIS 1 - C
(objectives)
THE COURSE IS INTENDED TO GIVE THE FUNDAMENTALS OF NUMERICAL APPROXIMATION TECHNIQUES, WITH A SPECIAL EMPHASIS ON THE SOLUTION OF LINEAR SYSTEMS AND NONLINEAR SCALAR EQUATIONS, POLYNOMIAL INTERPOLATION AND APPROXIMATE INTEGRATION FORMULAE. BESIDES BEING INTRODUCTORY, SUCH TECHNIQUES WILL BE USED IN THE SEQUEL AS BUILDING BLOCKS FOR MORE COMPLEX SCHEMES.
|
7
|
MAT/08
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402300 -
CP410 - PROBABILITY 2 - C
(objectives)
To gain a solid knowledge of the basic aspects of probabilità theory: construction of probabilità measures on measurable spaces, 0-1 law, independence, conditional expectation, random variables, convergence of random variables, characteristic functions, central limit theorem, branching processes, discrete martingales.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402301 -
FM410 - MATHEMATICAL PHYSICS 3 - C
(objectives)
CONTINUING THE STUDY, BEGAN DURING FM210, OF DYNAMIC SYSTEMS OF PHYSICAL INTEREST WITH MOST STYLISH AND POWERFUL TECHNIQUES, SUCH AS THE LAGRANGIAN AND HAMITONIAN FORMALISM, THAT ARE IN THE VAST RANGE OF APPLICATIONS OF ANALYSIS AND MATHEMATICAL PHYSICS.
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402302 -
GE410 - ALGEBRAIC GEOMETRY 1 - C
(objectives)
Introduction to the study of topological and geometrical structures defined using algebraic methods. Refinement of the algebraic knowledge using applications to the study of algebraic varieties in affine and projective spaces.
|
7
|
MAT/03
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402303 -
LM410 - MATHEMATICAL LOGIC 1 - C
|
Also available in another semester or year
|
20402304 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C
|
Also available in another semester or year
|
20402305 -
MC410 - COMPLEMENTARY MATHEMATICS 1 - C
(objectives)
To acquire deep understanding of the principal geometry arguments treated in high-school mathematics
|
7
|
MAT/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402306 -
AN420 - NUMERICAL ANALYSIS 2 - C
|
Also available in another semester or year
|
20402309 -
CP430 - STOCHASTIC CALCULUS - C
(objectives)
Acquire a good knowledge in stochastic processes, Brownian motion, stochastic differential equations and their applications.
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402312 -
GE430 - DIFFERENTIAL GEOMETRY 2 - C
|
Also available in another semester or year
|
20402313 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C
(objectives)
Problem solving with examples from secondary school mathematical curricula, with the help of a computer and a direct use of numerical and symbolic calculus and dynamical geometry software (MATHEMATICA, introduction on CABRI and GEOGEBRA). All examples, in an interactive and “laboratorial” lessons, point at experience limits and opportunities of using computers at school on selected arguments like numerical approximation or visualization in geometry as well as analysis.
|
7
|
MAT/04
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402314 -
AL440 – GROUP THEORY - C
|
Also available in another semester or year
|
20402315 -
AM440 - SPECIAL TOPICS OF ORDINARY DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402329 -
MC440 - FIRST ORDER CLASSICAL LOGIC - C
|
Also available in another semester or year
|
20402330 -
AL420 - ALGEBRAIC NUMBER THEORY - C
|
Also available in another semester or year
|
20402332 -
CP420 - STOCHASTIC PROCESSES (READING COURSE) - C
|
Also available in another semester or year
|
20402334 -
MC520 - AXIOMATIC SET THEORY
|
Also available in another semester or year
|
20402335 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C
|
Also available in another semester or year
|
20402337 -
IN460 - COMPUTER SCIENCE 10, COMPUTATIONAL GRAPHICS
|
Also available in another semester or year
|
20402339 -
MA420 - GEOMETRIC AND PHYSICAL MODELLING
|
Also available in another semester or year
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA AIT E IN530 - (show)
|
4
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)
|
10
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO TRE INSEGNAMENTI (21 CFU) NEGLI SSD MAT/01,02,03,04,05 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
28
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE ALMENO UN INSEGNAMENTO (7 CFU) NEGLI SSD MAT/06,07,08,09 TRA LE ATTIVITÀ CARATTERIZZANTI (B) - (show)
|
7
|
|
|
|
|
|
|
|
20402086 -
FM310 - MATHEMATICAL PHYSICS 2
(objectives)
The aim of the course is to develop a good knowledge of fundamental methods in the solution of elementary problems in partial differential equations
|
7
|
MAT/07
|
72
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402088 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20402092 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402093 -
CP410 - PROBABILITY 2
|
Also available in another semester or year
|
20402101 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20402103 -
FM410 - MATHEMATICAL PHYSICS 3
|
Also available in another semester or year
|
20402123 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402327 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS
(objectives)
The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
20402331 -
CP420 - STOCHASTIC PROCESSES (READING COURSE)
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Core compulsory activities
|
ITA |
|
Optional Group:
comune Orientamento unico SCEGLIERE QUATTRO INSEGNAMENTI (28 CFU) TRA LE ATTIVITÀ AFFINI INTEGRATIVE (C) - (show)
|
28
|
|
|
|
|
|
|
|
20402089 -
IN410 - COMPUTER SCIENCE 2
(objectives)
The course Theory of Computation and Interaction provides a in-deep view of theoretical aspects related to the concept of computation and the study of relations between different models of computation. The basic knowledge on information technology is here extended with new concepts and theoretical viewpoints. The course is divided into two units of 6 CFU. At choice, the student can decide to pass the first unit or both (12 CFU). More specifically, the course provides a formal presentation of the concepts of algorithm and computability. After the introduction of the classical concept of computability as formalized by Alan M. Turing, we address the basic concepts of algorithmic complexity and problem decidability, functional models and functional programming. In the second unit, we focus on interactive paradigms in the theory of computation which allow the description of additional complexity classes and their use in the semantics of programming languages.
