ECMI


ECMI Master in Industrial Mathematics at University of Milan.

For any information about the ECMI Programme please contact the email:

ecmi@unimi.it

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All students which are following or will follow the ECMI programme in Milan are requested to fill in the form which can be found here (it is not a formal registration. It is just to keep track of the number and names of students attending the programme).

Background

During the academic year 1986-1987, representatives of Universität Kaiserslautern (D), Johannes Kepler Universität Linz (A), Technische Universiteit Eindhoven (NL), University of Oxford (UK), Università di Milano (I), Norges Teknisk Naturvitenskapelige Universitet (Trondheim, N) and Rolf Nevanlinna Instituutti (Helsinki, SF, acting as coordinating centre for several cooperating Finnish universities) formed the European Consortium for Mathematics in Industry (ECMI) and initiated two year postgraduate programmes, where industrial problem solving is a prominent aim using mathematics. Note that with “Industrial problems” it is meant every problem which has an economical or societal impact. The purpose of these industrial mathematics programmes is threefold:

  • To promote the use of mathematical models in industry,
  • To educate industrial mathematicians to meet the growing demand for such experts,
  • To operate on a European scale.

The main instruments in obtaining these goals are collaboration on the development of course curriculum in mathematical disciplines relevant for applications in industry and commerce. The educational coordination is conducted by the ECMI Educational Committee with representatives from each participating university. The Department of Mathematics of the University of Milan is a member of the European Consortium for Mathematics in Industry (E.C.M.I.) Today the following ECMI universities offer industrial mathematics programmes: |   University of Kaiserslautern   |   Technical University of Dresden   |   Johannes Kepler University   | |   University of Milan   |   Technical University of Eindhoven   |   Technical University of Denmark   | |   University of Oxford   |   University of Strathclyde   |   University of Bristol   | |   Lappeenranta University of Technology   |   
Chalmers University of Technology   |   Lund University   | |   The Norwegian University of Science and Technology   | |   Wroclaw University of Technology   |   The Autonomous University of Barcelona   |   Carlos III University, Madrid   | |   
University of Novi Sad   |   University of South Hampton   |   Technical University of Graz   | |   University of Grenoble   |   University of Rouen   | Universidade Tecnica de Lisboa (Instituto Superior Tecnico) | Universidade de Coimbra | University of Sofia |

The Consortium issues a Certificate in Industrial Mathematics, signed by the president of ECMI, with two different branches: Technomatematics or Economathematics. The Certificate, that is a “quality statement” recognised by all the universities of the Consortium, can be awarded to students of the MSc (Laurea Magistrale) in Mathematics – Curriculum C, Industrial, who fulfil the following requirements:

  1. Have participated to a Modelling Week, organized every year by ECMI, usually in August (Click here for a list of past editions of ECMI Summer Schools and Modelling Weeks)
    • It is advised to participate to a modelling week during the second year of the Laurea Magistrale (MSc)
    • Starting from 2010, the modelling week may be preceded by a Summer School, one week long, which is not compulsory for the diploma but is anyway strongly adviced.
  1. Have spent at least one semester at one of the universities of the ECMI Consortium, to follow courses or to prepare the final thesis (possibly using the Erasmus+ programme)
    • Note that most of the ECMI universities offer courses in English during the MSc studies. Students who want to use an Erasmus/Socrates programme to spend a period in an ECMI university are advised to inform the Milan representative in the ECMI Educational Committee (Dr. P. Causin), in order to keep contacts with the local representative of the hosting university.
  2. Have prepared a final  Thesis in Industrial Mathematics, in collaboration with companies or research centres, written in English (or at least an English summary of  the thesis has been produced)
    • The thesis can also be prepared during a period spent abroad, with an advisor from the hosting university and an advisor from the University of Milan. It can be joined to an industrial internship

The MSc curriculum should respect the rules of the Laurea Magistrale in Matematica at Università degli Studi di Milano – curriculum C, which is described below (for detailes on programs and scheduling of the courses see the web page of the Department of Mathematics – teaching).

The master  programme in Industrial Mathematics (laurea magistrale in Matematica- Curriculum C) at Universita’ degli Studi di Milano

The duration of the master programme is two years (120 ECTS). There are three course blocks (0C, 1C and 2C) for each of the branches Techno-mathematics and Econo-mathematics. The course blocks are related to both the requirements for admission and the implementation of the programme. The main intention is that the student should acquire sufficient skills in both mathematics and scientific computing in order to carry out the modelling of industrial problems.

