Double degree programme in ECO-MATHEMATICS
between
Universitŕ degli Study di Milano
and
Lappeenranta
University of Technology
|
Degree
programme at UNIMI |
Degree
programme of Mathematics/ Master’s programme in Mathematics |
|
Degree
awarded |
Laurea Magistrale in Matematica (120 ECTS) |
|
Language
of instruction |
English |
|
Entrance
admission criteria |
Laurea triennale in Matematica or related fields or
equivalent studies (≥180 ECTS) |
|
|
|
|
Degree
programme at LUT |
Master’s Degree Programme in Technomathematics and
Technical Physics |
|
Degree
awarded |
Master of Science in Engineering (120 ECTS) |
|
Language
of instruction |
English |
|
Entrance
admission criteria |
Bachelor of Science in Mathematics, Physics, Engineering
or related fields (≥180 ECTS) |
|
|
|
|
Number
of students |
Maximum of 5 |
|
Application
deadline |
February (annually) |
Schematic
study plan
|
Option
1 |
|
|
|
|
Year |
Institution |
Studies |
Remarks |
|
1 |
UNIMI |
Compulsory and elective courses |
60 ECTS |
|
2 |
LUT |
Courses + Master thesis (co-supervised) |
30 + 30 ECTS |
|
Option 2 |
|
|
|
|
Year |
Institution |
Studies |
Remarks |
|
1 |
LUT |
Compulsory and elective courses |
60 ECTS |
|
2 |
UNIMI |
Courses + Master thesis (co-supervised) |
30 +30 ECTS |
|
The schematic study plan is applicable to students
originated from UNIMI and LUT indifferently. For each student, a detailed
study plan must be defined by the academic coordinators and registered in a
Learning Agreement avoiding redundant courses. The annual modifications
implemented in the curriculum will be notified in the students’ learning
agreement. |
|||
Selection
of students to double degree programme:
1)
students must meet admission criteria of the Master’s
programme of both institutions
2)
students are selected to double degree option based on
their academic results, prerequisite requirements, motivation and language
skills
Double degree 120 ECTS
Universitŕ degli Studi di Milano (UNIMI)
Faculty of
Mathematical, Physical and Natural Sciences
Degree Course
Council in Mathematical Sciences (Department of Mathematics)
Laurea
Magistrale in Matematica (Curriculum Industriale – double degree programme
Master in Mathematics – Industrial Curriculum)
2-year
programme, language of instruction: English
UNIMI programme entrance admission criteria: Admission
criterion to the Master’s programme in Mathematics (Industrial curriculum) is a high quality Bachelor's degree
encompassing a minimum of 180 ECTS credits in Mathematics or related fields
(including Computer Science, Statistics, Physics and Mathematical Engineering)
or equivalent studies i.e., it must be a degree of at least three years of
full-time studies.
Required
background for the applicants includes
·
strong
background in mathematics (in particular linear algebra, calculus)
·
basic
numerical analysis
·
basic
probability theory and statistics
·
basic
knowledge in Physics and/or Mechanics
·
basic
programming skills
and at least one half of the following topics:
·
Minor
field of study related to mathematics 6 ECTS
In addition
a basic knowledge of the following subject areas will be an advantage:
·
Scientific
computing
·
Mathematical
Statistics
·
Mathematical
and statistical physics
·
Numerical
methods for PDE
·
Mathematical
modeling
·
Dynamical
systems
UNIMI degree requirements
-
the minimum requirements for conferring the UNIMI
degree are the following:
-
120
ECTS credits including supervised 30 ECTS credits Master thesis (= 90 ECTS credits +
30 ECTS credits thesis)
-
in practice at least the following options are
possible:
-
first year studies at UNIMI (autumn and spring
semester, total 60 credits) OR
-
second year studies at UNIMI including courses
totalizing 30 ECTS credits and supervised thesis (spring term) totalizing 30
ECTS credits
-
thesis:
-
always supervised by an UNIMI professor, with an assisting supervisor from LUT
-
the thesis will be defended at UNIMI and
submitted to Faculty reviewing process
at LUT (videoconference possible)
Faculty of Technology
Department of Mathematics and Physics
Programme: Master’s Degree programme in
Technomathematics
2 year
programme (120 ECTS), language of instruction: English.
