DOUBLE DEGREE PROGRAMME IN TECHNOMATHEMATICS
Degree programme at UNIMI  Corso di Laurea Magistrale in Matematica (Curriculum Industriale – double degree programme) 
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 UC3M  Master Universitario en Matemática Industrial 
Degree awarded  Master en Matemática Industrial /Master in Industrial Mathematics 
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  June (annually) 
Schematic study plan
Option 1  
Year  Institution  Studies  Remarks 
1  UNIMI  Compulsory and elective courses  60 ECTS 
2  UC3M  Courses + Master thesis (cosupervised)  30 + 30 ECTS 
Option 2  
Year  Institution  Studies  Remarks 
1  UC3M  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 UC3M indifferently. For each student, a detailed study plan must be defined by the academic coordinators, 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
Department of Mathematics
Laurea Magistrale in Matematica (Curriculum Industriale – double degree program)
2year programme, language of instruction: English
Entrance admission criteria to UNIMI programme: 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 field (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 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 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
– the thesis will be defended both at UNIMI and UC3M (videoconference possible)
UC3M ADMISSION CRITERIA & UC3M degree requirements:
Programme: Master Universitario en Matemática Industrial
2year programme (120 ECTS), language of instruction: English.
Entrance admission criteria to UC3M programme: Admission criteria to the Industrial Mathematics Master programme are:
– The student can access the Master programme after successfully completing a high quality Bachelor’s degree encompassing a minimum of 180 ECTS credits in Mathematics, Physics, Engineering or related field (including Mechanical Engineering, Statistics and Electrical 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 following subject areas will be an advantage:
 scientific computing
 mathematical and statistical physics
 numerical methods for PDE
 asymptotic analysis
 dynamical systems
 mathematical modeling
UC3M degree requirements
The minimum requirements for conferring the UC3M 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 UC3M (autumn and spring semester, total 60 credits) OR
– second year studies at UC3M including courses totalizing 30 ECTS credits and supervised thesis (spring term) totalizing 30 ECTS credits
– thesis:
– always supervised by an UC3M professor
– the thesis will be defended both at UNIMI and UC3M (videoconference possible)
Agreed curriculum
A. STUDENTS OF UNIMI AS HOME UNIVERSITY
FIRST YEAR AT UNIMI UNIVERSITY
Course code 
course name 
ECTS 
First semester (First autumn courses) 

MAT05  Real Analysis 
9 
MAT06  Mathematical statistics 
9 
MAT08  Numerical methods for PDE 1 
9 
INF01  Numerical signal analysis 
6 
Total 
33 

Second semester (First spring courses) 

MAT05  PDE 1 
6 
f  Laboratory of mathematical modelling 
6 
Total 
12 

and at least 15 ECTS from the following (with at least one course in the sectors from MAT06 to MAT09): 

MAT05  Harmonic analysis 
6 
MAT05  Advanced functional Analysis 
6 
MAT05  Calculus of variations 
6 
MAT05  Evolution equations 
6 
MAT06  Probability 
9 
MAT06  Stochastic calculus and Applications 
9 
MAT06  Statistics of random processes 
6 
MAT07  Theory of relativity 1 
6 
MAT08  Scientific Computing 
6 
MAT08  Constructive Approximation 
6 
MAT08  Numerical linear algebra 
6 
MAT08  Numerical Methods for PDE II 
9 
MAT08/MAT06  Biomathematics 2 
6 
MAT09  Introductory Operation Research 
6 
Total 
15 

Total minimum of 
60 
SECOND YEAR AT UC3M UNIVERSITY
Course code 
course name 
ECTS 
Third semester (Second autumn courses) 

At least 12 ECTS from the following: 

MAT07 (258 – 15645)  Dynamical Systems and Chaos 
6 
MAT07 (258 – 15644)  Boltzmann Equation and its Applications 
6 
MAT08 (258 – 15657)  Inverse Problems and imaging 
6 
Total 
12 

At least 12 ECTS from the following: 


FIS (258 – 15647)  Fluid Mechanics 
6 
FIS (258 – 15655)  Heat and Mass Transfer 
6 
FIS (258 – 15661)  Combustion 
6 
FIS (258 – 15660)  Hydrodynamic stability 
6 
FIS (258 – 15656)  Computational Fluid Dynamics 
6 
FIS (258 – 15648)  Solid Mechanics 
6 
FIS (258 – 15662)  Modelling in Solid Mechanics 
6 
ING (258 – 15665)  Electronic Transport in Micro and Nanostructures 
6 
Total 
12 

Total minimum of 24 ECTS  
Fourth semester (Second spring courses) 

At least 6 ECTS from the following: 

f  Modelling in Science and Industry II 
6 
f  ECMI Modelling Week 
3 
f  ECMI Summer School 
2 
f  Seminar/Report 
1 
f  Industrial internship 
6 
Total 
6 

Thesis supervised by both partners 
30 

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 UC3M and UniMI  
Total minimum of 
60 
B. STUDENTS OF UC3M AS HOME UNIVERSITY
FIRST YEAR AT UC3M UNIVERSITY
Course code 
course name 
ECTS 
First semester (First autumn courses) 

258 – 15644 
Models with Partial Differential Equations 
6 
258 – 15645 
Dynamical Systems and Chaos 
6 
258 – 15646 
Numerical methods for ODE 
6 
258 – 15647 
Fluid Mechanics 
6 
258 – 15648 
Solid Mechanics 
6 
Total 
30 

Second semester (First spring courses) 

258 – 15649 
Singular Perturbations (Asymptotic Analysis) 
6 
258 – 15650 
Numerical methods for Partial Differential Equations 
6 
258 – 15651 
Modelling in Science and Industry I 
6 
Total 
18 

At least 12 ECTS from the following: 

258 – 15652 
Nonlinear dynamics in extended Systems 
6 
258 – 15660 
Hydrodynamic stability 
6 
258 – 15654 
Stochastic numerical methods 
6 
258 – 15653 
Finite element methods 
6 
Total 
12 

Total minimum of 
60 
SECOND YEAR AT UNIMI UNIVERSITY
Course code 
course name 
ECTS 
Third semester (Second autumn courses) 

MAT05  Real Analysis 
9 
MAT06  Mathematical statistics 
9 
Total 
18 

At least 6 ECTS from the following: 

MAT06  Stochastic calculus and applications 
9 
MAT06  Probability 
9 
MAT08  (Numerical) Optimization 
6 
MAT09  Introductory Operation Research 
6 
Total minimum 
6 

Total minimum of 24 ECTS 

Fourth semester (Second spring courses) 

At least 6 ECTS from the following: 

f  Laboratory of mathematical modelling 
6 
f  ECMI Modelling Week 
3 
f  ECMI Summer School 
2 
f  Seminar/Report 
1 
Total 
6 

Thesis supervised by both partners 
30 

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 UC3M and UniMI  
Total minimum of 
60 