 

  Prerequisites and procedures  for admission  

The students with a BSc in Mathematics of the Università degli Studi di Milano who obtained a final evaluation of at least 100/110 are directly admitted to the Master (Laurea Magistrale) in Mathematics, if they apply for admission. All other applications will be evaluated by a commission that will meet at least 3 times per year. The commission may ask to have a colloquium with the candidates and may decide a)      to admit the candidate without any constraint b)      to admit the candidate prescribing some courses to be inserted in the study plan c)      not to admit the candidate. In particular the following is required for admission at either the ECMI techno- or econo-branch:

  • 180 ECTS of undergraduate study at university level, with a sufficient mathematical background
  • Prerequisite courses for at least 12 ECTS among the ones listed in tables 0C or 1C
  • Since the education may be given in English, good communication skills in English are required both orally and in writing (no official language certificate is required, but an interview, even by internet, can be required).

Applications and Admissions  

The first requirement is to apply  to the MSc in Mathematics (Laurea magistrale in Matematica) – Curriculum C – Industrial, at Universita’ degli Studi di Milano. Non Italian students may pre-apply or apply to the programme following the instructions and deadlines reported on this web page,  following the item “Second cycle application”. After having presented the (pre)application, all candidate ECMI students are requested to fill in the form which can be found here

 

Organization of the master

In order to get the diploma, the students have to gain at least 120 ECTS in total, corresponding to two years of studies. The courses are organized into 2 semesters,  lasting 13 weeks each. At the end of each course the student has to pass an exam, which may be written, oral or both.

 Double degrees  

In the framework of the ECMI Programme it is possible to get double degrees on the basis of specific agreeements of Universita’ degli Studi di Milano with other ECMI centers. In order to obtain double degrees the students have to spend a period abroad according to specific agreements with the partner(s). In order to obtain the degree from the Università degli studi di Milano the students have to pass at least one exam of the Master in Mathematics at the Università degli studi di Milano.

One double degree is  running between Università degli Studi di Milano  and the Technical University of Lappeenranta (Finland). Click below to see the details of the programme:

Double degree UniMI – LUT in Eco-mathematics (mathematics for ecology, environment, …)

Students interested in applying for the double degrees  should send an email with a curriculum to ecmi@unimi.it .

Summary of requirements for ECMI certificate

  • Participation in an ECMI Modelling Week
  • At least one semester spent at the other ECMI universities
  • A master thesis of 30 ECTS related to an industrial application
  • Further courses according to the specific rules of the two branches Technomathematics and Economathematics listed below

  Table 0C: prerequisites – Bachelor level (laurea triennale)

Sector Level

ECTS

Lang

Course name Links

Prerequisites

MAT05

BSc

6

I

Calculus 4 (Analisi 4) Calculus 1-3
MAT08

BSc

9

I

Numerical Calculus 2 (Calcolo Numerico 2) Numerical Calculus 1
MAT06

BSc

9

I

Probability and Statistics 2 (Calcolo delle Probabilità e Statistica Matematica 2) Probability and statistics 1

  Technomathematics: course requirements

At least 15 ects chosen among the following courses  (Tab 1C): Real analysis (Analisi reale)   9ects Elements of functional analysis (Elementi di analisi funzionale)    6ects Partial derivatives equations (Equazioni alle derivate parziali)   6ects At least 9 ects chosen among the following courses  (Tab 1C): Mthematical Statistics (Statistica Matematica)      9 ects Stochastic calculus and application (Calcolo stocastico ed applicazioni)     9ects At least 9 ects chosen among the following courses  (Tab 1C): Numerical methods for PDE’s I (Metodi numerici per EDP 1)   9 ects Numerical methods for PDE’s II (Metodi numerici per EDP 2)    9ects Optimization (Ottimizzazione)           6ects At least 6 ects  in the sectors MAT/06…09 chosen in the courses listed in table 2C At least 6 ects in the sectors MAT/xx chosen in the courses listed in tables 1C and 2C At least 18 ects chosen in the courses in the sectors different from MAT/xx listed in table 2C  including Numerical signal analysis (Elaborazione numerica dei segnali)    6ects or Statistical image and signal analysis (Elaborazione Statistica dei Segnali e delle Immagini) 6 ects 15 ects free choice, preferably  in tables 1C or 2C  

