Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period | From | To |
---|---|---|
Semester 1 | Oct 2, 2023 | Jan 26, 2024 |
Semester 2 | Mar 4, 2024 | Jun 14, 2024 |
Session | From | To |
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Winter exam session | Jan 29, 2024 | Mar 1, 2024 |
Summer exam session | Jun 17, 2024 | Jul 31, 2024 |
Autumn exam session | Sep 2, 2024 | Sep 30, 2024 |
Session | From | To |
---|---|---|
Summer graduation session | Jul 22, 2024 | Jul 22, 2024 |
Autumn graduation session | Oct 22, 2024 | Oct 22, 2024 |
December graduation session | Dec 11, 2024 | Dec 11, 2024 |
Sessione invernale | Mar 19, 2025 | Mar 19, 2025 |
Period | From | To |
---|---|---|
Festa di Ognissanti | Nov 1, 2023 | Nov 1, 2023 |
Festa dell'Immacolata | Dec 8, 2023 | Dec 8, 2023 |
Vacanze di Natale | Dec 24, 2023 | Jan 7, 2024 |
Festività pasquali | Mar 29, 2024 | Apr 1, 2024 |
Ponte della Festa della Liberazione | Apr 25, 2024 | Apr 26, 2024 |
Festa del Lavoro | May 1, 2024 | May 1, 2024 |
Festività del Santo Patrono: San Zeno | May 21, 2024 | May 21, 2024 |
Festa della Repubblica | Jun 2, 2024 | Jun 2, 2024 |
Vacanze estive | Aug 12, 2024 | Aug 17, 2024 |
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Academic staff

Rossi Francesca
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
Modules | Credits | TAF | SSD |
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2° Year activated in the A.Y. 2024/2025
Modules | Credits | TAF | SSD |
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3° Year It will be activated in the A.Y. 2025/2026
Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Modules | Credits | TAF | SSD |
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Type D and Type F activities
Le attività formative di tipologia D sono a scelta dello studente, quelle di tipologia F sono ulteriori conoscenze utili all’inserimento nel mondo del lavoro (tirocini, competenze trasversali, project works, ecc.). In base al Regolamento Didattico del Corso, alcune attività possono essere scelte e inserite autonomamente a libretto, altre devono essere approvate da apposita commissione per verificarne la coerenza con il piano di studio. Le attività formative di tipologia D o F possono essere ricoperte dalle seguenti attività.
1. Insegnamenti impartiti presso l'Università di Verona
Comprendono gli insegnamenti sotto riportati e/o nel Catalogo degli insegnamenti (che può essere filtrato anche per lingua di erogazione tramite la Ricerca avanzata).
Modalità di inserimento a libretto: se l'insegnamento è compreso tra quelli sottoelencati, lo studente può inserirlo autonomamente durante il periodo in cui il piano di studi è aperto; in caso contrario, lo studente deve fare richiesta alla Segreteria, inviando a carriere.scienze@ateneo.univr.it il modulo nel periodo indicato.
2. Attestato o equipollenza linguistica CLA
Oltre a quelle richieste dal piano di studi, per gli immatricolati dall'A.A. 2021/2022 vengono riconosciute:
- Lingua inglese: vengono riconosciuti 3 CFU per ogni livello di competenza superiore a quello richiesto dal corso di studio (se non già riconosciuto nel ciclo di studi precedente).
- Altre lingue e italiano per stranieri: vengono riconosciuti 3 CFU per ogni livello di competenza a partire da A2 (se non già riconosciuto nel ciclo di studi precedente).
Tali cfu saranno riconosciuti, fino ad un massimo di 6 cfu complessivi, di tipologia F se il piano didattico lo consente, oppure di tipologia D. Ulteriori crediti a scelta per conoscenze linguistiche potranno essere riconosciuti solo se coerenti con il progetto formativo dello studente e se adeguatamente motivati.
Gli immatricolati fino all'A.A. 2020/2021 devono consultare le informazioni che si trovano qui.
