Double degree programme in ECOMATHEMATICS
between
Università 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 (cosupervised)  30 + 30 ECTS 
Option 2  
Year  Institution  Studies  Remarks 
1  LUT  Compulsory and elective courses  60 ECTS 
2  UNIMI  Courses + Master thesis (cosupervised)  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
Università 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)
2year 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 fulltime 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:
 Transforms, linear systems, basics in ODE 6 ECTS
 Basics in PDE 6 ECTS
 Numerical methods for differential equations 6 ECTS
 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)
Lappeeranta University of Technology (LUT)
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 Milan (application period in August) according to the above mentioned local entrance criteria at UNIMI admission, may apply to this double degree programme in September. An application must contain transcript of study record, BSc degree certificate, English language certificate and other necessary documents. Application must arrive to LUT by 15. September. Decision regarding admission at LUT Faculty of Technology will be available by 15. October.
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 1^{st} 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 – 35 
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/cosupervised by a Company. The thesis will be academically jointly supervised by teachers at LUT and UniMI  