Academic Year 2016/17





School of Industrial and Information Engineering



Degree Programme of:


Mathematical Engineering
Laurea Magistrale (Equivalent To Master Of Science)


Milano Campus

1. General Information

School School of Industrial and Information Engineering
Code Reference Law487
NameMathematical Engineering
Reference LawOrdinamento 270/04
Class of degreeLM-44 - Mathematical modelling for engineering
Degree level Laurea Magistrale (Equivalent To Master Of Science)
First year of activation 2009/2010
Official length of the programme 2
Years of the programme already activated 1,2
Official language(s) English
Campus Milano
Dean of the School Giovanni Gustavo Lozza
Coordinator of the Study programme Maurizio Verri
Website of the School http://www.ingindinf.polimi.it
Website of the Study programme
http://www.mate.polimi.it/im/


Student Office (Study programme) - Milano Leonardo
Reference office
Segreteria didattica del Dipartimento di Matematica
Address Via Bonardi 9, 20133 Milano
Phone 02 2399 4504/4625


Central Student Office - Milano Leonardo
Address VIA C. GOLGI, 42 (MI)

2. General presentation of the study programme

The study programme in Mathematical Engineering, started at Politecnico di Milano in 2001, aims at giving graduates the knowledge of appropriate mathematical methods and the ability to use them in an effective way in the context of technological and management applications. This corresponds to a professional profile having basic engineering skills joined to a deep expertise in modern mathematical, numerical and statistical methods for the modelling, the analysis and the solution of various engineering problems.

 

This profile is different from other engineering educational profiles, and at the same time very different from the ones acquired in study programmes in Mathematics (pure or applied) since it includes education in Physics, Chemistry, Economics, Computer Science and many other technological disciplines typical of Engineering, which turns out to give the graduates adequate ability in solving practical problems and the mental attitudue of an engineer.

At the international level, many institutions offer similar educational programmes. The professional profile of the Mathematical Engineer is gradually receiving great appreciation in the social, industrial and economical context.

At present, programmes in Mathematical Engineering at Politecnico di Milano span three levels:

  • Bachelor of Science (three years).
  • Master of Science (two years).
  • PhD in Mathematical Models and Methods in Engineering (three years).

3. Learning objectives

The aim of the Master programme in Mathematical Engineering is to prepare professionals able to analyze complex systems where a strong interdisciplinarity is required and it is necessary to master basic scientific knowledge as well as advanced methods and techniques. To this end, Mathematical Enigineers are trained in basic engineering disciplines but also acquire a broad knowledge of modern mathematical, numerical and statistical methods needed for the modelling, the analysis and the solution of practical design and management problems. This training is a heritage for their entire professional life.

The study programme is characterized by a continuous synergy between mathematics (especially its applied sides) and engineering. Mathematical courses include advanced general topics and more specific applied subjects, for instance in the area of statistics and computational science. An adequate knowledge of some specialized technological contexts gives the students the opportunity to apply their general methodological skills and will eventually allow them to work also in more traditional fields of engineering.

Besides a general scientific background, graduates in Mathematical Engineering master modern computer programming techniques; they have adequate knowledge to understand large classes of mathematical models (differential, discrete or other types); they are aware of mathematical models for the analysis of random phenomena or phenomena subject to high variability and incertitude; they know statistical modelling for exploration and analysis of data.

The Master of Science in Mathematical Engineering offers three different tracks:

  • Computational Science and Engineering
  • Applied Statistics
  • Quantitative Finance
Students can modify their Study Plans in a rather flexible way in order to acquire specific professional skills. During their students' career they are given the opportunity to spend a period in a foreign university, within one of the many international exchange agreeements.

 

The professional environments for a graduate in Mathematical Engineering are fairly various. Among them we mention: Research and Development divisions of big firms, study centers of industrial and consultancy companies, engineering firms and laboratories with computing and designing activities and specialized in the treatment of complex computational problems, banks, insurance and financial companies, institutions involved in scientific or technological research. The highly satisfactory job placement of graduates witnesses on the high consideration that this professional profile is gaining in the industrial, economical and social context.


