Degree Course: Mathematics
A.Y. 2020/2021
Conoscenza e capacità di comprensione
Il Corso di Laurea in Matematica si propone la formazione di laureati che abbiano una solida preparazione di base nell'ambito delle discipline matematiche e abbiano acquistato familiarità con il metodo scientifico.
In particolare, il laureato
- sarà provvisto di una robusta preparazione scientifica nelle discipline che caratterizzano la classe di laurea, precipuamente nell'analisi (calcolo differenziale e integrale), nell'algebra lineare, nella geometria di curve e superfici, nella geometria algebrico-proiettiva, nella topologia, nelle principali strutture algebriche, nella fisica matematica, nelle equazioni differenziali e nella teoria della probabilità;
- possiederà conoscenze di base di fisica generale e di informatica;
- avrà conseguito un'approfondita conoscenza degli strumenti matematici, sia di base che avanzati, e delle loro applicazioni pratiche, con particolare attenzione alla fisica e all'informatica;
- sarà fornito di adeguate competenze computazionali e informatiche, inclusa la conoscenza di linguaggi di programmazione e software specifici;
- sarà in grado di riconoscere e riprodurre dimostrazioni rigorose e avrà la capacità di costruire e sviluppare argomenti di matematica con una chiara identificazione di assunti e conclusioni;
- sarà capace di leggere e comprendere testi avanzati di matematica, nonché di consultare articoli di ricerca in matematica, anche in lingua inglese.
Le conoscenze sono acquisite attraverso sia gli insegnamenti comuni ai vari percorsi formativi che gli insegnamenti curricolari avanzati.
Per ogni insegnamento, l'apprendimento è verificato mediante il superamento di una prova finale secondo quanto previsto dal Regolamento Didattico del Corso di Laurea.Capacità di applicare conoscenza e comprensione
Il Corso di Laurea in Matematica si propone la formazione di laureati che siano familiari con il metodo scientifico e siano in grado di applicarlo in situazioni pratiche.
In particolare il laureato
- avrà conseguito un'approfondita conoscenza degli strumenti matematici, sia di base che avanzati, e sarà in grado di applicarli proficuamente in contesti lavorativi e in ambito scientifico, con particolare attenzione alla fisica, all'informatica e al calcolo numerico;
- sarà in grado di formalizzare matematicamente problemi formulati nel linguaggio naturale;
- sarà in grado di produrre dimostrazioni rigorose e risolvere problemi di moderata difficoltà in ambito matematico;
- sarà in grado di comprendere, utilizzare ed elaborare modelli matematici che descrivano situazioni d'interesse scientifico o economico;
- sarà in grado di svolgere compiti tecnici o professionali definiti, che richiedano eventualmente anche responsabilità e capacità organizzativa e manageriale;
- avrà la capacità di estrarre informazioni qualitative da dati quantitativi, e di utilizzare strumenti informatici e linguaggi di programmazione o software specifici come supporto ai processi matematici;
- avrà acquisito una solida preparazione di base, un'elevata capacità di apprendimento e un'adeguata autonomia di giudizio, tali da consentire di seguire un corso di laurea magistrale in Matematica o in altre discipline di carattere scientifico.
La capacità di applicare le conoscenze acquisite è
- conseguita svolgendo esercizi, anche guidati, relativi ai programmi degli insegnamenti seguiti e prendendo parte ad attività di didattica integrativa e di studio assistito, in aula o in laboratorio, previste per la maggior parte degli insegnamenti;
- verificata attraverso il superamento di prove scritte e/o colloqui orali relativi agli insegnamenti curricolari, eventualmente sostituiti o integrati da prove di esonero in itinere, attraverso apposite attività seminariali o di laboratorio e attraverso la discussione di elaborati, previsti per alcuni insegnamenti e per la prova finale.Autonomia di giudizio
Il Corso di Laurea in Matematica dell'Università Roma Tre si propone la formazione di laureati che:
- siano in grado di svolgere in modo autonomo attività esterne, come tirocini formativi presso aziende, strutture della pubblica amministrazione e laboratori, e siano pronti a soggiorni presso altre università italiane ed europee, utilizzando in modo appropriato le competenze matematiche, computazionali e linguistiche acquisite;
- siano in grado di costruire e sviluppare argomentazioni logiche con una chiara identificazione d'assunti e conclusioni;
- siano in grado di riconoscere dimostrazioni corrette e di individuare ragionamenti fallaci;
- siano in grado di proporre e analizzare modelli matematici associati a situazioni concrete derivanti da altre discipline, e di usare tali modelli per facilitare lo studio della situazione originale;
- abbiano esperienza di lavoro di gruppo, ma sappiano anche lavorare bene autonomamente.
L'autonomia di giudizio è conseguita seguendo la varie attività formative offerte dal corso di laurea e verificata attraverso gli esami degli insegnamenti curricolari e la prova finale del corso di studio.Abilità comunicative
Il Corso di Laurea in Matematica dell'Università Roma Tre si propone la formazione di laureati che:
- siano in grado di comunicare problemi, idee e soluzioni riguardanti la Matematica, sia proprie sia di altri autori, ad un pubblico specializzato o generico, nella propria lingua e in inglese, sia in forma scritta sia orale;
- siano capaci di lavorare in gruppo e di operare con definiti gradi d'autonomia.
Le abilità comunicative sono conseguite seguendo la varie attività formative offerte dal corso di laurea e verificate attraverso gli esami degli insegnamenti curricolari, in particolare durante il colloquio orale e la discussione di un elaborato, ove previsto.
Capacità di apprendimento
Il Corso di Laurea in Matematica dell'Università Roma Tre si propone la formazione di laureati che:
- siano in grado di inserirsi prontamente nei vari ambienti di lavoro adattandosi a nuove problematiche acquisendo facilmente e con rapidità eventuali conoscenze specifiche;
- siano in grado di adattarsi rapidamente all'evoluzione degli strumenti informatici e di mantenere adeguate le loro competenze scientifiche;
- siano in grado di proseguire gli studi con un buon grado d'autonomia, sia in Matematica sia in altre discipline.
Le capacità di apprendimento sono conseguite seguendo la varie attività formative offerte dal corso di laurea e verificate attraverso il superamento degli esami degli insegnamenti curricolari e della prova finale.Requisiti di ammissione
Possono essere ammessi al Corso di Laurea in Matematica gli studenti in possesso di un diploma di scuola secondaria superiore italiana o di altro titolo di studio conseguito all'estero riconosciuto idoneo.
Requisiti utili per iniziare regolarmente gli studi sono l'abitudine al ragionamento rigoroso, la familiarità con il linguaggio matematico dell'aritmetica, dell'algebra e della geometria.
Per l'accesso al Corso di Laurea in Matematica sono anche richieste, oltre che una buona capacità di comunicazione scritta e orale, adeguate conoscenze e competenze di matematica elementare.
Il Regolamento Didattico del Corso di Laurea riporta con precisione l'elenco delle conoscenze e competenze di matematica elementare richieste.
Precisa, inoltre, le modalità con cui la struttura didattica procede alla verifica di tali conoscenze e competenze e rende disponibili agli studenti e ai pre-iscritti opportune forme di autovalutazione e corsi introduttivi per aiutare a colmare eventuali inadeguatezze della preparazione.
Nel caso in cui la verifica non risulti positiva, il Regolamento Didattico del Corso di Laurea indica specifici obblighi formativi aggiuntivi da soddisfare nel primo anno di corso.