LUT
programme Entrance admission criteria: Admission criteria to the Industrial Mathematics Master
programme are:
Students who
apply to the Master’s Degree programme and major in Technomathematics are
assumed to have a B.Sc. (180 ECTS) in applied mathematics, computer science,
information technology or engineering with sufficient background in mathematics.
The student
should master calculus, also in functions of several variables. He/she is
assumed to know basics of matrices, linear algebra, differential equations and
optimization, numerical algorithms, statistics and probability. Knowledge of discrete models, fuzzy models
and methods is of advantage. The students should have basic knowledge in
computing including data structures and some programming skills. Furthermore,
the students must have familiarity with PC work stations and basic data manipulation
tools.
It is assumed
that student has knowledge in physics covering basic phenomena in mechanics,
electricity, thermal and wave phenomena. The education is given in English,
thus good communication skills in English are necessary both orally and in
writing.
LUT degree requirements
The
minimum requirements for conferring the LUT degree are the following:
-
120
ECTS credits including supervised 30 ECTS credits Master thesis (= 90 ECTS credits +
30 ECTS credits thesis)
-
in practice at least following options are possible:
-
first year studies at LUT (autumn and spring semester,
total 60 credits) OR
-
second year studies at LUT including courses
totalizing 30 ECTS credits and supervised thesis (spring term) totalizing 30
ECTS credits
-
thesis:
-
always supervised by an LUT professor or docent,
second supervisor from UNIMI
-
the thesis will be defended at UNIMI and and submitted for faculty review process at
LUT (videoconference possible)
Students
selection to double degree program requires that student meets the application
procedures of both universities.
Student selection to double degree programme
In the student selection to the double degree programme specific criteria
will be applied in addition to the general admission requirements. Students must meet admission
criteria of the Master’s programme of both institutions. Students
are selected to double degree option based on their academic results, prerequisite
requirements, motivation and language skills. Knowledge on a field of
application, suitable minor studies, projects or work experience, specific
computer skills, motivation etc. may be counted as credit.
Application procedure when UNIMI is the home
university
A
student who has been accepted to MS programme in
Application procedure when LUT is the home university
A
student who has been accepted to MS programme at LUT (application period in
January http://www.universityadmissions.fi/)
according to the above mentioned local entrance criteria at LUT admission, may
apply to this double degree programme. An application must contain transcript
of study record, BSc degree certificate, English language certificate and other
necessary documents. Application must arrive to UNIMI by 1st of August. Decision regarding admission at UNIMI will be
available by 30 of September.
Agreed curriculum
FIRST
YEAR
|
First year studies |
|
|
UNIMI as home university |
LUT as home university |
|
First autumn courses for students studying at
UNIMI as home university |
First autumn courses for students studying at
LUT as home university |
|
Course code - course name - ECTS |
Course code - Course name - ECTS |
|
|
|
|
MAT05 Real Analysis - 9 |
Introduction to M.Sc.