4. Organization of the study programme and further studies

4.1 Structure of the study programme and Qualifications

Some terminology.

1) Study plan. It is the list of courses that each student chooses for her/his student career. Students have to pass the corresponding exams and carry out a final work in order to complete their studies and get the final degree. The choice of the Study Plan is subject to precise conditions, as described below. The study plan includes indication of year, semester and credits (see below) for every course. Other equivalent terminology is "student's curriculum", "exam record", "learning agreement".

2) Credit. It is a unit to measure the "size" of each course, consistent with the ECTS (European Credit Transfer System). For instance, a 10-credit course may consist in 60 hours of lectures and 40 hours of exercise classes, or a 5-credit course may consist in 26 hours of lectures, 20 hours of exercise classes, 12 hours of labs.

3) CCS. The Faculty of the Master study programme (italian acronym for "Consiglio di Corso di Studio"). The Faculty takes main decisions about students' careers. Members of the CCS may join Committees for specific purposes (e.g. admission of students, approvals of study plans etc.), as described below.


The Master’s degree in Mathematical Engineering has a two-year duration, corresponding to 120 credits.  The Faculty (CCS) expects each student to choose a Study Plan. To this purpose, the CCS proposes a number of Study Plan templates, called PSPA (from the italian acronym). Each PSPA corresponds to a particular specialization track, called Major. The following PSPAs are currently available:

  • Computational Science and Engineering
  • Applied Statistics
  • Quantitative Finance

They are presented at paragraph 7 below.

As an alternative to PSPA, students may choose their Study Plan within the so-called Applied Study Plans (PAA, from the italian acronym), with the following features:

  • Each PAA is part of one of the three Majors tracks, but it focuses on a selected applied field and gives a further specialization to students.
  • The PAAs are automatically approved (as well as the PSPAs).

The PAAs currently available are not listed below in this document: they can be found at the website http://www.mate.polimi.it/im.

Specific Study Plans, other than PSPAs and PAAs, may also be taken into consideration by the CCS. Students interested in submitting specific Study Plan proposals are invited to contact the Committee of Study Plans (email: piani-lm-ingegneria-matematica@polimi.it). Approval is not automatic. All proposals must be adequately motivated and basic rules of the study programme should be fulfilled.

4.2 Further Studies

The qualification grants access to "Dottorato di Ricerca" (Research Doctorate), "Corso di Specializzazione di secondo livello" (2nd level Specialization Course) and "Master Universitario di secondo livello" (2nd level University Master)


Upon completion of a Master Degree in Mathematical Engineering, graduates may apply for admission to Doctoral (PhD) courses, the 3rd university education level. We mention in particular the PhD course in Mathematical Models and Methods in Engineering, run by the Department of Mathematics of Politecnico di Milano. For further information consult: https://www.mate.polimi.it/dottorato/

Access to a second Master degree

  • Graduates from the Master programme in Mathematical Engineering can apply for admission to the second year of the Master degree in Mathematics at Università degli Studi di Milano-Bicocca. As a rule, they will be required to pass three exams (8 credits each), to be chosen in agreement with the Committee of Study Plans of that programme, plus a Master thesis (amounting to 40 credits).
  • With one further year of study, it is possible to obtain the Master degree in Nuclear Engineering at Politecnico di Milano. To this end it is assumed that a student has obtained a Master degree in Mathematical Engineering with PAA in Mathematical-Physical Modelling in Nuclear Applications (see paragraph 4.1) and a thesis in the area of Nuclear Engineering. In this case she/he needs to acquire an extra amount of 55 credits of courses during the third year of study. The thesis already defended to obtain the Master degree in Mathematical Engineering will be deemed equivalent to the required final work (amounting to 15 credits).
  • With one further year of study it is also possible to obtain the Master degree in Civil Engineering at Politecnico di Milano. To this purpose, one of the following alternatives is required:
    • A student has obtained a Master degree in Mathematical Engineering with a PAA in Structure Mechanics (see paragraph 4.1) and a thesis in the area of Structural Analysis. In this case, she/he needs to acquire an extra amount of 57 credits of courses during the third year of study. The thesis already defended to obtain the Master degree in Mathematical Engineering will be deemed equivalent to the required final work (amounting to 14 credits).
    • A student has obtained a Master degree in Mathematical Engineering  with a PAA in Hydraulics (see  paragraph 4.1) and a thesis in the area of Hydraulics/Fluid Mechanics. In this case, she/he needs to acquire an extra amount of 58 credits of courses during the third year of study. The thesis already defended to obtain the Master degree in Mathematical Engineering will be deemed equivalent to the required final work (amounting to 14 credits).

