#ABOUT Semester 1 in L'Aquila;

Foundations of Applied Mathematics

The first semester at UAQ is common to all students. It provides a sound background in applied mathematics based on advanced theoretical subjects such as functional analysis, applied partial differential equations, dynamical systems, continuum mechanics, and control systems.

This semester prepares the students to perform simulations in diverse modelling frameworks, as well as to successfully tackle subjects in semester 2 such as advanced numerical calculus, optimization, and stochastic calculus. To perform this task, Semester 1 courses provide a systematic approach to the formulation of applied problems in interdisciplinary fields, and a rigorous approach to mathematical modelling. More precisely, students in this semester are provided “exact” resolution methods for (ordinary and partial) differential equations, the “infinite dimensional” approach of functional analysis (needed in approximation theory, variational calculus, and numerical analysis), a modern and “engineering oriented” approach to control, and an introduction to the mathematical theory of continuum media, a subject that is touched by several specialization tracks.

Teaching staff with longstanding experience with international joint programs in applied mathematics is in charge of this semester. The University of L’Aquila features a research group in mathematical analysis combining three generations of applied mathematicians with excellent international reputation in their field and with an outstanding research record, with main focus on partial differential equations with applications to physics, engineering, social sciences, biology and medicine.

#Semester 1 in L'Aquila EMJMD InterMaths Study Track

Foundations of Applied Mathematics;


University of L'Aquila





ECTS Credits




ECTS Credits: 6   |   Semester: 1   |   Year: 1   |   Campus: University of L'Aquila   |   Language: English   |   Code: DT0626

Unit Coordinator: Michele Palladino


  • Introducing basic tools of advanced real analysis such as metric spaces, Banach spaces, Hilbert spaces, bounded operators, weak convergences, compact operators, weak and strong compactness in metric spaces, spectral theory, in order to allow the student to formulate and solve linear ordinary differential equations partial differential equations, classical variational problems, and numerical approximation problems in an "abstract" form.


  • Metric spaces, normed linear spaces. Topology in metric spaces. Compactness.
  • Spaces of continuous functions. Convergence of function sequences. Approximation by polynomials. Compactness in spaces of continuous functions. Arzelà's theorem. Contraction mapping theorem.
  • Crash course on Lebesgue meausre and integration. Limit exchange theorema. Lp spaces. Completeness of Lp spaces.
  • Introduction to the theory of linear bounded operators on Banach spaces. Bounded operators. Dual norm. Examples. Riesz' lemma. Norm convergence for bounded operators.
  • Hilbert spaces. Elementary properties. Orthogonality. Orthogonal projections. Bessel's inequality. Orthonormal bases. Examples.
  • Bounded operators on Hilbert spaces. Dual of a Hilbert space. Adjoin operator, self-adjoint operators, unitary operators. Applications. Weak convergence on Hilbert spaces. Banach-Alaoglu's theorem.
  • Introduction to spectral theory. Compact operators. Spectral theorem for self-adjoint compact operators on Hilbert spaces. Hilbert-Schmidt operators. Functions of operators.
  • Introduction to the theory of unbounded operators. Linear differential operators. Applications.
  • Introduction to infinite-dimensional differential calculus and variational methods.


Basic calculus and analysis in several variables, linear algebra.

Reading list:

  • John K. Hunter, Bruno Nachtergaele, Applied Analysis. World Scientific.
  • H. Brezis, Funtional Analysis, Sobolev Spaces, and partial differential equations. Springer.

ECTS Credits: 6   |   Semester: 1   |   Year: 1   |   Campus: University of L'Aquila   |   Language: English   |   Code: I0459

Unit Coordinator: Bruno Rubino


The course is intended to introduce and develop an understanding of the concepts in nonlinear dynamical systems and bifurcation theory, and an ability to analyze nonlinear dynamic models of physical systems. The emphasis is to be on understanding the underlying basis of local bifurcation analysis techniques and their applications to structural and mechanical systems.


Review of: first-order nonlinear ODE, first-order linear systems of autonomous ODE. Local theory for nonlinear dynamical systems: linearization, stable manifold theorem, stability and Liapunov functions, planar non-hyperbolic critical points, center manifold theory, normal form theory. Global theory for nonlinear systems: limit sets and attractors, limit cycles and separatrix cycles, Poincaré map. Hamiltonian systems. Poincaré-Bendixson theory. Bifurcation theory for nonlinear systems: structural stability, bifurcation at non-hyperbolic equilibrium points, Hopf bifurcations, bifurcation at non hyperbolic periodic orbits. Applications.


