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:
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:
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:
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 get the diploma, the
students have to gain 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
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 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 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 |
Very important! Contact
the representative of the Universita’ degli Studi di Milano of ECMI
Educational Committee to plan your study programme:
prof. Paola Causin (paola.causin at unimi.it)