 


5. Professional opportunities and work market

5.1 Professional status of the degree

Master graduates in Mathematical Engineering have a sound engineering education joined with broad knowledge of modern methods of applied mathematics, numerical analysis and statistics, which are basic tools for modelling, analyzing, and solving concrete design and management problems.


According to the classification of Master degrees made by the Italian Ministry of University and Research under the educational system 270/04, the Master of Science in Mathematical Enginnering belongs to the Class LM 44 - Mathematical-Physical Modelling for Engineering.

This Class corresponds to a new professional profile and it is not currently included in the traditional Classes of Engineering. As a consequence, the qualification of Master of Science does not grant access to the State Examination for the profession of Senior Engineer or to the corresponding Professional Orders for Section A.

However, it should be noted that the School does not consider this to be a limiting factor both in terms of employment and for professional growth of Master graduates in Mathematical Engineering. Actually, in the area of Engineering, the Italian legislation for the Professional Orders establishes two Sections: A and B, corresponding to Senior and Junior, respectively. It is worth noting that the Bachelor of Science graduates in Mathematical Engineering can be included in Section B by taking the State Examination. In addition, no type of professional activity is explicitly indicated as exclusively belonging to Section A, while the differentiation between the two sections is generically based on the level of complexity. This is also consistent with the fact that the recent fees for professional services provided by members of the Order do not exhibit differences between the two sections.

5.2 Careers options and profiles

The Master graduate in Mathematical Engineering has an innovative professional profile, possessing basic engineering skills joined to a deep expertise in modern mathematical, numerical and statistical methods for modelling, analysing and solving practical problems in design and management. He can therefore find a placement in a large number of professional contexts in traditional or modern areas of Engineering, bringing new knowledge and professional skills.

Among the many possible professional environments we mention the following:

  • Research and Development divisions of big firms;
  • study centers  of industrial companies, consultancy and/or management societies; the mathematical engineers can act as data scientists, with skills for treatment and statistical interpretation of high dimensional data (big data, data mining) and for simulation of scenarios with great complexity;
  • engineering firms and laboratories with computing and designing activities, specialized in the treatment of complex computational problems, requiring a multidisciplinary knowledge as well as the use of advanced mathematical methods;
  • banks, insurance and financial companies, needing to develop financial products, manage investments (trading, asset allocation), or evaluating risks (risk management);
  • public or private institutions involved in scientific or technological research.

The job placement of Master graduates in Mathematical Engineering is extremely satisfactory, in spite of the difficult economical context. Leaving aside a fraction of graduates that continue their studies at a higher level, typically a PhD course in Italy or abroad, all of them find a job in a very short time. Detailed statistics can be found at the Career Service of Politecnico di Milano( http://www.careerservice.polimi.it/en-US/Home/Index/ ). We mention that the Career Service acts as a contact point between graduates or  students near to graduation and the job market, coordinates the offer of industrial stages, informs on job opportunities and organizes presentations for interested companies.

 


Surveys of University Assessment Commission
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4201

6. Enrolment

6.1 Access requirements

First cycle degree (level 6 EQF) or comparable qualification


Admission to the study programme is based on evaluation of the applicants’ careers. This process, in accordance with the existing rules, verifies possession of the needed curriculum requirements and adequacy of personal preparation. Admission to the programme is decided by an Evaluation Committee appointed by the CCS.