Prova finale
Dopo aver superato le prove didattiche relative alle attività formative regolamentate dall'ordinamento del Corso di Laurea, lo studente accede alla prova finale per il conseguimento della Laurea in Matematica di fronte ad una Commissione designata in accordo con le modalità generali previste dal Regolamento Didattico di Ateneo.
Al fine del superamento della prova finale per il conseguimento della Laurea in Matematica si richiede anche l'accertamento della conoscenza della lingua inglese, mediante lettura e traduzione di testi scientifici.
Per la prova finale, lo studente potrà scegliere tra due opzioni:
1.
l'esposizione di una relazione su un argomento matematico di particolare interesse teorico, algoritmico o applicativo, proposto da un relatore,
2.
una prova scritta di tipo interdisciplinare su argomenti fondamentali riguardanti il curriculum del Corso di Laurea, consigliata agli studenti che intendono proseguire gli studi in un Corso di Laurea Magistrale in Matematica o in Scienze Computazionali.
Le modalità di svolgimento della Prova finale vengono precisate dal Regolamento Didattico del Corso di Laurea e possono prevedere anche attività pratiche, di laboratorio e/o tirocinio.Orientamento in ingresso
Le azioni di orientamento in ingresso sono improntate alla realizzazione di processi di raccordo con la scuola secondaria di secondo grado.
Si concretizzano in attività di carattere informativo sui Corsi di Studio (CdS) dell'Ateneo ma anche come impegno condiviso da scuola e università per favorire lo sviluppo di una maggiore consapevolezza da parte degli studenti nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attività promosse si articolano in:
a) autorientamento;
b) incontri e manifestazioni informative rivolte alle future matricole;
c) sviluppo di servizi online e pubblicazione di guide sull'offerta formativa dei CdS.
Tra le attività svolte in collaborazione con le scuole per lo sviluppo di una maggiore consapevolezza nella scelta, il progetto di autorientamento è un intervento che consente di promuovere un raccordo particolarmente qualificato con alcune scuole superiori.
Il progetto, infatti, è articolato in incontri svolti presso le scuole ed è finalizzato a sollecitare nelle future matricole una riflessione sui propri punti di forza e sui criteri di scelta.
La presentazione dell'offerta formativa agli studenti delle scuole superiori prevede tre eventi principali distribuiti nel corso dell'anno accademico ai quali partecipano tutti i CdS:
- Salone dello studente, si svolge presso la fiera di Roma fra ottobre e novembre e coinvolge tradizionalmente tutti gli Atenei del Lazio e molti Atenei fuori Regione, Enti pubblici e privati che si occupano di Formazione e Lavoro.
Roma Tre partecipa a questo evento con un proprio spazio espositivo, con conferenze di presentazione dell'offerta formativa dell'Ateneo e promuove i propri Dipartimenti scientifici grazie all'iniziativa 1,2,3 Scienze!;
- Giornate di Vita Universitaria (GVU), si svolgono ogni anno da dicembre a marzo e sono rivolte agli studenti degli ultimi due anni della scuola superiore.
Si svolgono in tutti i Dipartimenti dell'Ateneo e costituiscono un'importante occasione per le future matricole per vivere la realtà universitaria.
Gli incontri sono strutturati in modo tale che accanto alla presentazione dei Corsi di Laurea, gli studenti possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente circa 5.000 studenti;
- Orientarsi a Roma Tre, rappresenta la manifestazione che chiude le annuali attività di orientamento in ingresso e si svolge in Ateneo a luglio di ogni anno.
L'evento accoglie, perlopiù, studenti romani che partecipano per mettere definitivamente a fuoco la loro scelta universitaria.
Durante la manifestazione viene presentata l'offerta formativa e sono presenti, con un proprio spazio, tutti i principali servizi di Roma Tre, le segreterie didattiche e la segreteria studenti.
I servizi online messi a disposizione dei futuri studenti universitari nel tempo sono aumentati tenendo conto dello sviluppo delle nuove opportunità di comunicazione tramite web.
Inoltre, durante tutte le manifestazioni di presentazione dell'offerta formativa, sono illustrati quei servizi online (siti web di Dipartimento, di Ateneo, Portale dello studente, ecc.) che possono aiutare gli studenti nella loro scelta.
Il Dipartimento di Matematica e Fisica attribuisce una particolare importanza a tutte le attività volte a fornire informazioni necessarie per orientare gli studenti nella scelta del corso di studio in linea con le politiche d'Ateneo.
Infatti partecipa a tutte le principali iniziative d'Ateneo dedicate all'orientamento: il Salone dello Studente, in cui viene allestito lo stand con esperimenti e presentazioni 1, 2, 3 Scienze!; le Giornate di Vita Universitaria e la manifestazione "Orientarsi a Roma Tre".
Per la realizzazione dei propri progetti di orientamento il Dipartimento inoltre:
- aderisce al Piano nazionale Lauree Scientifiche, promosso dal MIUR, dalla Conferenza Nazionale dei Presidenti e dei Direttori delle strutture Universitarie di Scienze e Tecnologie (Con.Scienze) e dalla Confindustria, offrendo alle scuole partner laboratori di matematica e di fisica;
- propone percorsi all'interno del progetto ministeriale Alternanza Scuola-Lavoro, come definito dalla legge 107 del 2015 (La Buona Scuola);
- promuove iniziative di divulgazione e comunicazione scientifica rivolte alle scuole (studenti ed insegnanti) e più in generale alla società.
Particolare rilievo assumono le seguenti attività:
- Masterclass in Astrofisica, Fisica delle Particelle, Fisica Terrestre e dell'Ambiente, Ottica e Fisica della Materia, e di prossima attivazione in Algebra e crittografia a chiave pubblica, Geometria: gruppi di simmetria del piano, Logica: dai sillogismi al computer, che offrono la possibilità di trascorrere una giornata da ricercatore ad alcune centinaia di studenti fra i più motivati degli ultimi due anni della scuola secondaria;
- Gare di Matematica, che comprendono la selezione provinciale delle Olimpiadi di Matematica, con circa 500 partecipanti studenti delle scuole superiori di tutta la provincia di Roma, e il concorso "Immatricolazione gratuita a Roma Tre", con più di 400 partecipanti studenti dell'ultimo anno della scuola secondaria;
- La Fisica incontra la Città, seminari serali aperti al pubblico in cui vengono trattate le principali tematiche e scoperte della Fisica Moderna;
- "Notte dei Ricercatori" e "Occhi su Luna/Marte/Giove/Saturno", serate aperte al pubblico con la presenza di migliaia di partecipanti, nelle quali studenti e ricercatori diffondono conoscenze ed esperienze attraverso esperimenti, laboratori, dimostrazioni scientifiche, spettacoli, conferenze e seminari divulgativi.
Per la diffusione e la consultazione di questi eventi il Dipartimento dedica sulla propria home page del sito una sezione ad hoc: "Il Dipartimento per la Città e per la Scuola".
Inoltre, in tale sezione è disponibile una piattaforma E-learning, che, tramite opportuni quesiti, aiuta gli studenti delle scuole superiori nell'autovalutazione della propria preparazione, evidenziando possibili lacune da colmare eventualmente con l'ausilio delle dispense sugli argomenti di base disponibili in rete a fianco dei quesiti.
