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

 

Universitŕ 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:

·         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:

·         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