Admission may be subordinated to curriculum integrations and/or constraints in the choice of the Study Plan (see paragraph 6.2).Curriculum integrations are obligations for the student to pass specific exams before the admission to the study programme; the corresponding credits are not comprised in the total number of 120 credits and the corresponding grades do not affect the final Master grade. Constraints in the choice of the Study Plan may be imposed to some students in order to design a sensible student's career. Both integrations and constraints will be communicated before enrolment in order to provide a transparent information and help students to make a thoughtful choice of the Study Plan. 

For any question related to the knowledge of a foreign language, see paragraph 7.4.


6.1.1. Curriculum requirements


The student's career of each applicant will be examined individually. For those familiar with the italian university system, in this paragraph we review the criteria that will be applied in the evaluation process.

Bachelor Degree in Mathematical Engineering at the Politecnico di Milano

The curriculum requirements are automatically fulfilled for graduates with a Bachelor of Science with MFO-Propedeutic track. In case of admission to the Master programme, and in order to recover the credits devoted to stage activity, the Bachelor graduates with MAP-Applied track need a curriculum integration of 15 credits (see § 6.1.1.1). For Bachelor graduates with an autonomous Study Plan, the fulfillment of requirements may result in a possible curriculum integration. Credits of courses from the Master programme that have been acquired during the Bachelor study and exceed the minimum amount of 180, or credits that have been acquired through “single courses” of university level may be validated as well, up to a maximum amount of 32 credits.

Bachelor degree in Mathematical Engineering obtained at another University or Bachelor degree in other Engineering  Courses.

The curriculum requirements are considered fulfilled only if the candidate has acquired at least 36 credits for basic education courses and at least 45 credits in courses characterizing one of the following two degree classes: L-8 (degrees in Information Engineering) or L-9 (degrees in Industrial Engineering). Any credit from Master of Science courses acquired during the Bachelor degree and exceeding the minimum of 180, or earned through university-level “individual courses”, can be validated as well, up to a maximum of 32 credits.

All other categories of Bachelor degrees; foreign country Bachelor degree.

The curriculum requirements are considered fulfilled only if the candidate has acquired at least 36 credits for basic education courses and at least 45 credits in courses characterizing one of the following two degree classes: L-8 (degrees in Information Engineering) or L-9 (degrees in Industrial Engineering). The Evaluation Commitee may take into account possible correspondences among courses in programs different from the program in Mathematical Engineering.

 

6.1.1.1 Curricula integrations.

In the case of curriculum integration assigned to a student, during the period between the Bachelor degree acquisition and the enrolment into the MSc programme, the student can:

  • A1)  acquire credits by registering to single courses from the Master study programme and passing the corresponding exams; these anticipated credits  are considered  as part of the 120 credits necessary for the MSc degree.
  • A2)  acquire attendance status only to courses from the Master study program.
  • A3)  earn credits from courses assigned as curriculum integration by the Evaluation Commitee: these credits consitute the proper curriculum integration and must be added to the regular 120 credits needed for the Master programme.

 

The following limitations are to be taken into account:

  1. the total number of credits (by passing exams and/or by acquiring attendance status) that can be considered part of the 120 credits needed to acquire the Master programme (A1+A2) is limited to 32. Thus any additional credit earned exceeding 32 will not be taken into account.
  2. In any case the number of credits acquired through registration to “single courses” cannot be greater than 80, including  those in A3.

6.1.2 Adequacy of preparation level


For students possessing:

  • a) a Bachelor Degree in Mathematical Engineering at the Politecnico di Milano:
    Admission to the Master programme is automatic, without any other requirement, if at the time of enrolling into the third year of the Bachelor study the applicant has acquired at least 110 credits with an average score greater than equal to 25/30 and if the Bachelor degree has been obtained within 4 academic years from the initial enrolment (see note box).

  • b)  any of the other categories of Bachelor degrees:
    Admission is possible only if the applicant has achieved a final score greater than or equal to 85/110 in the final Bachelor exam. In this case the Evaluation Committee will examine the applicant’s curriculum and her/his attitude, possibly by an individual colloquium.