Per entrambi i Corsi di Laurea e di Laurea Magistrale in Matematica sono predisposti opuscoli e guide informative, tra cui benvenuto@matematica è disponibile anche in formato pdf sul sito web del Dipartimento al link: http://dmf.matfis.uniroma3.it/matematica/orientamento/benvenuto.php, che vengono distribuiti in occasione degli eventi dedicati all'orientamento e in fase di iscrizione ai corsi stessi.Il Corso di Studio in breve
Il Corso di Laurea, attraverso l'offerta di piani di studio differenziati ma culturalmente coerenti, è rivolto sia a coloro che intendano acquisire rapidamente un'alta professionalità nelle discipline matematiche, tecnologiche e informatiche, sia a coloro che mirino a gettare le basi di un percorso destinato ad approfondimenti di alto livello, che trovano sbocco naturale sia nel Corso di Laurea Magistrale in Matematica che nel Corso di Laurea Magistrale in Scienze Computazionali.
Alcune iniziative, ideate per consentire agli studenti un rapido e proficuo inserimento in ambito universitario nonché per facilitare il superamento di eventuali difficoltà iniziali, sono le seguenti:
- corsi di preparazione alla prova di valutazione, obbligatoria ma non selettiva, richiesta per l'accesso;
- corsi di raccordo e di recupero per colmare eventuali lacune nella preparazione iniziale;
- servizi di tutorato di varia natura, specialmente per i primi due anni, tra cui quello in classe svolto da studenti magistrali meritevoli e retribuiti;
- servizi di didattica on line, completi e aggiornati;
- borse di studio per studenti immatricolati meritevoli.
Il primo e il secondo anno, i cui insegnamenti sono comuni a tutti gli indirizzi, hanno caratteristiche orientative ad ampio spettro.
In essi, oltre ai fondamenti delle materie matematiche di base, si offrono le basi per le competenze di tipo informatico e modellistico.
Al terzo anno i percorsi formativi si differenziano a seconda che si scelga il curriculum teorico-didattico, consigliato a chi sia interessato agli aspetti più teorici, o il curriculum modellistico-applicativo, professionalizzante e pensato anche per un rapido inserimento nel mondo del lavoro.
All'interno del curriculum teorico-didattico sono consigliati i due percorsi formativi "Matematica generale" e "Matematica per l'insegnamento", che sono rivolti, rispettivamente, a chi intenda proseguire gli studi nell'ambito della ricerca matematica teorica (curriculum teorico del Corso di Laurea Magistrale in Matematica) e a chi preveda di dedicarsi all'insegnamento o comunque all'approfondimento di tematiche legate alla didattica della matematica (curriculum didattico del Corso di Laurea Magistrale in Matematica).
Il curriculum modellistico-applicativo prevede il percorso formativo consigliato "Matematica per l'informatica e il calcolo scientifico", rivolto principalmente agli studenti che vogliano acquisire maggiori competenze di carattere modellistico, computazionale e informatico (curriculum applicativo del Corso di Laurea Magistrale in Matematica o Corso di Laurea Magistrale in Scienze Computazionali).
In particolare, nel presentare il proprio piano di studio, gli studenti hanno la facoltà di inserire insegnamenti di carattere avanzato che anticipino e completino tematiche che saranno poi approfondite in un successivo corso di laurea magistrale o che forniscano loro competenze utili ad un proficuo inserimento in ambito lavorativo.
Inoltre, lo studente interessato può svolgere un tirocinio formativo ("stage") presso enti di ricerca, laboratori o aziende, utile ai fini della prova finale, oppure usufruire delle molte opportunità di svolgere parte del proprio percorso formativo in mobilità internazionale.
La grande flessibilità dei percorsi formativi offerti, che lasciano largo margine ad attività a scelta ampia e comunque prevedono la possibilità di presentare piani di studio individuali, consente agli studenti di predisporre il proprio piano di studio sulla base dei propri interessi culturali e delle proprie prospettive lavorative.
Nell'ambito del percorso formativo "Matematica per l'insegnamento" lo studente può scegliere insegnamenti non solo di matematiche complementari, ma anche di chimica, geologia o biologia, in modo da conseguire già nel corso della laurea triennale conoscenze di base fondamentali per l'insegnamento; agli studenti che optino per il percorso "Matematica generale" sono offerti insegnamenti avanzati in tutti i settori scientifico-disciplinari della matematica, in modo da avviare una specializzazione che sarà poi completata nel prosieguo degli studi; infine, chi scelga il percorso "Matematica per l'informatica e il calcolo scientifico" ha a sua disposizione una vasta scelta di insegnamenti applicativi che preparano in modo naturale a successivi approfondimenti, nel campo della gestione e protezione dei dati, dell'informatica, della simulazione numerica e della modellistica fisica.
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.
Teorico-didattico
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
|
20410386 -
AL110-ALGEBRA 1
(objectives)
Provide the elements of the "mathematical language" (set theory, elementary logic, numerical sets) and the knowledge of the basic tools of modern algebra (notions of operation, group, ring, field) through the development of examples that provide the motivations.
|
9
|
MAT/02
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410405 -
AM110 - MATHEMATICAL ANALYSIS 1
(objectives)
To acquire a good knowledge of the basic concepts and methods of Mathematical Analysis with particular regard to the structure of real numbers, to the theory of limits, to the study of functions and to the first applications and models.
|
9
|
MAT/05
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410336 -
IN110 - Algorithms and Data Structure
(objectives)
Provide a good knowledge in the design of algorithms for the solution of problems and in algorithm coding with a programming language (C language). Introduce the student to some of the fundamental concepts of discrete mathematics (with brief overview on graph theory) and in particular to the basic elements of discrete optimization (optimization algorithms on graphs, visit of graph, shortest paths, spanning trees).
|
9
|
INF/01
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
Optional Group:
SCEGLIERE 1 idoneità di lingua (3 cfu) - (show)
|
3
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20410335 -
GE110 - Geometry and linear algebra 1
(objectives)
Acquire a good knowledge of the concepts and methods of basic linear algebra, with particular attention given to the study of linear systems, matrices and determinants, vector spaces and linear applications, affine geometry.
|
9
|
MAT/03
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410388 -
AM120 - MATHEMATICAL ANALYSIS 2
(objectives)
To complete the basic preparation of Mathematical Analysis with particular regard to derivation and integration theory,ÿand to series developments.
|
9
|
MAT/05
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410406 -
FS110 - Physics 1
(objectives)
The course provides the fundamental theoretical knowledge in developing mathematical modeling for mechanics and thermodynamics.
|
9
|
FIS/01
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
SECOND YEAR
First semester
Course
|
Credits
|
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
|
Language
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20402075 -
AL210 - ALGEBRA 2
(objectives)
Introduce the basic notions and techniques of abstract algebra through the study of the first properties of fundamental algebraic structures: groups, rings and fields.
|
9
|
MAT/02
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20402076 -
AM210 - MATHEMATICAL ANALYSIS 3
(objectives)
To acquire a good knowledge of some fundamental methods and results in the study ofÿfunctions of several variables and of differential equations.
|
9
|
MAT/05
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48
|
30
|
-
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-
|
Core compulsory activities
|
ITA |
20410340 -
GE210 - Geometry and linear algebra 2
(objectives)
Acquire a good knowledge of the theory of bilinear forms and their geometric applications. An important application will be the study of Euclidean geometry, mainly in the plane and in the space, and the Euclidean classification of the conics and of the quadratic surfaces.