Ordinary differential equations

Reading list:

Lawrence Perko, Differential equations and dynamical systems, Springer-Verlag, 2001

Practical information for your semester in L'Aquila

Academic Calendar & Term dates

Key Dates

2024/2025 academic year

Semester 1

23 September - 12 January (PDF Schedule)

Christmas vacation

23 December - 6 January

Semester 1 examinations

13 January - 23 February

Semester 2

March - September

TUHH Semester2 starts with some preliminary activities run in L'Aquila in March, then continues in Hamburg as of April 1.
Holidays (Italy)

1 November, 8 December, 6 April, 25 April, 1 May, 2 June, 10 June, 15 August

Visa information

Applying for an Italian study visa

Non-EU students selected to study at the University of L'Aquila will need to apply for a student visa at the nearest Italian Embassy/Consulate. The visa application requirements and processing time can be lengthy, taking anywhere from a few weeks up to several months. It is very important that you contact the nearest Italian Embassy for information as early as possible.

Please notice that, before joining our programmes, you will only need to apply for one visa only at an Italian Embassy/Consulate, as Italy is the location for your first semester/year. Afterwards, while you're spending your semester(s) in Italy, you will have the chance to apply for another visa or residence permit, e.g. a German one if you're spending your Semester 2 in Hamburg, at the German Consulate based in Rome.

Web-based visa application on Universitaly.it

The visa application procedure is completely web-based. All non-EU students not living in Italy are requested to pre-enrol using the online platform called UNIVERSITALY. Once your pre-enrolment request on Universitaly.it has been approved by the University of L'Aquila, you will receive a confirmation email. After that, you will have to get in contact with the local Italian Diplomatic-consular mission for the visa request process. Please note that the university confirmation email does not automatically imply the issue of a study visa for you, which is all up to the Diplomatic mission you're in contact with, instead.

Documents required

Please get in contact with the local embassy/consulate to learn more about the specific requirements they might have in that region.

valid until 3 months after the expiry of your visa
See here for more information.

Recognition of Qualifications

To complete your visa application first and finalize your enrolment after reaching L'Aquila, you'll have to submit verification of your previous university qualifications

Residence Permit

If you need a visa to stay in Italy, remember that you will also have to apply for an Italian residence permit within 8 days of arriving in our country.

Italian Residence Permit

If you need a visa to stay in Italy, remember that you will also have to apply for an Italian residence permit within 8 days after arriving in our country. A residence permit is indeed required when a foreigner stays in Italy for longer than three months.
The InterMaths team will assist you with preparing all the required documentation, which includes a couple of forms to be filled in and, among others:

A full copy of your passport (every single page, cover included)

A copy of your health insurance card

Accommodation proof

Financial proof

Enrolment certificate

All you need to do is visit an Italian post office and withdraw the required form known as "kit permesso di soggiorno" ("soggiorno" sounds like "sojjorno"). Then, bring it to campus and we'll fill it in together!
After that, put all the required documents (including blank forms) back in the envelope, visit an Italian post office once again and complete the submission process (including payment of the required fees) with the post office clerks. After that, your application will be submitted to the L'Aquila police station ("questura" in Italian, which sounds like "kuestura") via the post office itself. Note that you may withdraw and drop your application form at any Italian post office, not necessarily the ones in L'Aquila, but the envelope must be addressed to the L'Aquila Questura, as it's the one in charge of the place where you're going to live and study.

At the end of the submission process, the clerk at the post office will hand you out three receipts, which will be considered as your temporary residence permit (always carry a copy with you whenever you're around and drop one to our Registrar's Office to confirm your enrolment).
On such receipts you'll also find the date and time of the appointment fixed for you at the L'Aquila police station (Questura) to complete the rest of the required procedures, which includes an interview for fingerprints (carry with you passport & ID-size photos). Eventually, you'll be summoned for another appointment to collect your final (plastic) permit card - the one you can see on this page.
The whole process will be complete in approximately 2 months (but it might even take longer) and will cost you around 120 euros.

