Degree Course: Mathematics
A.Y. 2019/2020
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 attività di orientamento, tirocinio, stage e placement, a livello di Ateneo, sono promosse e coordinate dal Gruppo di Lavoro per l'Orientamento di Ateneo (GLOA) costituito dal Delegato del Rettore per le politiche di orientamento, con ruolo di coordinatore, da due delegati dei Direttori per ciascun Dipartimento, un Delegato dei Presidenti per le due Scuole e dal Responsabile della Divisione Politiche per gli Studenti.
Il GLOA promuove azioni relative all'orientamento in ingresso, all'orientamento in itinere (tutorato, tirocini e stage) e all'orientamento in uscita (politiche attive per il lavoro e placement) la cui organizzazione e realizzazione è affidata, rispettivamente, all'Ufficio orientamento, all'Ufficio stage e tirocini e all'Ufficio Job Placement.
Le azioni di orientamento in ingresso sono improntate alla realizzazione di processi di raccordo con la scuola media secondaria.
Si concretizzano in attività di carattere informativo sui Corsi di Studio dell'Ateneo, molte delle quali svolte in collaborazione con la Scuola, e volte a favorire lo sviluppo di una maggiore consapevolezza da parte degli studenti nel compiere scelte coerenti con le proprie conoscenze, competenze, attitudini e interessi.
Le attività promosse si articolano in:
a) seminari e attività formative realizzate in collaborazione con i docenti delle scuole medie secondarie;
b) incontri e manifestazioni informative rivolte alle future matricole;
c) sviluppo di servizi on line per l'orientamento e l'auto-orientamento.
Tra le attività svolte in collaborazione con le scuole per lo sviluppo di una maggiore consapevolezza nella scelta, il "progetto di auto-orientamento" è un intervento che consente di promuovere un raccordo particolarmente qualificato con alcune scuole secondarie di secondo grado che insistono sul territorio limitrofo a Roma Tre.
Il progetto, infatti, è articolato in incontri svolti presso le scuole dagli esperti dell'Ufficio Orientamento con la collaborazione di studenti seniores ed è finalizzato a sollecitare nelle future matricole una riflessione sui propri punti di forza e sui criteri di scelta (gli incontri si svolgono nel periodo ottobre-dicembre).
La presentazione dell'offerta formativa agli studenti delle scuole superiori prevede tre eventi principali, distribuiti nel corso dell'anno accademico, ai quali partecipano tutti i Corsi di Studio:
- Salone dello studente "Campus orienta"
si svolge 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 propri spazi espositivi (tra i quali uno dedicato ai Corsi di Studio scientifici, chiamato 1, 2, 3,… Scienze) e con conferenze di presentazione dell'offerta formativa dell'Ateneo.
- Le Giornate di Vita Universitaria (GVU)
si svolgono ogni anno da gennaio a marzo e sono rivolte agli studenti degli ultimi due anni della scuola secondaria superiore.
Si svolgono in tutti i Dipartimenti dell'Ateneo e costituiscono una importante occasione per le future matricole per vivere la realtà universitaria.
Gli incontri sono strutturati in modo tale che accanto alla presentazione dei Corsi di Studio, gli studenti possano anche fare un'esperienza diretta di vita universitaria con la partecipazione ad attività didattiche, laboratori, lezioni o seminari, alle quali partecipano anche studenti seniores che svolgono una significativa mediazione di tipo tutoriale.
Partecipano annualmente oltre 6.000 studenti delle secondarie.
- Orientarsi a Roma Tre
rappresenta la manifestazione che chiude le annuali attività di orientamento in ingresso e si svolge in Ateneo a luglio di ogni anno.
L'evento accoglie mediamente circa 3.000 studenti romani e non solo, che partecipano per mettere definitivamente a fuoco la loro scelta universitaria.
Oltre all'offerta formativa sono presentati tutti i principali servizi di Roma Tre rivolti agli studenti e le segreterie didattiche sono a disposizione per tutte le informazioni relative alle pratiche di immatricolazione.
In tutte le manifestazioni di presentazione dell'offerta formativa, sono illustrati anche i vari servizi on line che possono aiutare gli studenti nella scelta: dai siti web dei Dipartimenti al sito del POS (Prove di Orientamento Simulate) che consente alle future matricole di autovalutarsi rispetto ai requisiti di accesso per tutti i Corsi di Studio di Roma Tre.
Infine, in tutte le manifestazioni che si svolgono in Ateneo sono somministrati ai partecipanti questionari di soddisfazione che vengono elaborati ed utilizzati per proporre miglioramenti all'organizzazione degli eventi.
Il 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 dell'Ateneo.