  • c) another Master of Science or equivalent degree:
    The Evaluation Committee will examine the complete applicant’s curriculum. Job experiences are not valid for acquisition of credits.
  • d) Foreign candidates
    Admission is not allowed if the pre-evalutation index given by the International Office of Politecnico is less than 75/100.

 

Note

Verification of attainment of the Bachelor of Science in no more than four academic years from enrolment considers all the academic years over which the academic curriculum is distributed.
Closure of the academic curriculum coincides with acquisition of all the 180 credits of the Bachelor of Science, including the final exam, language test and, where required, completion of curricular internships. Particular care must therefore be taken in presenting the Study Plan, since the presentation of a Study Plan designed to achieve missing attendance or additional attendance for Master of Science courses automatically generates an additional academic year.
Specifically, note that the April graduation session is considered the last one of the previous academic year for students who have not submitted a new Study Plan for the current academic year  (since not obliged to acquire missing attendance and/or not interested in incorporating additional attendance of Master of Science courses), whilst it is considered the first one of the current academic year (to acquire missing or additional attendance for the Master of Science).

6.2 Requested knowledge

To access the Master of Science in Mathematical Engineering, the candidate must possess specific curricular requirements, as detailed in the previous paragraph, or a knowledge  background consistent with the educational program of the  Bachelor of Science in Mathematical Engineering. Otherwise, curriculum integrations may be required for admission. Therefore, whenever necessary, an ad hoc examination of curricula will take place.


6.2.1 Constraints on the Study Plan


In some cases, admission to the Master of Science programme is subordinated to constraints in the choice of the Study Plan, that is, obligations or prohibitions concerning the Study Plan to be presented are imposed. The required constraints, if any, will be communicated together with the positive assessment of admission and before enrolment in order to provide students with the information needed to choose and propose their Study Plan. 


The educational offer at the Politecnico di Milano
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4975

6.3 Deadlines for admission and number of places available

As explained above, admission to the Master programme is possibile only upon positive assessment by the Evalutation Committee mentioned at paragraph 6.1, to which specific requests of information may be addressed (e-mail address: ammissioni-lm-ingegneria-matematica@polimi.it).

Positive evaluation of the application is only valid for the semester in which it has been submitted. The applications for admissions and career evaluations must be submitted within the required deadlines even by those applicants who are automatically admitted on the basis of the criteria explained in paragraph 6.1.2.

We recall that at Politecnico di Milano admission to the Master of Science programmes is possible in both the first and second semester.


How to become a student at Politecnico di Milano
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4307

6.4 Tutoring and students support

The present document contains many contact links for getting further information, see in particular paragraph 10 below. Other contacts may be found in the study programme website

http://www.mate.polimi.it/im/

Students will be informed on tutoring activities during their career by the School and the CCS. Politecnico di Milano, in the web site Polinternational reported below, provides a lot of general information.


Polinternational
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4276

7. Contents of the study Program

7.1 Programme requirements

120 credits are required to obtain the Master degree. They correspond to all the educational activities, including a final work.


In particular, the credits required for the various educational activities are classified as follows in the tables below:

  • A - basic topics
  • B - characteristic topics
  • C - additional topics
  • D - others (e.g. final work, professional thesis etc.)

7.2 Mode of study

This programme requires a full time attendance. Educational activities include lectures, exercise classes, and possibly computer and experimental laboratories.

7.3 Detailed learning objectives

The paragraphs that follow  describe the basic Study Plan templates (PSPA) for the academic year 2016/17.

As already mentioned in paragraph 4.1, the CCS offers a number of PSPAs, which characterize the specialization track (Major).