|
9
|
MAT/03
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
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Personal Study Hours
|
Type of Activity
|
Language
|
20410338 -
CP210 - Introduction to Probability
(objectives)
Elementary probability theory: discrete distributions, repeated trials, continuous random variables. Some basic limit theorems and introduction to Markov chains.
|
9
|
MAT/06
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410339 -
FM210 - Analytical Mechanics
(objectives)
To acquire a basic knowledge of the theory of conservative mechanical systems and of the elements of analytical mechanics, in particular of Lagrangian and Hamiltonian mechanics.
|
9
|
MAT/07
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410341 -
GE220 - Topology
(objectives)
Acquire a good knowledge of concepts and methods of general topology, with particular regard to the study of the main properties of topological spaces such as connection and compactness. Introduce the student to the basic elements of algebraic topology, through the introduction of the fundamental group and the topological classification of curves and surfaces.
|
9
|
MAT/03
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410586 -
AM220 - MATHEMATICAL ANALYSIS 4
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
9
|
MAT/05
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
THIRD YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20402082 -
FS220- Physics 2
(objectives)
The course provides the fundamental theoretical knowledge in developing mathematical modeling for electromagnetism, optics and special relativity.
|
9
|
FIS/01
|
48
|
30
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402131 -
SCIENTIFIC ENGLISH
|
Also available in another semester or year
|
Optional Group:
SCEGLIERE 1 INSEGNAMENTO (9 cfu) oppure 2 INSEGNAMENTI (6 cfu+ 3 cfu) NEL GRUPPO 1 - (show)
|
9
|
|
|
|
|
|
|
|
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410561 -
FS230 - Elements of contemporary theoretical physics
|
Also available in another semester or year
|
20410562 -
FS240 - Principles of condensed matter
|
Also available in another semester or year
|
20410563 -
FS250 - Principles of earth and environment physics
|
Also available in another semester or year
|
20410564 -
FS260 - Elements of philosophy of science
|
Also available in another semester or year
|
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
|
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
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410461 -
FS460 - Dydactics of Physics
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410588 -
IN400 - MODULE B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLA Band its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410587 -
IN400 - MODULE 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 |
20410591 -
FS290 - L'Agenda 2030 delle Nazioni Unite per lo sviluppo sostenibile: le implicazioni per le scienze matematiche e fisiche
|
Also available in another semester or year
|
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
|
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 -
MODULE 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 -
MODULE B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLA Band its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
CURRICULUM TEORICO: SCEGLIERE 2 INSEGNAMENTI (18 cfu) NEL GRUPPO 2 - (show)
|
18
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410412 -
MC310 - Fundaments of Complementary Mathematics
(objectives)
1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.
|
9
|
MAT/04
|
48
|
24
|
-
|
-
|
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 |
20410453 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20410451 -
LM410 -THEOREMS IN LOGIC 1
(objectives)
To acquire a good knowledge of first order classical logic and its fundamental theorems
|
|
20410451-1 -
LM410 -THEOREMS IN LOGIC 1 - Module A
(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 |
20410415 -
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.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410593 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
Optional Group:
SCEGLIERE 2 INSEGNAMENTI A SCELTA AMPIA (12 cfu) - (show)
|
12
|
|
|
|
|
|
|
|
20410446 -
BL410-Introduction to Biology
(objectives)
Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods
|
6
|
BIO/13
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410439 -
CH410 - ELEMENTS OF CHEMISTRY
(objectives)
Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.
|
6
|
CHIM/03
|
52
|
-
|
-
|
-
|
Elective 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
|
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
|
Also available in another semester or year
|
20410450 -
GL410-Elements of Geology I
(objectives)
The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.
|
6
|
GEO/03
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
|
Also available in another semester or year
|
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
|
-
|
-
|
Elective activities
|
ITA |
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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410454 -
GL420-Elements of Geology II
|
Also available in another semester or year
|
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
Also available in another semester or year
|
20410456 -
MC420-Dydactics of Mathematics
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
|
Also available in another semester or year
|
20410458 -
LM430 - LOGICAL THEORIES 2
|
Also available in another semester or year
|
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410460 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410461 -
FS460 - Dydactics of Physics
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
|
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
|
-
|
-
|
Elective activities
|
ITA |
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
|
Also available in another semester or year
|
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410523 -
MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿelliptic partial differential equations
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410567 -
GE470 - Riemann surfaces
(objectives)
Acquire a sufficiently broad knowledge of the topological, analytical and geometric aspects of the theory of Riemann surfaces.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
|
Also available in another semester or year
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20402131 -
SCIENTIFIC ENGLISH
(objectives)
To be able to translate in Italian mathematical books or papers written in English.
|
1
|
|
-
|
-
|
-
|
-
|
Other activities
|
ITA |
Optional Group:
SCEGLIERE 1 INSEGNAMENTO (9 cfu) oppure 2 INSEGNAMENTI (6 cfu+ 3 cfu) NEL GRUPPO 1 - (show)
|
9
|
|
|
|
|
|
|
|
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 |
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410561 -
FS230 - Elements of contemporary theoretical physics
(objectives)
Introduce at an elementary level about the concepts and principles of research in contemporary theoretical physics.
|
3
|
FIS/02
|
24
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410562 -
FS240 - Principles of condensed matter
(objectives)
Provide the student with an introduction to some of the topics important for research in condensed matter physics.
|
3
|
FIS/03
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410563 -
FS250 - Principles of earth and environment physics
(objectives)
Acquire skills related to the basic physical principles of the study of the planet earth and the interactive dynamics between geosphere, hydrosphere, atmosphere and cryosphere and of the Physics of the Environment.
|
1,5
|
FIS/06
|
12
|
-
|
-
|
-
|
Attività formative affini ed integrative
|
1,5
|
FIS/07
|
12
|
-
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20410564 -
FS260 - Elements of philosophy of science
(objectives)
The course of Philosophy of Science is part of the program in Philosophy and it is included among the characterizing training activities. The course is an introduction to the key problems of the philosophy of science. Among these, students will have to familiarize with issues concerning the nature of scientific explanation, of laws of nature, of the relationship between hypothesis and evidence, and of the cognitive content of scientific theories in light of radical scientific changes. These general topics will be introduced by a direct reading of some classics of 20th century philosophy of science, with the aim to develop the competences that are necessary to formulate and evaluate philosophical arguments. Students will be able to apply the knowledge acquired in the discussion and argument both from a theoretical and a historical-philosophical perspective. At the end of the course the student will acquire: -) Ability to analyze and interpret philosophical texts; -) Properties of language and argumentation; -) Ability to contextualize the acquired knowledge in the Philosophical debate.
|
3
|
M-FIL/02
|
24
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
(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
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410461 -
FS460 - Dydactics of Physics
(objectives)
The objectives of the course are to enable the students to acquire the necessary skills to practice an affective teaching of Physics in the secondary school, with particular attention to: a) knowledgeÿof literature research on Physic teaching; the Italian educational system and school regulations; b) the design of culturally significant educational paths for Physics teaching; c) the production of materials for the measurement and verification of learning through the exercise of formative evaluation; d) the role of the "laboratory" as a way of working that involves students in an active and participated way, which encourages experimentation and planning.
