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 (co-supervised) | 30 + 30 ECTS |
| Option 2 | |||
| Year | Institution | Studies | Remarks |
| 1 | UC3M | 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 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)
2-year 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 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:
- 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
2-year 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 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:
- 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/co-supervised 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/co-supervised by a Company. The thesis will be academically jointly supervised by teachers at UC3M and UniMI | ||
| Total minimum of |
60 |
|