Studies – 1 |
|
MAT06 Mathematical statistics - 9 |
Academic Writing in
English – 4 |
|
MAT08 Numerical methods
for PDE 1 - 9 |
Advanced Mathematical
Methods – 6 |
|
MAT07 Dynamical Systems
1 or 2 - 6 |
Basic Course on Environmental Management and Economics – 5 |
|
|
Solid Waste Management
Related to Energy Production – 4 |
|
|
Linear Algebra and
Normed Spaces – 3 |
|
|
|
|
|
At least 9 ECTS from
the following: |
|
|
Statistical Analysis in
Modelling – 5 |
|
|
Statistics II – 3 |
|
|
Simulation – 4 |
|
|
|
|
Total:
minimum of 33 ECTS |
Total:
minimum of 32 ECTS |
|
|
|
|
First spring courses for students studying at
UNIMI as home university |
First spring courses for students studying at
LUT as home university |
|
Course code - course name - ECTS |
Course code - Course name - ECTS |
|
MAT05 PDE’s 1 - 6 |
Emission Trading – 3 |
|
f - Laboratory of mathematical
modelling- 6 |
Air Pollution Control – 3 |
|
|
Waste Heat Recovery Techniques - 6 |
|
At least 6 ECTS from the following |
Differential Equations – 5 |
|
Mathematical finance 1
– 9 |
Integral Transforms - 3 |
|
Mathematical finance 2
– 6 |
Numerical Analysis II – 3 |
|
General and animal physiology – 6/9 |
|
|
At least 9 ECTS from the following: |
At least 5 ECTS from the following |
|
MAT05 Armonic analysis –
6 |
Stochastic theory and models – 3-5 |
|
MAT05 Advanced functional Analysis -
6 |
Design of Experiments – 4 |
|
MAT05 Calculus of variations – 6 |
Fuzzy Data Analysis – 6 |
|
MAT05 Evolution equations - 6 |
Fuzzy Engineering – 6 |
|
|
Advanced Mathematical
Methods - 6 |
|
MAT06 Stochastic calculus and Applications – 9 |
Nonlinear Optimization
– 4 |
|
MAT06 Statistics of random processes – 6 |
Discrete optimization – 5 |
|
MAT08 Scientific Computing - 6 |
|
|
MAT08 Constructive Approximation - 6 |
Project Work in Applied Mathematics - 10 |
|
MAT08 Numerical linear algebra - 6 |
Introduction to Inverse Problems - 6 |
|
MAT08 Numerical Methods for PDE II – 9 |
|
|
MAT08/MAT06
Biomathematics 2 – 6 |
|
|
MAT09 Introductory Operation Research - 6 |
|
|
|
|
|
|
|
|
Total
minimum of 60 ECTS |
Total
minimum of 60 ECTS |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
SECOND
YEAR
|
Second year studies |
|
|
LUT |
UNIMI |
|
Second autumn courses for students studying
at LUT coming from UNIMI |
Second autumn courses for students studying
at UNIMI coming from LUT |
|
Course
name, ECTS |
Course
name, ECTS |
|
Basic Course on Environmental Management and Economics – 5 |
MAT08 (Numerical) Optimization - 6 |
|
Solid Waste Management
Related to Energy Production - 4 |
|
|
|
At least 9 ECTS from the following: |
|
At least 3 ECTS from
the following: |
MAT07 Biomathematics 1 – 6 |
|
Statistical Analysis in
Modelling – 5 |
MAT08 Mathematical statistics - 9 |
|
Evolutionary
Computation – 5 |
BIO Genetics – 6/9 |
|
Statistics II – 3 |
MAT06 Probability - 9 |
|
Fuzzy Sets and Fuzzy
logic – 6 |
MAT08 Numerical methods for PDE’s 1 – 9 |
|
Advanced Mathematical
Methods - 6 |
|
|
Complex Analysis - 3 |
|
|
Applied Functional
Analysis – 5 |
|
|
Project Work in Applied
Mathematics - 10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Total
minimum of 12 ECTS |
Total
minimum of 15 ECTS |
|
Second
spring |
Second
spring |
|
Emission Trading – 3 |
At least 9
ECTS from the following: |
|
Air Pollution Control – 3 |
Mathematical Finance 1 - 9 |
|
Waste Heat Recovery Techniques - 6 |
MAT06 Stochastic calculus and applications – 9 |
|
|
MAT06 Statistics of random processes – 6 |
|
|
Biomathematics 2 - 6 |
|
|
General and animal physiology – 6/9 |
|
|
MAT09 Introductory Operation Research - 6 |
|
At least 6
ECTS from the following: |
At least 6
ECTS from the following: |
|
Case Study Seminar – 6 |
f - Laboratory of mathematical modelling-
6 |
|
f ECMI Modelling Week - 3 |
f ECMI Modelling Week - 3 |
|
f ECMI Summer School - 2 |
f ECMI Summer School - 2 |
|
f Seminar/Report – 1 |
f Seminar/Report – 1 |
|
|
|
|
|
|
|
Total
minimum of 30 ECTS |
Total
minimum of 30 ECTS |
|
|
|
|
|
|
|
|
|
|
Thesis 30 ECTS supervised by both partners |
|
|
The student will develop his/her Master Thesis full
time for a value of 30 ECTS, to be developed in ENGLISH, together with/ for/co-supervised
by a Company. The thesis will be
academically jointly supervised by teachers at LUT and UniMI |
|
|
|
|