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
20410588 -
IN400 - MODULE B - MATLAB programming
|
Also available in another semester or year
|
20410587 -
IN400 - MODULE A - PYTHON programming
|
Also available in another semester or year
|
20410591 -
FS290 - L'Agenda 2030 delle Nazioni Unite per lo sviluppo sostenibile: le implicazioni per le scienze matematiche e fisiche
(objectives)
• Introduction to the United Nations Sustainable Development Agenda 2030 as a whole and in its general structure • Analysis of the 17 SDGs (Sustainable Development Goals) • Critical discussion on the organization of the Agenda and the links between its various objectives, both in terms of synergies and of conflicts • Insights on some of the Agenda objectives, especially concerning the specific interests and/or study plans of the students The main objective of the course is to make the student aware of the 2030 Agenda document, illustrating its birth, the main SDGs (Sustainable Development Goals) and the connections between them. The student will also learn what are the strategies that can be implemented and the physical-mathematical models that can be used for the achievement of the SDGs within sustainable development.
|
3
|
FIS/06
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
(objectives)
To Introduce students to themes, concepts, methods and results of logic that are at the basis of every discipline, in order to provide students - having any kind of background- with a deep interdisciplinary approach and an appropriate training for school teaching
|
6
|
M-FIL/02
|
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 -
MODULE A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULE B - MATLAB programming
|
Also available in another semester or year
|
|
Optional Group:
CURRICULUM TEORICO: SCEGLIERE 2 INSEGNAMENTI (18 cfu) NEL GRUPPO 2 - (show)
|
18
|
|
|
|
|
|
|
|
|
Optional Group:
SCEGLIERE 2 INSEGNAMENTI A SCELTA AMPIA (12 cfu) - (show)
|
12
|
|
|
|
|
|
|
|
20410446 -
BL410-Introduction to Biology
|
Also available in another semester or year
|
20410439 -
CH410 - ELEMENTS OF CHEMISTRY
|
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
|
-
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410450 -
GL410-Elements of Geology I
|
Also available in another semester or year
|
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410454 -
GL420-Elements of Geology II
(objectives)
The course aims to provide an adequate overview of the scientific contents of Earth Sciences. The course deals with the modern aspects of Earth Sciences, framing geological phenomena in the framework of the most modern theories and illustrating the hazards and risks associated with natural phenomena such as, for example, seismic and volcanic phenomena, also referring to the geology of the Italian territory. The course also aims to provide the basis for understanding the rocks cycle and their rocks genetic processes through laboratory and field experiences. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.
|
6
|
GEO/03
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410456 -
MC420-Dydactics of Mathematics
(objectives)
1. Critical analysis of the evolution of ideas and methodologies in teaching mathematics, with particular emphasis on the role of the teacher. 2. The mathematics curriculum in compulsory schooling and in the various secondary schools (high schools, technical schools and trade schools), in an international context. 3. Didactic planning and methodologies for teaching mathematics: programming and rhythm, principles and methods for the construction of activities, classroom management. 4. Problem solving. Logic, intuition and history in teaching mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
(objectives)
Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
(objectives)
Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented paradigm. Introduce the fundamental notions of parallel and concurrent programming.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410458 -
LM430 - LOGICAL THEORIES 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
1. Mathematics software, with particular attention to their use for teaching mathematics in school. 2. Analysis of the potential and criticality of the use of technological tools for teaching and learning mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410460 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410461 -
FS460 - Dydactics of Physics
(objectives)
The objectives of the course are to enable the students to acquire the necessary skills to practice an affective teaching of Physics in the secondary school, with particular attention to: a) knowledgeÿof literature research on Physic teaching; the Italian educational system and school regulations; b) the design of culturally significant educational paths for Physics teaching; c) the production of materials for the measurement and verification of learning through the exercise of formative evaluation; d) the role of the "laboratory" as a way of working that involves students in an active and participated way, which encourages experimentation and planning.
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis)
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410523 -
MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES
|
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
|
-
|
-
|
Elective activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
(objectives)
To Introduce students to themes, concepts, methods and results of logic that are at the basis of every discipline, in order to provide students - having any kind of background- with a deep interdisciplinary approach and an appropriate training for school teaching
|
6
|
M-FIL/02
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
|
20410466 -
FINAL EXAM
(objectives)
Written test on fundamental topics of Mathematics or discussione of a brief essay.
|
11
|
|
-
|
-
|
-
|
-
|
Final examination and foreign language test
|
ITA |
Modellistico-applicativo
FIRST YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20410386 -
AL110-ALGEBRA 1
(objectives)
Provide the elements of the "mathematical language" (set theory, elementary logic, numerical sets) and the knowledge of the basic tools of modern algebra (notions of operation, group, ring, field) through the development of examples that provide the motivations.
|
9
|
MAT/02
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410405 -
AM110 - MATHEMATICAL ANALYSIS 1
(objectives)
To acquire a good knowledge of the basic concepts and methods of Mathematical Analysis with particular regard to the structure of real numbers, to the theory of limits, to the study of functions and to the first applications and models.
|
9
|
MAT/05
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410336 -
IN110 - Algorithms and Data Structure
(objectives)
Provide a good knowledge in the design of algorithms for the solution of problems and in algorithm coding with a programming language (C language). Introduce the student to some of the fundamental concepts of discrete mathematics (with brief overview on graph theory) and in particular to the basic elements of discrete optimization (optimization algorithms on graphs, visit of graph, shortest paths, spanning trees).
|
9
|
INF/01
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
Optional Group:
SCEGLIERE 1 idoneità di lingua (3 cfu) - (show)
|
3
|
|
|
|
|
|
|
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20410335 -
GE110 - Geometry and linear algebra 1
(objectives)
Acquire a good knowledge of the concepts and methods of basic linear algebra, with particular attention given to the study of linear systems, matrices and determinants, vector spaces and linear applications, affine geometry.
|
9
|
MAT/03
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410388 -
AM120 - MATHEMATICAL ANALYSIS 2
(objectives)
To complete the basic preparation of Mathematical Analysis with particular regard to derivation and integration theory,ÿand to series developments.
|
9
|
MAT/05
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
20410406 -
FS110 - Physics 1
(objectives)
The course provides the fundamental theoretical knowledge in developing mathematical modeling for mechanics and thermodynamics.
|
9
|
FIS/01
|
48
|
42
|
-
|
-
|
Basic compulsory activities
|
ITA |
SECOND YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20402075 -
AL210 - ALGEBRA 2
(objectives)
Introduce the basic notions and techniques of abstract algebra through the study of the first properties of fundamental algebraic structures: groups, rings and fields.
|
9
|
MAT/02
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20402076 -
AM210 - MATHEMATICAL ANALYSIS 3
(objectives)
To acquire a good knowledge of some fundamental methods and results in the study ofÿfunctions of several variables and of differential equations.
|
9
|
MAT/05
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410340 -
GE210 - Geometry and linear algebra 2
(objectives)
Acquire a good knowledge of the theory of bilinear forms and their geometric applications. An important application will be the study of Euclidean geometry, mainly in the plane and in the space, and the Euclidean classification of the conics and of the quadratic surfaces.
|
9
|
MAT/03
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20410338 -
CP210 - Introduction to Probability
(objectives)
Elementary probability theory: discrete distributions, repeated trials, continuous random variables. Some basic limit theorems and introduction to Markov chains.
|
9
|
MAT/06
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410339 -
FM210 - Analytical Mechanics
(objectives)
To acquire a basic knowledge of the theory of conservative mechanical systems and of the elements of analytical mechanics, in particular of Lagrangian and Hamiltonian mechanics.