|
7
|
INF/01
|
72
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402091 -
TN410 - INTRODUCTION TO NUMBER THEORY
(objectives)
TO ACQUIRE A GOOD KNOWLEDGE OF CONCEPTS AND METHODS OF ELEMENTARY NUMBER THEORY, WITH PARTICULAR RESPECT OF STUDY OF DIOPHANTINE EQUATIONS AND POLYNOMIAL CONGRUENCES. TO GIVE PREREQUISITES FOR ADVANCED COURSES OF ALGEBRAIC AND ANALYTIC NUMBER THEORY.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402102 -
CR410 - CRYPTOGRAPHY 1
(objectives)
ACQUIRE GOOD KNOWLEDGE OF THE CONCEPTS AND MATHEMATICAL METHODS OF PUBLIC KEY CRYPTOGRAPHY PROVIDING AN OVERVIEW OF THOSE WHICH ARE CURRENTLY IN USE.
|
7
|
MAT/02
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402107 -
GE510 - ALGEBRAIC GEOMETRY 2
(objectives)
Introduction and applications od the language of modern algebraic geometry through the theory of sheaves and the theory of schemes. In depth examination of the interactions of geometry and algebra. Description of research themes and open problems in modern algebra and geometry.
|
7
|
MAT/03
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402108 -
IN430 - INFORMATICS 4: ADVANCED COMPUTING TECHNIQUES
(objectives)
THE COURSE IN430 – COMPUTER SCIENCE 4, ADVANCED COMPUTATIONAL TECHNIQUES IS FOCUSED ON THE ACQUISITION OF OBJECT ORIENTED PROGRAMMING LANGUAGES AND APPLICATION OF CONCEPTUAL TOOLS FOR ANALYSIS AND DEVELOPMENT IN OBJECT ORIENTEND PROGRAMMING. THIS COURSE INCLUDES AN INTRODUCTION TO MODELING AND DESIGN OF CLASSES THROUGH UML DIAGRAMS, AND THE STUDY OF SPECIFICATION AND IMPLEMENTATION OF ALGORITHMS ON GRAPHS. THREAD CONCORRENCY OPPORTUNITIES AND CAVEATS ARE DISCUSSED. DISTRIBUTED (MOBILE) COMPUTING OVER THE NETWORK AND IN THE CLOUD IS INTRODUCED AND DISCUSSED.
|
7
|
INF/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402110 -
IN450 - INFORMATICS 6: ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20402111 -
IN520 - INFORMATICS 8: TECHNIQUES FOR DATA AND NETWORK SECURITY
(objectives)
Nowadays, information is often stored and transmitted electronically. Ensuring the security of the vast and complex infrastructure of computers, servers and networks is an immense challenge. In this scenario, this course aims at describing: - The relationship between number theory and information security techniques; - How to protect networks, secure electronic assets, prevent attacks, ensure the privacy of computer users, and build secure infrastructures.
|
7
|
INF/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402114 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
|
Also available in another semester or year
|
20402115 -
ST410 - STATISTICS 1
|
Also available in another semester or year
|
20402117 -
FS410 - PHYSICS 3: RELATIVITY AND RELATIVISTIC THEORIES
|
Also available in another semester or year
|
20402120 -
LM510 - LINEAR TYPES AND LOGIC
(objectives)
A DEEP AND CRITICAL INTRODUCTION TO A SPECIFIC LOGICAL THEORY WHICH CONCERNS THE THEME OF THE INTERACTION AND IS CENTRAL IN THE CONTEMPORARY RESEARCH ON INFROMATION AND COMMUNICATION: LINEAR LOGIC AND ITS DEVELOPMENTS.