In each Major the 120 credits are divided into the following categories:

 

    Code

Category of course

  Credits

 

 

 

OB

Mandatory for all students

18

MA

Mandatory for a specific major

30

ING

Engineering courses

20

MTM

Mathematics courses

24

SC

Elective courses

16

 

Subtotal Credits    

108

 

Final work (Master thesis)

12

 

Total Credits    

120

 

 


1 Year courses - Track: MCS - Computational Science and Engineering


Code Educational activities SSD Course Title Language Sem CFU CFU Group
095958BMAT/05REAL AND FUNCTIONAL ANALYSIS18.08.0
095959BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.010.0
------Courses to be chosen from Group ING------10.0
095963BMAT/05ADVANCED PARTIAL DIFFERENTIAL EQUATIONS28.08.0
095964B,CMAT/08NUMERICAL ANALYSIS FOR PARTIAL DIFFERENTIAL EQUATIONS210.010.0
------Courses to be chosen from Group MOX------10.0

2 Year courses - Track: MCS - Computational Science and Engineering


Code Educational activities SSD Course Title Language Sem CFU CFU Group
097634B,CMAT/07
MAT/08
COMPUTATIONAL FLUID DYNAMICS [C.I.]110.010.0
095962BICAR/01FLUIDS LABS110.010.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group FREE------8.0
------Courses to be chosen from Group FREE------8.0
097690----FINAL WORK--112.012.0
097690----FINAL WORK--212.0

1 Year courses - Track: MMF - Quantitative Finance


Code Educational activities SSD Course Title Language Sem CFU CFU Group
095958BMAT/05REAL AND FUNCTIONAL ANALYSIS18.08.0
095959BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.010.0
095975BMAT/06STOCHASTIC DIFFERENTIAL EQUATIONS18.08.0
095981CSECS-S/06MATHEMATICAL FINANCE II210.010.0
095982CSECS-S/06FINANCIAL ENGINEERING210.010.0
096297BING-INF/04MODEL IDENTIFICATION AND DATA ANALYSIS110.010.0
089234BING-INF/04IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI210.0
------Courses to be chosen from Group FREE------8.0

2 Year courses - Track: MMF - Quantitative Finance


Code Educational activities SSD Course Title Language Sem CFU CFU Group
097658B,CMAT/08
SECS-S/06
COMPUTATIONAL FINANCE110.010.0
------Courses to be chosen from Group ING------10.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group FREE------8.0
097690----FINAL WORK--112.012.0
097690----FINAL WORK--212.0

1 Year courses - Track: MST - Applied Statistics


Code Educational activities SSD Course Title Language Sem CFU CFU Group
095958BMAT/05REAL AND FUNCTIONAL ANALYSIS18.08.0
095959BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.010.0
095966BMAT/06STOCHASTIC DYNAMICAL MODELS18.08.0
095967CSECS-S/01APPLIED STATISTICS210.010.0
096297BING-INF/04MODEL IDENTIFICATION AND DATA ANALYSIS110.010.0
089234BING-INF/04IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI210.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group FREE------8.0

2 Year courses - Track: MST - Applied Statistics


Code Educational activities SSD Course Title Language Sem CFU CFU Group
097659B,CMAT/06
SECS-S/01
BAYESIAN STATISTICS110.010.0
------Courses to be chosen from Group STAT------10.0
------Courses to be chosen from Group ING------10.0
------Courses to be chosen from Group MTM------8.0
------Courses to be chosen from Group FREE------8.0
097690----FINAL WORK--112.012.0
097690----FINAL WORK--212.0