Economathematics: course requirements At least 15 ects chosen among the following courses  (Tab 1C): Real analysis (Analisi reale)   9ects Elements of functional analysis (Elementi di analisi funzionale)    6ects Partial derivatives equations (Equazioni alle derivate parziali)   6ects 18 ects for the following courses  (Tab 1C): Mathematical Statistics  (Statistica Matematica)      9 ects Stochastic calculus and applicastions (Calcolo stocastico ed applicazioni)     9ects At least 9 ects chosing among the following courses  (Tab 1C): Numerical methods for PDE’s  1(Metodi numerici per EDP 1)   9 ects Optimization (Ottimizzazione)           6 ects   (strongly adviced) At least 6 ects chosing among the following courses  (Tab 2C) Operation Research (Ricerca Operativa) 6 ects Complements of Operation research (Complementi di Ricerca Operativa) 6 ects At least 18 ects chosing among the corse with sector different from MAT/xx listed in table 2C, including Mathematical Finance 1 (Finanza matematica 1)   9 ects Mathematical Finance 2 (Finanza matematica 2)    6 ects 12 ects free choice, preferably in SECS/xx or MAT/xx sectors.  

Modelling Activities for both Techno- and Econo-math At least 12 ECTS should be obtained from the following modelling activities (Modelling week is compulsory for the ECMI certificate):

It is advised to follow these activities during the second year of studies.

Sector

ECTS

Lang

Course name

2+1

E

ECMI Summer School + seminar(if activated)

3

E

ECMI Modelling Week

6

I/E

Laboratory of Mathematical Modelling Modelling (Laboratorio di Modellistica Matematica)

6

I/E

Stage/ Industrial Internship

 

Industrial Curriculum C
TABLE 1C
Course name notes

ECTS

Sector
semester 1 Analisi reale

9

MAT/05
semester 1 Elementi di Analisi Funzionale

6

MAT/05
semester 1 Metodi numerici per equazioni alle derivate parziali 1

9

MAT/08
semester 1 Ottimizzazione

6

MAT/08
semester 1 Sistemi dinamici 1

6

MAT/07
semester 1 Sistemi hamiltoniani 1 (tot. cfu: 6+3) sistemi hamiltoniani mod/01

6

MAT/07
sistemi hamiltoniani mod/02 (additional-not compulsory)

3

MAT/07
semester 1 Statistica matematica

9

MAT/06
semester 2 Calcolo stocastico ed applicazioni

9

MAT/06
semester 2 Equazioni alle derivate parziali

6

MAT/05
semester 2 Metodi numerici per equazioni alle derivate parziali 2

9

MAT/08
TABLE 2C
semester 1 Argomenti avanzati di equazioni alle derivate parziali

6

MAT/05
semester 1 BIOINFORMATICA

6

INF/01
semester 1 Calcolo delle probabilità

9

MAT/06
semester 1 Calcolo Scientifico

6

MAT/08
semester 1 ELABORAZIONE NUMERICA DEI SEGNALI

6

INF/01
semester 1 Geometria 5

6

MAT/03
semester 1 Metodi matematici della meccanica quantistica

6

MAT/07
semester 1 Metodi numerici per equazioni alle derivate parziali 3

9

MAT/08
semester 1 Problemi inversi

6

MAT/05
semester 1 Programmazione 3

6

INF/01
semester 1 Sistemi dinamici 2

6

MAT/07
semester 1 Teoria dei giochi e delle decisioni

6

SECS-S/06
semester 2 Algebra Lineare Numerica

6

MAT/08
semester 2 Approssimazione Costruttiva

6

MAT/08
semester 2 Argomenti avanzati di analisi funzionale

6

MAT/05
semester 2 Biomatematica 2

6

MAT/06, MAT/08
semester 2 Calcolo delle variazioni

6

MAT/05
semester 2 Economia matematica 1

6

SECS-S/06
semester 2 Equazioni di evoluzione

6

MAT/05
semester 2 Finanza matematica 1

9

SECS-S/06
semester 2 Finanza matematica 2

6

SECS-S/06
semester 2 Soft Computing

12

INF/01
semester 2 Statistica dei processi aleatori

6

MAT/06
semester 2 Teoria della relatività 1

6

MAT/07

Please look also the official  web page of the courses in Mathematics: http://www.ccdmat.unimi.it/it/index.html and contact the representative of the Universita’ degli Studi di Milano in the ECMI Educational Committee to plan your study programme: Dr. Paola Causin