|
9
|
MAT/07
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410341 -
GE220 - Topology
(objectives)
Acquire a good knowledge of concepts and methods of general topology, with particular regard to the study of the main properties of topological spaces such as connection and compactness. Introduce the student to the basic elements of algebraic topology, through the introduction of the fundamental group and the topological classification of curves and surfaces.
|
9
|
MAT/03
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
20410586 -
AM220 - MATHEMATICAL ANALYSIS 4
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
9
|
MAT/05
|
48
|
30
|
-
|
-
|
Core compulsory activities
|
ITA |
THIRD YEAR
First semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20402082 -
FS220- Physics 2
(objectives)
The course provides the fundamental theoretical knowledge in developing mathematical modeling for electromagnetism, optics and special relativity.
|
9
|
FIS/01
|
48
|
30
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20402131 -
SCIENTIFIC ENGLISH
|
Also available in another semester or year
|
Optional Group:
SCEGLIERE 1 INSEGNAMENTO (9 cfu) oppure 2 INSEGNAMENTI (6 cfu+ 3 cfu) NEL GRUPPO 1 - (show)
|
9
|
|
|
|
|
|
|
|
20410442 -
IN420 - Information Theory
|
Also available in another semester or year
|
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
|
Also available in another semester or year
|
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
(objectives)
Acquire techniques in parallel and distributed programming, and the knowledge of modern hardware and software architectures for high-performance scientific computing. Learn distributed iterative methods for simulating numerical problems. Acquire the knowledge of the newly developed languages for dynamic programming in scientific computing, such as the Julia language.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410427 -
IN490 - PROGRAMMING LANGUAGES
(objectives)
Introduce the main concepts of formal language theory and their application to the classification of programming languages. Introduce the main techniques for the syntactic analysis of programming languages. Learn to recognize the structure of a programming language and the techniques to implement its abstract machine. Study the object-oriented paradigm and another non-imperative paradigm.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410561 -
FS230 - Elements of contemporary theoretical physics
|
Also available in another semester or year
|
20410562 -
FS240 - Principles of condensed matter
|
Also available in another semester or year
|
20410563 -
FS250 - Principles of earth and environment physics
|
Also available in another semester or year
|
20410564 -
FS260 - Elements of philosophy of science
|
Also available in another semester or year
|
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
|
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
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410461 -
FS460 - Dydactics of Physics
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410588 -
IN400 - MODULE B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLA Band its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410587 -
IN400 - MODULE 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 |
20410591 -
FS290 - L'Agenda 2030 delle Nazioni Unite per lo sviluppo sostenibile: le implicazioni per le scienze matematiche e fisiche
(objectives)
• Introduction to the United Nations Sustainable Development Agenda 2030 as a whole and in its general structure • Analysis of the 17 SDGs (Sustainable Development Goals) • Critical discussion on the organization of the Agenda and the links between its various objectives, both in terms of synergies and of conflicts • Insights on some of the Agenda objectives, especially concerning the specific interests and/or study plans of the students The main objective of the course is to make the student aware of the 2030 Agenda document, illustrating its birth, the main SDGs (Sustainable Development Goals) and the connections between them. The student will also learn what are the strategies that can be implemented and the physical-mathematical models that can be used for the achievement of the SDGs within sustainable development.
|
3
|
FIS/06
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
|
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 -
MODULE 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 -
MODULE B - MATLAB programming
(objectives)
Acquire the ability to implement high-level programs in the interpreted language MATLAB. Understand the main constructs used in MATLA Band its application to scientific computing and data processing scenarios.
|
3
|
INF/01
|
24
|
6
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
|
Optional Group:
CURRICULUM MODELLISTICO - APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (9 cfu) NEL GRUPPO 2 - (show)
|
9
|
|
|
|
|
|
|
|
20410408 -
AL310 - ELEMENTS OF ADVANCED ALGEBRA
(objectives)
Acquire a good knowledge of the concepts and methods of the theory of polynomial equations in one variable. Learn how to apply the techniques and methods of abstract algebra. Understand and apply the fundamental theorem of Galois correspondence to study the "complexity" of a polynomial.
|
9
|
MAT/02
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410409 -
AM310 - ELEMENTS OF ADVANCED ANALYSIS
(objectives)
To acquire a good knowledge of the theory of abstract integration. Introduction to functional analysis: Banach and Hilbert spaces.
|
9
|
MAT/05
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410411 -
GE310 - ELEMENTS OF ADVANCED GEOMETRY
(objectives)
Topology: topological classification of curves and surfaces. Differential geometry: study of the geometry of curves and surfaces in R^3 to provide concrete and easily calculable examples on the concept of curvature in geometry. The methods used place the geometry in relation to calculus of several variables, linear algebra and topology, providing the student with a broad view of some aspects of mathematics.
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410412 -
MC310 - Fundaments of Complementary Mathematics
(objectives)
1. Conceptual basis of mathematics: first principles in arithmetic, geometry, probability; the idea of proof; mathematics, philosophy and scientific knowledge. 2. Discrete and continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. 3. Mathematics in culture: social and economic role of mathematics, mathematics in education, the international mathematical community. 4. Planning and developing methodologies for teaching mathematics, with the aim of building a curriculum in mathematics for high schools and technical and trade schools.
|
9
|
MAT/04
|
48
|
24
|
-
|
-
|
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 |
20410415 -
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.
|
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 |
20410453 -
TN410 - INTRODUCTION TO NUMBER THEORY
|
Also available in another semester or year
|
20410593 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
Optional Group:
CURRICULUM MODELLISTICO - APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (6 cfu) NEL Gruppo 3 - (show)
|
9
|
|
|
|
|
|
|
|
|
Optional Group:
SCEGLIERE 2 INSEGNAMENTI A SCELTA AMPIA (12 cfu) - (show)
|
12
|
|
|
|
|
|
|
|
20410446 -
BL410-Introduction to Biology
(objectives)
Introduction to the methods of biological research, intended as a systematic, controlled, empirical and critical study of natural phenomenology, which is developed from the formulation of an hypothesis until the construction of the explanation. Setting the basic skills relative to the processing of experimental results and the communication in the written form. Also, a lessons cycle will be dedicated to the most profitable study methods
|
6
|
BIO/13
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410439 -
CH410 - ELEMENTS OF CHEMISTRY
(objectives)
Knowing the basic principles of general chemistry and being able to apply the acquired knowledge to the solution of simple problems of chemistry.
|
6
|
CHIM/03
|
52
|
-
|
-
|
-
|
Elective 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
|
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
|
Also available in another semester or year
|
20410450 -
GL410-Elements of Geology I
(objectives)
The course aims to provide an overview of the planet Earth, introducing the basis for understanding the main geological aspects that characterize our planet. The course will also deal with the interactions between endogenous and exogenous processes in order to understand how these processes influence the shapes of the landscape. Moreover, the course aims to provide the tools to acquire knowledge about the Solar System and its planets, defining the planet Earth as an integrated system and highlighting its role within the Solar System. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.
|
6
|
GEO/03
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
|
Also available in another semester or year
|
20410438 -
MF410 - Computational Finance
|
Also available in another semester or year
|
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
|
-
|
-
|
Elective activities
|
ITA |
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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410454 -
GL420-Elements of Geology II
|
Also available in another semester or year
|
20410455 -
LM420 - THEOREMS IN LOGIC 2
|
Also available in another semester or year
|
20410456 -
MC420-Dydactics of Mathematics
|
Also available in another semester or year
|
20410421 -
AN430- Finite Element Method
(objectives)
Introduce to the finite element method for the numerical solution of partial differential equations, in particular: computational fluid dynamics, transport problems; computational solid mechanics.