Enrolment procedure

After getting to L'Aquila, you'll have to complete your enrolment at the University of L'Aquila, which is the coordinating institution of your MSc programme. 
The enrolment process involves a preliminary online phase to be performed on our university info system "Segreteria Virtuale", which is usually taken care of by the InterMaths consortium.
The process consists of:

  • Account registration

  • Online pre-enrolment (it has nothing to do with the Pre-Enrolment on Universitaly.it to get a study visa)

  • Fee payment.

Afterwards, to finalize your online enrolment, you'll have to submit:

  1. Qualifications (i.e., transcript and degree certificate) from your university of origin in their original format.

  2. Verification of your previous university qualifications. To do so, you'll have to submit ONE of the following certificates:

CIMEA Statements of comparability

CIMEA (ENIC/NARIC network) has implemented a service of certification and comparison of Italian and foreign qualifications - note that you'll only need to request a statement of comparability.

Apply here

Declaration of Value (DoV)

The DoV is a document providing an official description of your academic certificates, duly legalized by the Consular office of the Italian Embassy in the country where such a degree was gained.

Diploma Supplement

You may submit a Diploma Supplement to verify your previous qualification only if it is issued by the institution where you gained your undergraduate degree.

Direct Verification via UAQ

Starting this year (2024 edition) you may entitle the University of L'Aquila to contact the institution where you obtained your previous degree and verify the genuine nature of your qualifications. Further information about this procedure will be emailed to you by our staff.

Note that some local Diplomatic-consular missions might still require you to obtain a Declaration of Value (DoV) or a CIMEA statement before they issue your study visa, even though they know that our university accepts other types of verification (any of the 4 listed above).

If that is the case, you will have to go through the DoV/CIMEA request process, otherwise, you will never obtain any visa from that specific embassy. Please check in good time in advance the particular requirements in force at the Diplomatic-consular you're about to visit for your visa.

For further information on this topic, check out the related webpage on the UAQ site: www.univaq.it/international


All our students (either non-EU or EU) must hold valid insurance covering risks related to health, accidents, death, permanent invalidity, and civil responsibility (including travel assistance) while they are outside their home country.

An insurance card will also be necessary to apply for a residence permit.

↘ Erasmus Mundus (EMJMD) InterMaths students (either scholarship holders or not)

Before their arrival, they will receive free of charge an insurance card covering risks related to health, accidents, death, permanent invalidity, and civil responsibility, as per the minimum requirements set out by EACEA

↘ Other students (enrolled in the RealMaths or MathMods programs).

  • Non-European students must ensure they hold valid insurance to obtain a visa, a residence permit, and enrolment at university. Requirements may vary a lot from country to country even within the Schengen area. Generally speaking, such insurance must offer coverage of medical costs for min. 30,000 EUR, as well as risks related to health, accidents, permanent invalidity, urgent health attention and/or emergency hospital treatment or even death, including possible repatriation for medical reasons.

  • EU students, on the other hand, won't need to purchase any additional private insurance if they don't think they need one, as long as they hold a valid European Health Insurance Card (EHIC).

Though you may get an Italian residence permit even by providing cheap insurance, we encourage everybody to ensure that the insurance coverage you are about to purchase is as comprehensive as possible.

Note that some of the options listed below, though officially valid throughout the Schengen area, may not be sufficient to obtain a visa/permit when you are going to spend a semester in another country, in Germany or Austria for instance. Please double-check before completing your purchase for a whole year or more, and contact the related staff at our partners in advance, because in other countries than Italy, they might require that you purchase a more comprehensive one and/or even public health insurance to obtain a visa/permit and even to seek enrolment at their university.

All the below-listed companies offer insurance that complies with the minimum requirements to obtain an Italian residence permit. Once again, though they are all officially valid within the Schengen area, they might not be enough to obtain a visa/residence/enrolment in other countries.

  • AON 
    [AON 24/7 emergency assistance: # +31 (0)10 44 88 260]

  • Expat & Co

  • Protrip-World by DrWalter

  • Waitaly This is the cheapest option (direct link). However, note that it is not EACEA compliant (thus, not valid for Erasmus Mundus programs), but it is still valid to obtain an Italian residence permit to attend other programmes, like RealMaths for instance.
    [Waitaly 24/7 emergency assistance via Europ Assistance 800046421 (toll free from Italian phones only) or +39 0258286966]

Find the nearest open pharmacy

Looking for an open pharmacy nearby?