Modalità di inserimento a libretto: richiedere l’attestato o l'equipollenza al CLA e inviarlo alla Segreteria Studenti - Carriere per l’inserimento dell’esame in carriera, tramite mail: carriere.scienze@ateneo.univr.it
3. Competenze trasversali
Scopri i percorsi formativi promossi dal TALC - Teaching and learning center dell'Ateneo, destinati agli studenti regolarmente iscritti all'anno accademico di erogazione del corso https://talc.univr.it/it/competenze-trasversali
Modalità di inserimento a libretto: non è previsto l'inserimento dell'insegnamento nel piano di studi. Solo in seguito all'ottenimento dell'Open Badge verranno automaticamente convalidati i CFU a libretto. La registrazione dei CFU in carriera non è istantanea, ma ci saranno da attendere dei tempi tecnici.
4. CONTAMINATION LAB
Il Contamination Lab Verona (CLab Verona) è un percorso esperienziale con moduli dedicati all'innovazione e alla cultura d'impresa che offre la possibilità di lavorare in team con studenti e studentesse di tutti i corsi di studio per risolvere sfide lanciate da aziende ed enti. Il percorso permette di ricevere 6 CFU in ambito D o F. Scopri le sfide: https://www.univr.it/clabverona
ATTENZIONE: Per essere ammessi a sostenere una qualsiasi attività didattica, incluse quelle a scelta, è necessario essere iscritti all'anno di corso in cui essa viene offerta. Si raccomanda, pertanto, ai laureandi delle sessioni di dicembre e aprile di NON svolgere attività extracurriculari del nuovo anno accademico, cui loro non risultano iscritti, essendo tali sessioni di laurea con validità riferita all'anno accademico precedente. Quindi, per attività svolte in un anno accademico cui non si è iscritti, non si potrà dar luogo a riconoscimento di CFU.
5. Periodo di stage/tirocinio
Oltre ai CFU previsti dal piano di studi (verificare attentamente quanto indicato sul Regolamento Didattico): qui informazioni su come attivare lo stage.
Verificare nel regolamento quali attività possono essere di tipologia D e quali di tipologia F.
Insegnamenti e altre attività che si possono inserire autonomamente a libretto
years | Modules | TAF | Teacher |
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1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
1° 2° 3° | Basis of general chemistry | D |
Silvia Ruggieri
|
1° 2° 3° | Genetics | D |
Massimo Delledonne
(Coordinator)
|
1° 2° 3° | Introduction to quantum mechanics for quantum computing | D |
Claudia Daffara
(Coordinator)
|
1° 2° 3° | Introduction to Robotics for students of scientific courses. | D |
Andrea Calanca
(Coordinator)
|
1° 2° 3° | Web and mobile app design using react and react native | D |
Graziano Pravadelli
(Coordinator)
|
1° 2° 3° | Firmware development with bluetooth low energy (BLE) protocol and freertos operating system | D |
Franco Fummi
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° 2° 3° | Algebraic Geometry | F |
Rosanna Davison Laking
(Coordinator)
|
1° 2° 3° | Algorithms | D |
Roberto Segala
(Coordinator)
|
1° 2° 3° | Artificial intelligence | D |
Alessandro Farinelli
(Coordinator)
|
1° 2° 3° | Introduction to Robotics for students of scientific courses. | D |
Andrea Calanca
(Coordinator)
|
1° 2° 3° | LaTeX Language | D |
Enrico Gregorio
(Coordinator)
|
1° 2° 3° | Python programming language | D |
Carlo Combi
(Coordinator)
|
1° 2° 3° | Organization Studies | D |
Serena Cubico
(Coordinator)
|
1° 2° 3° | Scientific Programming | F |
Pietro Sala
(Coordinator)
|
1° 2° 3° | Programming Challanges | D |
Romeo Rizzi
(Coordinator)
|
years | Modules | TAF | Teacher |
---|---|---|---|
1° | Subject requirements: mathematics | D |
Franco Zivcovich
(Coordinator)
|
Dynamical Systems (2024/2025)
Teaching code
4S00244
Credits
9
Language
Italian
Also offered in courses:
- Dynamical Systems of the course Bachelor's degree in Applied Mathematics
Scientific Disciplinary Sector (SSD)
MAT/05 - MATHEMATICAL ANALYSIS
Courses Single
Authorized
The teaching is organized as follows:
Teoria
Esercitazioni
Credits
3
Period
Semester 2
Academic staff
Not yet assigned
Learning objectives
The aim of the course is to introduce the theory and some applications of dynamical systems, which describe the time evolution of quantitative variables. By the end of the course, the students will be able to investigate the stability and the character of an equilibrium, the qualitative analysis of a system of ordinary differential equations, the phase portrait of a (parametric) dynamical system in dimension 1 and 2, and to analyse finite-dimensional Hamiltonian systems. Moreover, the students will be able to study some basic applications of dynamical systems arising from population dynamics, mechanics and traffic flows. Finally, students will be also able to produce proofs using the typical tools of modern dynamical systems and will be able to read and report specific books and articles on dynamical systems and related applications.