Infatti partecipa a tutte le principali iniziative d'Ateneo, sopra menzionate, dedicate all'orientamento:
- ll Salone dello Studente, in cui viene allestito lo stand con esperimenti e presentazioni 1, 2, 3… Scienze;
- la Giornata di Vita Universitaria;
- la Giornata "Orientarsi a Roma Tre".
Per la realizzazione dei propri progetti di orientamento, il Dipartimento aderisce inoltre 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.
In particolare nell'ambito del Piano Lauree Scientifiche il Corso di Laurea in Matematica si è mosso lungo due linee di azione:
1) lo sviluppo di vocazioni scientifiche e l'approfondimento di temi scolastici, mediante la creazione di laboratori nelle scuole e presso la sede universitaria per gli studenti più motivati;
2) la presentazione e la verifica delle conoscenze richieste per l'ingresso al corso di laurea in matematica tramite lo sviluppo di una piattaforma e-learning congiunta con il corso di Laurea in Fisica.
A tali fini il Dipartimento ha sviluppato e approfondito la conoscenza e la collaborazione con gli insegnanti delle scuole secondarie.
Inoltre il Dipartimento promuove iniziative di divulgazione e comunicazione scientifica rivolte sia alle scuole (studenti ed insegnanti) sia a tutti i cittadini, e corsi di formazione ed aggiornamento per insegnanti.
Particolare rilievo assumono le seguenti attività:
- Masterclass in Astrofisica, Fisica delle Particelle, Fisica Terrestre e dell'Ambiente, Ottica e Fisica della Materia 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: 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.
- Alternanza Scuola/Lavoro: accoglienza, presso i laboratori del Dipartimento, di studenti del terzo, quarto e quinto anno delle Scuole Superiori per la realizzazione di specifici progetti formativi concordati con i docenti referenti delle stesse.
- 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 ......": serate aperte al pubblico (alcune migliaia di presenze in totale) in cui 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: "Per la città e la scuola" (http://dmf.matfis.uniroma3.it/eventi/outreach.php).
Per entrambi i Corsi di Laurea e di Laurea Magistrale in Matematica sono predisposti Guide Informative e Opuscoli, tra cui benvenuto@matematica, disponibile anche in formato pdf sul sito web del Dipartimento (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.
Infine, il Corso di Laurea in Matematica aderisce alla prova nazionale di verifica delle conoscenze promossa e coordinata da Con.Scienze, gestita dal Consorzio Interuniversitario Sistemi Integrati per l'Accesso (CISIA, http://www.cisiaonline.it/).
Il Corso di Laurea in Matematica, per aiutare gli studenti a scegliere con maggiore consapevolezza il proprio percorso di studi, organizza test di valutazione delle conoscenze in ingresso che si svolgono in due date: una a primavera ed una a Settembre.
Vengono inoltre offerti corsi di preparazione ai test con lezioni in presenza e materiale on line disponibile nella piattaforma e-learning del Dipartimento.
Agli studenti che risultino avere una preparazione non adeguata vengono attribuiti degli Obblighi Formativi Aggiuntivi (OFA) i quali si concretizzano nel dover seguire un corso di recupero di Matematica di base offerto dal Dipartimento tra Settembre ed Ottobre di ogni anno e nel dover poi superare un nuovo test di verifica.
Il Corso di Studio in breve
Il Corso di Laurea, attraverso un'ampia scelta 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 nel Corso di Laurea Magistrale in Matematica.
ALCUNE CARATTERISTICHE DEL CORSO DI LAUREA:
- 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 e consentire allo studente un rapido e proficuo inserimento in ambito universitario;
- servizi di tutorato di varia natura, 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.
- primo e secondo anno orientativo ad ampio spettro, comune a tutti gli indirizzi, in cui, oltre ai fondamenti delle materie matematiche di base, si offrono prospettive professionalizzanti di tipo informatico e modellistico;
- percorsi formativi a Y al terzo anno, che si differenziano a seconda che si scelga l'indirizzo per l'Informatica ed il Calcolo Scientifico, professionalizzante e pensato per un rapido inserimento nel mondo del lavoro, o l'indirizzo in Matematica Generale, consigliato a chi sia interessato agli aspetti più teorici o intenda proseguire nell'ambito della ricerca o dell'insegnamento.
- grande flessibilità dei percorsi offerti, che consento, virtualmente in un qualunque momento della carriera universitaria, passare da un percorso all'altro.