|
7
|
MAT/01
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402122 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20402247 -
AM520 - OPERATOR THEORY 1
|
Also available in another semester or year
|
20402291 -
ST420 – MULTIVARIATE STATISTICAL ANALYSIS, MATHEMATICAL STATISTICS
|
Also available in another semester or year
|
20402297 -
AL410 - COMMUTATIVE ALGEBRA - C
|
Also available in another semester or year
|
20402298 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402299 -
AN410 - NUMERICAL ANALYSIS 1 - C
|
Also available in another semester or year
|
20402300 -
CP410 - PROBABILITY 2 - C
|
Also available in another semester or year
|
20402301 -
FM410 - MATHEMATICAL PHYSICS 3 - C
|
Also available in another semester or year
|
20402302 -
GE410 - ALGEBRAIC GEOMETRY 1 - C
|
Also available in another semester or year
|
20402303 -
LM410 - MATHEMATICAL LOGIC 1 - C
|
Also available in another semester or year
|
20402304 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS - C
(objectives)
CALCULUS AND, IN PARTICULAR, DIFFERENTIAL EQUATIONS ARE IMPORTANT IN THE RESEARCH AND DEVELOPMENT OF APPLIED AND INDUSTRIAL MATEMATICS. THESE MATHEMATICAL TOOLS ARE NECESSARY TO UNDERSTAND A NUMBER OF PHYSICAL, CHEMICAL, BIOLOGICAL AND FINANCIAL PHENOMENA, AND TO IMPROVE THE QUALITY OF INDUSTRIAL PRODUCTS AND PROCESSES. MODELING AND SIMULATION COULD BE THE BEST TERMS TO DESCRIBE THE SPIRIT OF THIS COURSE. CONCRETE PROBLEMS WILL BE CONSIDERED AS EXAMPLES.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402305 -
MC410 - COMPLEMENTARY MATHEMATICS 1 - C
|
Also available in another semester or year
|
20402306 -
AN420 - NUMERICAL ANALYSIS 2 - C
(objectives)
THE COURSE PRESENTS A REVIEW OF NUMERICAL METHODS OF INCREASING IMPACT FOR APPLICATION. IN THIS LINE OF WORK, THE ELEMENTARY SCHEMES INTRODUCED IN THE FIRST COURSE ARE USED AS BUILDING BLOCKS FOR MORE COMPLEX METHODS, WITH THE FINAL GOAL OF INTRODUCING THE STUDENT (IN A SOMEWHAT SIMPLIFIED FRAMEWORK) TO THE GENERAL ASPECTS OF THE APPROXIMATE SOLUTION OF OPTIMIZATION PROBLEMS AND SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. ALL TECHNIQUES WILL BE TESTED ON SOME BENCHMARK PROBLEMS OF INTEREST FOR APPLICATION.
|
7
|
MAT/08
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402309 -
CP430 - STOCHASTIC CALCULUS - C
|
Also available in another semester or year
|
20402312 -
GE430 - DIFFERENTIAL GEOMETRY 2 - C
|
Also available in another semester or year
|
20402313 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS - C
|
Also available in another semester or year
|
20402314 -
AL440 – GROUP THEORY - C
|
Also available in another semester or year
|
20402315 -
AM440 - SPECIAL TOPICS OF ORDINARY DIFFERENTIAL EQUATIONS - C
|
Also available in another semester or year
|
20402329 -
MC440 - FIRST ORDER CLASSICAL LOGIC - C
|
Also available in another semester or year
|
20402330 -
AL420 - ALGEBRAIC NUMBER THEORY - C
|
Also available in another semester or year
|
20402332 -
CP420 - STOCHASTIC PROCESSES (READING COURSE) - C
|
7
|
MAT/06
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402334 -
MC520 - AXIOMATIC SET THEORY
|
Also available in another semester or year
|
20402335 -
FM450 - MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS - C
(objectives)
The main goal of the course is to provide an elemantary but self-contained presentation of the Hilbert space formulation of quantum mechanics. Some standard notions and results of operator theory will be applied to the analysis of the simplest quantum systems (free particle and harmonic oscillator) as well as the definition of atomic hamiltonians and their spectral properties. The existence and uniqueness of ground and bound states will be discussed in details. The last part of the course will be devoted to the study of many-body quantum systems (Thomas-Fermi theory and stability of matter, Bose-Einstein condensation etc.).
|
7
|
MAT/07
|
60
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402337 -
IN460 - COMPUTER SCIENCE 10, COMPUTATIONAL GRAPHICS
|
Also available in another semester or year
|
20402339 -
MA420 - GEOMETRIC AND PHYSICAL MODELLING
|
Also available in another semester or year
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA AIT E IN530 - (show)
|
4
|
|
|
|
|
|
|
|
|
Optional Group:
comune Orientamento unico SCEGLIERE UN INSEGNAMENTO TRA QLMA E QLMB - (show)
|
10
|
|
|
|
|
|
|
|
|
20410000 -
Prova finale
|
38
|
|
150
|
-
|
-
|
-
|
Final examination and foreign language test
|
ITA |