Prerequisites and basic notions
The material covered in first-year and second-year, first-semester courses - in particular, Mathematical Analysis 1 and 2, Linear Algebra.
Program
Part I
1. Topics in the theory of ordinary differential equations
Qualitative analysis of ODE: existence and uniqueness of solutions; maximal and global solutions; Gronwall’s Lemma; continuous dependence on the initial data.
2. Vector fields and ordinary differential equations
Vector fields: phase space, integral curves, orbits, equilibria, phase portrait. 1-dimensional examples of phase portraits. Second-order systems of differential equations; phase-space analysis and equilibria.
3. Linear systems
Linearisation of a vector field about an equilibrium. Classification of two-dimensional linear systems (over the real numbers) that are diagonalisable over the complex numbers. (If time permits, we will briefly discuss the nilpotent case as well.) n-dimensional linear systems: invariant subspace decomposition; the stable, unstable and central subspaces. Comparing a vector field with its linearisation about a hyperbolic equilibrium.
4. Flow of a vector field
Flow of a vector field. Change of coordinates: conjugate vector fields; pull-back and push-forward of a vector field by a diffeomorphism. Non-autonomous differential equations: time-dependent change of coordinates; scaling of vector fields and time reparametrisations. The local rectification theorem.
5. First integrals
Invariant sets; first integrals; Lie derivative. Invariant foliations; reduction of the order. First integrals and attractive equilibria.
6. Stability theory
Stability 'à la Lyapunov' of an equilibrium; the method of Lyapunov functions; the spectral method. Applications and examples.
7. 1-dimensional Newton equation.
Phase portraits of the 1-dimensional Newton equation, in the conservative case. Linearisation. Reduction of the order. Systems with friction.
Part II
8. Bifurcations
Bifurcatios from equilibria, with 1-dimensional examples; applications.
9. Introduction to the 1-dimensional Calculus of Variations
The indirect method for one-dimensional integral functionals. Necessary conditions for the existence of minimisers: the Euler-Lagrange equations. Jacobi integral; conservation laws. Geodesics on a surface.
10. Hamiltonian systems
Hamiltonian vector fields. Legendre transform. Poisson brackets. Canonical transformations. Lie conditions, generating functions. The Hamilton-Jacobi equations. Integrability. Geometry of the phase space: Liouville's theorem and Poincaré's recurrence theorem.
Bibliography
Didactic methods
Lectures and exercises (often, combined).
Learning assessment procedures
The exam consists of a written part, with exercises and/or questions on the course content, and an oral part.
Evaluation criteria
Knowledge of the content of the course. Ability to solve simple problems. Logical rigour. Clarity of presentation.
Criteria for the composition of the final grade
Please see the Italian version.
Exam language
Italiano
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and also via the Univr app.
Graduation
Documents
Title | Info File |
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pdf, it, 31 KB, 29/07/21 |
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pdf, it, 31 KB, 29/07/21 |
![]() |
pdf, it, 171 KB, 20/03/24 |
List of thesis proposals
theses proposals | Research area |
---|---|
Formule di rappresentazione per gradienti generalizzati | Mathematics - Analysis |
Formule di rappresentazione per gradienti generalizzati | Mathematics - Mathematics |
Mathematics Bachelor and Master thesis titles | Various topics |
Attendance modes and venues
As stated in the Teaching Regulations , except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.
Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.
The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus.
Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.
Career management
Student login and resources
Erasmus+ and other experiences abroad
Ongoing orientation for students
The committee has the task of guiding the students throughout their studies, guiding them in their choice of educational pathways, making them active participants in the educational process and helping to overcome any individual difficulties.
It is composed of professors Lidia Angeleri, Sisto Baldo, Marco Caliari, Paolo dai Pra, Francesca Mantese, and Nicola Sansonetto
To send an email to professors: name.surname@univr.it