In case of a real emergency, dial 118
Don't forget to contact your insurance too, which provides a 24/7 emergency helpline in English.
To check the current status of the local emergency room (Pronto Soccorso), see here

Doctor-on-call (Guardia medica)

Out-of-hours (on call) doctor.
Address: Ex ONPI, via Capo Croce 1 ("Torrione" neighbourhood).
Available Mon-Fri from 8pm till 8 am, and from 10 am on Sat till 8 am on the following Mon.

Psychological support

Psychological support and help provided to UAQ students.

Below you can find some information about finding a place to stay in L'Aquila, which is going to be your first destination in your study programme. For details about housing in the other partner universities, just browse the related section from the top menu (e.g. Consortium > Vienna).

Housing options in L'Aquila

Student's halls of residence

In Italy, students' halls of residence (including other facilities for students like cafeterias, gyms etc) are not managed by universities. The public body in charge of them is, in our case, the Abruzzo Regional Agency for Education, aka A.D.S.U. (Azienda per il Diritto agli Studi Universitari - L'Aquila).

If you wish to find a place in the dorms and shared flats managed by A.D.S.U., you will have to apply typically in the second half of August (in the last few years, the call was launched only at the end of September or even later). Note that:

  • Places are limited and usually reserved for students from low-income families.

  • Ranking lists might be published even in late October, which means you will be spending a lot for a temporary place to stay (e.g. bed and breakfast) in your first weeks in L'Aquila while you are waiting for the lists to be out.

Private halls

Lately, a new student hall has opened up in town - it's known as Camplus. It is a private one, with no relation whatsoever with our university, but it is ideally located in the heart of the city centre, it can be booked online in advance and their fares include Wi-Fi, cleaning, maintenance etc. Check out their website to submit your application and find out more.

Private shared flats

As L'Aquila is undergoing huge reconstruction after the 2009 earthquake, we strongly suggest you opt for renting a flat from private owners. The cost per person ranges from 200 to 350 euros per month depending on several factors, e.g. shared or private rooms, utility bills included or not, and neighbourhood. By the way, living near the campus (the area is in a suburb in west L'Aquila known as Coppito) can be cheaper, but this means living away from the city life (events, nightlife, restaurants...).

Please make contact with Aquilasmus - ESN L'Aquila to receive support from a buddy with finding a place to stay in L'Aquila. Note that support is provided free of charge by volunteers and only starts after your arrival in L'Aquila (weekends not included).

Housing Contact Form by Aquilasmus

Camplus is a newly-established hall of residence located right in L'Aquila city centre. It includes single and double ensuites, maintenance, wifi, cleaning, utilities etc. Check out the current selection announcement for more details and the applicaion form.

Camplus Application form

Accommodation options in L'Aquila

Your Aquilasmus buddy will typically meet you within a few days (excluding weekends) after your arrival to help you find a place to stay (note that they can't offer any kind of support before you get to L'Aquila). For your first days in L'Aquila you may refer to the links below

ADSU Hall of Residence

ADSU (Abruzzo regional agency for education)

Adverts on Univaq.it

Online ADs from private owners available on our university website


Rooms for rent - Ads in English


Vacation rentals in L'Aquila

FB group

"Cerco/Affitto Casa a L'Aquila!"

Bed & Breakfast in L'Aquila

Vacation rentals in L'Aquila


ADs listing on L'Aquila local newspaper

Below you can find some information about how to get to L'Aquila, which is going to be your first destination in your study programme. For details about reaching the other partner universities, just browse the related section from the top menu (e.g. Consortium > Nice).

How to get to L'Aquila

Ideally located in central Italy, L'Aquila is around 110 Km (68 miles) east of Rome and 100 Km (62 miles) west of Pescara. Choose one of the following means of transport to find out more.
The closest international airports are:

Rome Fiumicino

main hub, aka Leonardo Da Vinci Airport

Rome Ciampino

aka G.B. Pastine Airport
Both airports are connected to L'Aquila by express coach service operated by Gaspari or Flixbus. Read the section below ("By Bus") for further information.
Additional coach services (operated by T.U.A., aka as A.R.P.A. and Itabus) are available from the "Tiburtina train station" (Stazione Tiburtina) located in East Rome.  But that means you'll have to first get on a train/bus/undeground from the airport to get to the "Tiburtina train station", which will take you one hour or so, at least. So, we strongly suggest you use the other option above, as those coaches will be departing right from inside the aiport parking area.
Lastly, be informed that a bunch of European cities are also connected to the Abruzzo Airport in Pescara, located at about 100 km to the east of L'Aquila.