|
6
|
MAT/08
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
|
Also available in another semester or year
|
20410437 -
FS430- Theory of Relativity
|
Also available in another semester or year
|
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
|
Also available in another semester or year
|
20410458 -
LM430 - LOGICAL THEORIES 2
|
Also available in another semester or year
|
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
|
Also available in another semester or year
|
20410435 -
FS440 - Data Acquisition and Experimental Control
|
Also available in another semester or year
|
20410460 -
AM450 - FUNCTIONAL ANALYSIS
|
Also available in another semester or year
|
20410434 -
FS450 - Elements of Statistical Mechanics
|
Also available in another semester or year
|
20410424 -
IN450 - ALGORITHMS FOR CRYPTOGRAPHY
|
Also available in another semester or year
|
20410461 -
FS460 - Dydactics of Physics
|
Also available in another semester or year
|
20410425 -
GE460- GRAPH THEORY
|
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
|
-
|
-
|
Elective activities
|
ITA |
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
|
Also available in another semester or year
|
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
|
Also available in another semester or year
|
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
|
Also available in another semester or year
|
20410523 -
MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES
|
Also available in another semester or year
|
20410566 -
FS470 - Principles of astrophysics
|
Also available in another semester or year
|
20410569 -
FS480 - Reural Networks
(objectives)
Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
|
6
|
FIS/02
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410570 -
FS490 - Educational & Outreach - Science communication
(objectives)
To provide the student with the basic concepts of communication, such as techniques for public speaking and for the preparation of presentation materials and scientific communication texts. To acquire skills on the design and implementation of communication products (images, audio, video) and on the Communication Plan (plan to organize the communication of an event or scientific project).
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿelliptic partial differential equations
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410556 -
CP450 - Probabilistic methods and random algorithms
(objectives)
Get to know the main probabilistic methods and their application to computer science: random algorithms, random graphs and networks, stochastic processes on graphs, branching processes and spread of infection.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410567 -
GE470 - Riemann surfaces
(objectives)
Acquire a sufficiently broad knowledge of the topological, analytical and geometric aspects of the theory of Riemann surfaces.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
|
Also available in another semester or year
|
|
Second semester
Course
|
Credits
|
Scientific Disciplinary Sector Code
|
Contact Hours
|
Exercise Hours
|
Laboratory Hours
|
Personal Study Hours
|
Type of Activity
|
Language
|
20402131 -
SCIENTIFIC ENGLISH
(objectives)
To be able to translate in Italian mathematical books or papers written in English.
|
1
|
|
-
|
-
|
-
|
-
|
Other activities
|
ITA |
Optional Group:
SCEGLIERE 1 INSEGNAMENTO (9 cfu) oppure 2 INSEGNAMENTI (6 cfu+ 3 cfu) NEL GRUPPO 1 - (show)
|
9
|
|
|
|
|
|
|
|
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 |
20410423 -
IN440 - COMBINATORIAL OPTIMISATION
(objectives)
Acquire skills on key solution techniques for combinatorial optimization problems; improve the skills on graph theory; acquire advanced technical skills for designing, analyzing and implementing algorithms aimed to solve optimization problems on graphs, trees and flow networks.
|
9
|
INF/01
|
48
|
24
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410426 -
IN480 - PARALLEL AND DISTRIBUTED COMPUTING
|
Also available in another semester or year
|
20410427 -
IN490 - PROGRAMMING LANGUAGES
|
Also available in another semester or year
|
20410561 -
FS230 - Elements of contemporary theoretical physics
(objectives)
Introduce at an elementary level about the concepts and principles of research in contemporary theoretical physics.
|
3
|
FIS/02
|
24
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410562 -
FS240 - Principles of condensed matter
(objectives)
Provide the student with an introduction to some of the topics important for research in condensed matter physics.
|
3
|
FIS/03
|
30
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410563 -
FS250 - Principles of earth and environment physics
(objectives)
Acquire skills related to the basic physical principles of the study of the planet earth and the interactive dynamics between geosphere, hydrosphere, atmosphere and cryosphere and of the Physics of the Environment.
|
1,5
|
FIS/06
|
12
|
-
|
-
|
-
|
Attività formative affini ed integrative
|
1,5
|
FIS/07
|
12
|
-
|
-
|
-
|
Attività formative affini ed integrative
|
|
ITA |
20410564 -
FS260 - Elements of philosophy of science
(objectives)
The course of Philosophy of Science is part of the program in Philosophy and it is included among the characterizing training activities. The course is an introduction to the key problems of the philosophy of science. Among these, students will have to familiarize with issues concerning the nature of scientific explanation, of laws of nature, of the relationship between hypothesis and evidence, and of the cognitive content of scientific theories in light of radical scientific changes. These general topics will be introduced by a direct reading of some classics of 20th century philosophy of science, with the aim to develop the competences that are necessary to formulate and evaluate philosophical arguments. Students will be able to apply the knowledge acquired in the discussion and argument both from a theoretical and a historical-philosophical perspective. At the end of the course the student will acquire: -) Ability to analyze and interpret philosophical texts; -) Properties of language and argumentation; -) Ability to contextualize the acquired knowledge in the Philosophical debate.
|
3
|
M-FIL/02
|
24
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
(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
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
48
|
12
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
20410461 -
FS460 - Dydactics of Physics
(objectives)
The objectives of the course are to enable the students to acquire the necessary skills to practice an affective teaching of Physics in the secondary school, with particular attention to: a) knowledgeÿof literature research on Physic teaching; the Italian educational system and school regulations; b) the design of culturally significant educational paths for Physics teaching; c) the production of materials for the measurement and verification of learning through the exercise of formative evaluation; d) the role of the "laboratory" as a way of working that involves students in an active and participated way, which encourages experimentation and planning.
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Related or supplementary learning activities
|
ITA |
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
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
20410588 -
IN400 - MODULE B - MATLAB programming
|
Also available in another semester or year
|
20410587 -
IN400 - MODULE A - PYTHON programming
|
Also available in another semester or year
|
20410591 -
FS290 - L'Agenda 2030 delle Nazioni Unite per lo sviluppo sostenibile: le implicazioni per le scienze matematiche e fisiche
|
Also available in another semester or year
|
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
(objectives)
To Introduce students to themes, concepts, methods and results of logic that are at the basis of every discipline, in order to provide students - having any kind of background- with a deep interdisciplinary approach and an appropriate training for school teaching
|
6
|
M-FIL/02
|
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 -
MODULE A - PYTHON programming
|
Also available in another semester or year
|
20410560-2 -
MODULE B - MATLAB programming
|
Also available in another semester or year
|
|
Optional Group:
CURRICULUM MODELLISTICO - APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (9 cfu) NEL GRUPPO 2 - (show)
|
9
|
|
|
|
|
|
|
|
|
Optional Group:
CURRICULUM MODELLISTICO - APPLICATIVO: SCEGLIERE 1 INSEGNAMENTO (6 cfu) NEL Gruppo 3 - (show)
|
9
|
|
|
|
|
|
|
|
20410413 -
AN410 - NUMERICAL ANALYSIS 1
|
Also available in another semester or year
|
20410414 -
CP410 - Theory of Probability
|
Also available in another semester or year
|
20410418 -
MA410 - APPLIED AND INDUSTRIAL MATHEMATICS
(objectives)
Present a number of problems, of interest for application in various scientific and technological areas. Deal with the modeling aspects as well as those of numerical simulation, especially for problems formulated in terms of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410419 -
MS410-Statistical Mechanics
(objectives)
To acquire the mathematical basic techniques of statistical mechanics for interacting particle or spin systems, including the study of Gibbs measures and phase transition phenomena, and apply them to some concrete models, such as the Ising model in dimension d = 1,2 and in the mean field approximation.
