# ECMI Master in Industrial Mathematics at University of Milan.

### For any further information/registration in the ECMI Programme, please contact Paola Causin (email: paola.causin at unimi.it)

**Background**

During the academic year 1986-87, 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, Fin, acting as coordinating centre for several cooperating Finnish universities) formed the European Consortium for Mathematics in Industry(ECMI)

They initiated two year postgraduate programmes, where industrial problem solving -to be intended aimed under the broader meaning of problems of social impact – using mathematics is a prominent aim. 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 curricula 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.

Find here an up-to-date list of the ECMI teaching centers

The Consortium issues a Certificate in Industrial Mathematics with two different branches: Technomatematics or Economathematics.

The Certificate, that is a “quality statement” recognised by all the universities of the Consortium, is awarded to students of the MSc (Laurea Magistrale)

who, beyond the standard requirements of the Master programme, fulfil the following requirements:

- Have participated to a Modelling Week, organized every year by ECMI, usually (but non exclusively) in summer. It is advised to participate to a modelling week during the second year of the Laurea Magistrale (MSc)
- Have spent at least one semester at (preferably) one of the universities of the ECMI Consortium or (upon approval) another university, to follow courses or to prepare the final thesis. 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 (Prof. P.Causin)

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 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 (C0, C1 and C2) 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 to the Master programme in Mathematics**

** **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 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 the ECMI programme:

- 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

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

Italian sector |
Level |
ECTS |
Lang |
Course name |
Links |
Prerequisites |

MAT05 | BSc | 6 | I | Calculus 4 (Analisi 4) | Calculus 1-3 | |

MAT08 | BSc | 9 | I | Numerical Analysis 2 (Calcolo Numerico 2) | Numerical Analysis 1 | |

MAT06 | BSc | 9 | I | Probability and Statistics 2 (Calcolo delle Probabilità e Statistica Matematica 2) | Probability and statistics 1 |

**Organization of the master programme**

In order to obtain the certificate, students have to acquire at least 120 ECTS in total, corresponding to two years study. The teaching modules are organized into 2 semesters, lasting 13 weeks each. At the end of each module the student has to pass an exam, which may be written, oral or both.

Refer here for the tables listing the courses currently offered

Students enrolling in the ECMI certificate programme in Milano must fulfill the requirement of Curriculum C and, in addition, choose courses according to one of the following branches (which impose further, but minimal, constraints on Curriculum C):

** **

Branch A: Technomathematics

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):

Mathematical 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

15 ects free choice, preferably in tables 1C or 2C

** **

**Branch B: Economathematics**

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 applications (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 advised)

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 11 ECTS should be obtained from the following modelling activities (Modelling week is compulsory for the ECMI certificate):

Sector |
ECTS |
Lang |
Course name |

3 | E | ECMI Modelling Week | |

3 | E | Seminar | |

6 | I/E | Laboratory of Mathematical Modelling Modelling (Laboratorio di Modellistica Matematica) | |

6 | I/E | Stage/ Industrial Internship |