ECMI
Master in Industrial Mathematics at University
of Milan.
Academic
Year 2010/11
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 |
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:
- Have participated to a Modelling Week, organized every year
by ECMI, usually in August (click
here for an example)
- It is advised to participate to a modelling week
during the second year of the Laurea Magistrale (MSc)
- Starting from 2010, the modelling week will be
preceded by a Summer School, one week long, which is not compulsory for
the diploma but is anyway strongly adviced.
- Have spent at least one semester at one of the universities of the
ECMI Consortium, to follow courses or to prepare the final thesis
(Erasmus/Socrates programmes)
- 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
- 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
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 (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
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 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
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
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.
Double degrees
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.
Two double degrees are running between
Università degli Studi di Milano and University Carlos III of Madrid (Spain)
and the Technical University of Lappeenranta (Finland). Click below to see the
details of the programmes:
Double
degree UniMI – LUT in Eco-mathematics (mathematics for ecology, environment,
...)
Double
degree UniMI- UC3M in Technomathematics
Students interested in
applying for the double degrees for the academic year 2011/12 should send an
email with a curriculum to
alessandra.micheletti@unimi.it
by September 4, 2011
Further requirements for ECMI certificate
·
At least one semester spent at the other ECMI universities
- Participation in an ECMI Modelling Week
- 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
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 11
ECTS should be obtained from the following modelling activities (Modelling week
is compulsory for the ECMI certificate):
|
Sector |
ECTS |
Lang |
Course name |
|
|
2 |
E |
ECMI Summer School |
|
|
3 |
E |
ECMI Modelling Week |
|
|
1 |
E |
Seminar |
|
|
6 |
I/E |
Laboratory of Mathematical Modelling Modelling (Laboratorio di Modellistica Matematica) |
|
|
6 |
I/E |
Stage/ Industrial Internship |
It is
advised to follow these activities during the second year of studies.
|
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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:
prof. Alessandra Micheletti, alessandra.micheletti@unimi.it