|
9
|
MAT/07
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
20410420 -
AN420 - NUMERICAL ANALYSIS 2
(objectives)
Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
|
9
|
MAT/08
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
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 |
|
Optional Group:
SCEGLIERE 2 INSEGNAMENTI A SCELTA AMPIA (12 cfu) - (show)
|
12
|
|
|
|
|
|
|
|
20410446 -
BL410-Introduction to Biology
|
Also available in another semester or year
|
20410439 -
CH410 - ELEMENTS OF CHEMISTRY
|
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
|
-
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410448 -
FS410 - DIDACTICS OF PHYSICS WORKSHOP
(objectives)
Learn statistical and laboratory techniques for the preparation of didactic physics experiments.
|
6
|
FIS/08
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410450 -
GL410-Elements of Geology I
|
Also available in another semester or year
|
20410452 -
ME410 - ELEMENTARY MATHEMATICS FROM AN ADVANCED POINT OF VIEW
(objectives)
Illustrate, using a critical and unitary approach,ÿsome interesting and classical results and notions that are central for teaching mathematics in high school (focussing, principally, on arithmetics, geometry and algebra). The aim of the course is also to give a contribution to teachers training through the investigation on historical, didactic and cultural aspects of these topics
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410438 -
MF410 - Computational Finance
(objectives)
Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.
|
9
|
SECS-S/06
|
60
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
20410436 -
FS420 - QUANTUM MECHANICS
|
Also available in another semester or year
|
20410454 -
GL420-Elements of Geology II
(objectives)
The course aims to provide an adequate overview of the scientific contents of Earth Sciences. The course deals with the modern aspects of Earth Sciences, framing geological phenomena in the framework of the most modern theories and illustrating the hazards and risks associated with natural phenomena such as, for example, seismic and volcanic phenomena, also referring to the geology of the Italian territory. The course also aims to provide the basis for understanding the rocks cycle and their rocks genetic processes through laboratory and field experiences. During the didactical laboratories and field excursions students will learn to understand the different aspects of Italian territory, with particular regard to its environmental value e fragility.
|
6
|
GEO/03
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410455 -
LM420 - THEOREMS IN LOGIC 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410456 -
MC420-Dydactics of Mathematics
(objectives)
1. Critical analysis of the evolution of ideas and methodologies in teaching mathematics, with particular emphasis on the role of the teacher. 2. The mathematics curriculum in compulsory schooling and in the various secondary schools (high schools, technical schools and trade schools), in an international context. 3. Didactic planning and methodologies for teaching mathematics: programming and rhythm, principles and methods for the construction of activities, classroom management. 4. Problem solving. Logic, intuition and history in teaching mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410421 -
AN430- Finite Element Method
|
Also available in another semester or year
|
20410457 -
CP430 - STOCHASTIC CALCULUS
|
Also available in another semester or year
|
20410444 -
GE430 - RIEMANNIAN GEOMETRY
(objectives)
Introdue to the study of Riemannian geometry, in particular by addressing the theorems of Gauss-Bonnet and Hopf-Rinow
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410422 -
IN430 - ADVANCED COMPUTING TECHNIQUES
(objectives)
Acquire the conceptualskills in structuring problems according to the object-oriented programming paradigm. Acquire the ability to design algorithmic solutions based on the object-oriented paradigm. Acquire the basic concepts related to programming techniques based on the object-oriented paradigm. Introduce the fundamental notions of parallel and concurrent programming.
|
6
|
INF/01
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410458 -
LM430 - LOGICAL THEORIES 2
(objectives)
To acquire the basic notions of Zermelo-Fraenkel's axiomatic set theory and present some problems related to that theory.
|
6
|
MAT/01
|
36
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410459 -
MC430 - LABORATORY: DIDACTICS FOR MATHEMATICS
(objectives)
1. Mathematics software, with particular attention to their use for teaching mathematics in school. 2. Analysis of the potential and criticality of the use of technological tools for teaching and learning mathematics.
|
6
|
MAT/04
|
48
|
12
|
-
|
-
|
Elective 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
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410460 -
AM450 - FUNCTIONAL ANALYSIS
(objectives)
To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410434 -
FS450 - Elements of Statistical Mechanics
(objectives)
Gain knowledge of fundamental principles of statistical mechanics for classical and quantum systems.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
Elective 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
|
-
|
-
|
Elective activities
|
ITA |
20410461 -
FS460 - Dydactics of Physics
(objectives)
The objectives of the course are to enable the students to acquire the necessary skills to practice an affective teaching of Physics in the secondary school, with particular attention to: a) knowledgeÿof literature research on Physic teaching; the Italian educational system and school regulations; b) the design of culturally significant educational paths for Physics teaching; c) the production of materials for the measurement and verification of learning through the exercise of formative evaluation; d) the role of the "laboratory" as a way of working that involves students in an active and participated way, which encourages experimentation and planning.
|
6
|
FIS/08
|
48
|
-
|
-
|
-
|
Elective activities
|
ITA |
20410425 -
GE460- GRAPH THEORY
(objectives)
Provide tools and methods for graph theory.
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410469 -
AM430 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410465 -
GE450 - TOPOLOGIA ALGEBRICA
(objectives)
To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis)
|
6
|
MAT/03
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410520 -
AL420 - ALGEBRAIC THEORY OF NUMBERS
(objectives)
Acquire methods and techniques of modern algebraic theory of numbers through classic problems initiated by Fermat, Euler, Lagrange, Dedekind, Gauss, Kronecker.
|
6
|
MAT/02
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
20410523 -
MA430 - MATHEMATICAL METHODS FOR APPLIED SCIENCES
|
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
|
-
|
-
|
Elective activities
|
ITA |
20410569 -
FS480 - Reural Networks
|
Also available in another semester or year
|
20410570 -
FS490 - Educational & Outreach - Science communication
|
Also available in another semester or year
|
20410565 -
AM410 - ELLITTIC PARTIAL DIFFERENTIAL EQUATIONS
|
Also available in another semester or year
|
20410555 -
ST410- Statistics
|
Also available in another semester or year
|
20410556 -
CP450 - Probabilistic methods and random algorithms
|
Also available in another semester or year
|
20410567 -
GE470 - Riemann surfaces
|
Also available in another semester or year
|
20410568 -
IN470- COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
|
Also available in another semester or year
|
20410592 -
LM400 - INTRODUZIONE ALLA LOGICA
(objectives)
To Introduce students to themes, concepts, methods and results of logic that are at the basis of every discipline, in order to provide students - having any kind of background- with a deep interdisciplinary approach and an appropriate training for school teaching
|
6
|
M-FIL/02
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
|
20410466 -
FINAL EXAM
(objectives)
Written test on fundamental topics of Mathematics or discussione of a brief essay.
|
11
|
|
-
|
-
|
-
|
-
|
Final examination and foreign language test
|
ITA |