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
|
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 |
|
20410471 -
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.
|
|
|
20410471-1 -
AM220 - MATHEMATICAL ANALYSIS 4 - MODULE A
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
6
|
MAT/05
|
32
|
20
|
-
|
-
|
Core compulsory activities
|
ITA |
|
20410471-2 -
AM220 - ANALISI MATEMATICA 4 - MODULE B
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
3
|
MAT/05
|
16
|
10
|
-
|
-
|
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) 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 |
|
|
Optional Group:
CURRICULUM TEORICO: SCEGLIERE 2 INSEGNAMENTI (18 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 |
|
20410407 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
|
Also available in another semester or year
|
|
20410449 -
GE410 - ALGEBRAIC GEOMETRY 1
(objectives)
Introduce to the study of topology and geometry defined through algebraic tools. Refine the concepts in algebra through applications to the study of algebraic varieties in affine and projective spaces
|
9
|
MAT/03
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
|
20410417 -
IN410-Computability and Complexity
(objectives)
Improve the understanding of the mathematical aspects of the notion of computation, and study the relationships between different computational models and the computational complexity.
|
9
|
MAT/01
|
48
|
24
|
-
|
-
|
Core compulsory activities
|
ITA |
|
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 |
|
|
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
|
|
20410440 -
ST410-Introduction to 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 |
|
20410441 -
CP420-Introduction to Stochastic Processes
|
Also available in another semester or year
|
|
20410436 -
FS420 - QUANTUM MECHANICS
(objectives)
Provide a basic knowledge of quantum mechanics, discussing the main experimental evidence and the resulting theoretical interpretations that led to the crisis of classical physics, and illustrating its basic principles: notion of probability, wave-particle duality, indetermination principle. Quantum dynamics, the Schroedinger equation and its solution for some relevant physical systems are then described.
|
6
|
FIS/02
|
60
|
-
|
-
|
-
|
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
(objectives)
Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
|
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
(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
|
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
|
|
20410522 -
CP450 - DISCRETE PROBABILITY
|
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) 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
|
|
|
Optional Group:
CURRICULUM TEORICO: SCEGLIERE 2 INSEGNAMENTI (18 cfu) NEL GRUPPO 2 - (show)
|
9
|
|
|
|
|
|
|
|
|
|
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 |
|
20410440 -
ST410-Introduction to Statistics
|
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
|
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
|
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
(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
|
|
20410522 -
CP450 - DISCRETE PROBABILITY
(objectives)
Development of probabilistic techniques and advanced methods for the study of stochastic processes on graphs, randomized algorithms and random graphs, random walks and interacting particle systems.
|
6
|
MAT/06
|
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 |
|
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
|
|
|
|
|
|
|
|
|
|
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 |
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 |
|
20410471 -
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.
|
|
|
20410471-1 -
AM220 - MATHEMATICAL ANALYSIS 4 - MODULE A
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
6
|
MAT/05
|
32
|
20
|
-
|
-
|
Core compulsory activities
|
ITA |
|
20410471-2 -
AM220 - ANALISI MATEMATICA 4 - MODULE B
(objectives)
To acquire a good knowledge of the concepts and methods related to the theory of classical integration in more variables and on varieties.
|
3
|
MAT/05
|
16
|
10
|
-
|
-
|
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) 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 |
|
|
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 |
|
20410407 -
AC310 - Complex analysis
|
Also available in another semester or year
|
|
20410445 -
AL410 - COMMUTATIVE ALGEBRA
|
Also available in another semester or year
|
|
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
|
|
|
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
|
|
20410440 -
ST410-Introduction to 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 |
|
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
(objectives)
Elements of stochastic analysis: Gaussian processes, Brownian motion, probabilistic representation for the solution to partial differential equations, stochastic integration and stochastic differential equations.
|
6
|
MAT/06
|
48
|
12
|
-
|
-
|
Elective activities
|
ITA |
|
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
(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
|
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
(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
|
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
|
|
20410522 -
CP450 - DISCRETE PROBABILITY
|
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) 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
|
|
|
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 |
|
20410440 -
ST410-Introduction to Statistics
|
Also available in another semester or year
|
|
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
|
Also available in another semester or year
|
|
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
|
Also available in another semester or year
|
|
20410518 -
AM420 - SOBOLEV SPACES AND PARTIAL DERIVATIVE EQUATIONS
(objectives)
To acquire a good knowledge of the general methods andÿclassical techniques necessary for the study ofÿweak solutions of partial differential equations.
|
6
|
MAT/05
|
48
|
12
|
-
|
-
|
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
|
|
20410522 -
CP450 - DISCRETE PROBABILITY
(objectives)
Development of probabilistic techniques and advanced methods for the study of stochastic processes on graphs, randomized algorithms and random graphs, random walks and interacting particle systems.
|
6
|
MAT/06
|
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 |
Università Roma Tre