Courses of the Group FREE


Code Educational activities SSD Course Title Language Sem CFU
095978 -- ING-INF/03 AUDIO AND VIDEO SIGNALS 1 8.0
097667 B,C MAT/08
SECS-S/06
COMPUTATIONAL FINANCE 1 8.0
097482 C ING-IND/16 DESIGN AND ANALYSIS OF EXPERIMENTS A 1 8.0
095973 B MAT/05 DISCRETE DYNAMICAL MODELS 1 8.0
095974 B MAT/05 GAME THEORY 1 8.0
098637 -- GEO/11 GEOPHYSICAL DATA PROCESSING 1 8.0
097660 B MAT/07 METHODS AND MODELS FOR STATISTICAL MECHANICS 1 8.0
097670 B FIS/03 PLASMA PHYSICS 1 8.0
098516 B,C MAT/08
SECS-S/01
NUMERICAL AND STATISTICAL METHODS IN GEOSCIENCES 1 10.0
095976 B,C MAT/08 ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING 2 8.0
095977 C SECS-S/01 APPLIED STATISTICS 2 8.0
097661 B MAT/07 BIOMATHEMATICAL MODELING 2 8.0
096659 B,C MAT/08 COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS 2 8.0
097676 B ING-INF/05 ECONOMICS AND COMPUTATION 2 6.0
098512 -- ICAR/09 ENGINEERING SEISMOLOGY 2 8.0
088933 B FIS/01 FISICA QUANTISTICA 2 8.0
098513 B ICAR/01 GROUNDWATER HYDRAULICS 2 8.0
095980 C SECS-S/06 MATHEMATICAL FINANCE II 2 8.0
098388 C SECS-S/06 MATHEMATICAL MODELS AND METHODS FOR FINANCIAL AND INSURANCE MARKETS 2 8.0
095972 B,C MAT/09 OPTIMIZATION 2 8.0

Courses of the Group ING


Code Educational activities SSD Course Title Language Sem CFU
085930 B ING-INF/01 ELETTRONICA 1 10.0
096297 B ING-INF/04 MODEL IDENTIFICATION AND DATA ANALYSIS 1 10.0
097575 B ING-IND/10 TERMODINAMICA E PROCESSI ENERGETICI 1 10.0
089195 B ING-INF/04 DINAMICA DEI SISTEMI COMPLESSI 1 10.0
095962 B ICAR/01 FLUIDS LABS 1 10.0
089234 B ING-INF/04 IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI 2 10.0

Courses of the Group MOX


Code Educational activities SSD Course Title Language Sem CFU
095965 B,C MAT/08 ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING 2 10.0
097725 B MAT/07 MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.] 2 10.0

Courses of the Group MTM


Code Educational activities SSD Course Title Language Sem CFU
095973 B MAT/05 DISCRETE DYNAMICAL MODELS 1 8.0
095974 B MAT/05 GAME THEORY 1 8.0
097660 B MAT/07 METHODS AND MODELS FOR STATISTICAL MECHANICS 1 8.0
095975 B MAT/06 STOCHASTIC DIFFERENTIAL EQUATIONS 1 8.0
095966 B MAT/06 STOCHASTIC DYNAMICAL MODELS 1 8.0
095963 B MAT/05 ADVANCED PARTIAL DIFFERENTIAL EQUATIONS 2 8.0
097661 B MAT/07 BIOMATHEMATICAL MODELING 2 8.0
093153 B MAT/03 GEOMETRIA DIFFERENZIALE(a) 2 8.0
095972 B,C MAT/09 OPTIMIZATION 2 8.0

(a) Course offered every two years, active for A.Y. 2016/17

Courses of the Group STAT


Code Educational activities SSD Course Title Language Sem CFU
093267 -- ING-INF/03 DIGITAL SIGNAL PROCESSING 1 10.0
089167 B ING-INF/05 DATA MINING AND TEXT MINING (UIC 583) 2 5.0
097683 B ING-INF/05 MACHINE LEARNING 2 5.0
091754 C ING-IND/19 COMPUTATIONAL METHODS FOR SAFETY AND RISK ANALYSIS A+B 2 10.0

7.3.1 Correspondences relating to courses available in previous years

7.4 Foreign language

All of the regulations regarding test for foreign language skill can be found in the “English knowledge Test"  web site http://www.polimi.it/en/students/guidelines-and-rules/


Language courses
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4338

7.5 Degree examination

The general rules for graduation exams are set forth in the Regulation for final graduation exams (in Italian) approved by the School of Industrial and Information Engineering:

http://www.ingindinf.polimi.it/fileadmin/files/pdf_scuola/regolamenti_lauree/RegolamentoProvaFinale.pdf

In relation to these norms and according to specific needs and peculiarities, the Faculty of the Master programme in Mathematical Engineering (CCS) has introduced more specific rules, approved by the School, that are contained in the document (in Italian):

http://www.ingindinf.polimi.it/didattica/esami-di-laurea-e-laurea-magistrale/ 

A synthesis of such regulations is as follows:

  1. The subject of the Master degree thesis (=dissertation) is chosen by the student upon agreement with a Professor of Politecnico who acts as Supervisor.
  2. If the student wishes to carry out the work on the dissertation at another University or external Institution, she/he must obtain prior approval from the President of the CCS, who will appoint an official internal Supervisor within the Politecnico. Any external supervisor will act as Co-Supervisor, will submit a written report on the thesis work and will be invited to take part in the thesis defense.
  3. The dissertation can not have more than 2 authors. In the event of defense at separate sessions, the thesis must be defended by the second candidate within the next two sessions successive to that of the first defense.
  4. Students starting to prepare their dissertation are required to inform the Secretary of the Graduation Board (e-mail: lauree-lm-ingegneria-matematica@polimi.it) reporting the subject, the name of the Supervisor and of the second author (if any).
  5. As a rule, dissertations do not require a Referee report. Upon request of the Supervisor, who recognizes that the thesis is of particular significance, the President of the CCS will appoint an external Referee. The Referee is required to send a written report to the Secretary of the Graduation Board.
  6. A copy of the dissertation must be submitted to the Mathematics Department Student Office at least one day prior to the graduation session.
  7. The maximum score attributed to the thesis defense is 4 points (5 points in exceptional cases) in the case of a dissertation without Referee report, while it is 7 points (8 points in exceptional cases) in the case of a dissertation with Referee report. Detailed rules to determine the final grade, possibily cum laude, will be made available to students in due time.

Information concerning general rules and regulations, session calendars, registration and consignment of theses is available at
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4369

8. Academic calendar

On the web site of the School of Industrial and Information Engineering (http://www.ingindinf.polimi.it) the Calendar of the current academic year can be downloaded. The general Academic Calendar of Politecnico is available at the following web site:
Academic calendar
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4400

9. Faculty

The names of the teachers of the courses of the Master programme, as well as detailed information on each course, are made available to students much time in advance with respect to the beginning of the teaching sessions.


10. Infrastructures and laboratories

Teaching takes place in Milan at the Leonardo Campus of the Politecnico, in classical or computer-equipped lecture rooms.

Students are invited to regularly consult information and notices on the school websites:
School of Industrial and Information Engineering http://www.ingindinf.polimi.it
Mathematical Engineering Programme http://www.mate.polimi.it/im/

 

 

A list of e-mail contacts are made available to students for obtaining specific information or for sending applications and requests:
Evaluation Committee for admissions ammissioni-lm-ingegneria-matematica@polimi.it
Committee of Study Plans  piani-lm-ingegneria-matematica@polimi.it
Erasmus program and international exchanges erasmus-dmat@polimi.it
Stages tirocini-ingegneria-matematica@polimi.it
Secretary of the Graduation Board lauree-lm-ingegneria-matematica@polimi.it

11. International context

The international context, relative to European countries with an economy and cultural level comparable to Italy, is characterized by a wider and more diversified education spectrum in Mathematics with respect to the situation in Italy. This is also due  to a better connection between academy on one side and industrial and financial world on the other one, mainly concerning transfer of scientific and technological innovation. As a consequence, at the Technology Centers or Schools abroad it is often possible to enter educational projects characterized by mathematically oriented professional profiles.

Examples are the EPFL at Lausanne, the ETH at Zürich, the École Centrale de Paris, the TU Delft, the KTH at Stockholm, the TU at Eindhoven, the TU at Kaiserslautern, where there are educational projects in industrial mathematics and/or in computational science. These programs aim to form a professional mathematician with knowledge in the key technology sectors, or to form an engineer profile  specialized on the mathematical modelling of applied problems and on the consequent analytical and numerical analysis.

In USA we mention the projects (at the level of Bachelor, Master or PhD) at the University of Texas at Austin, at the University of California in Santa Barbara, at the Institute for Mathematics and its Applications (I.M.A) at the University of Minnesota, sponsored by the Society for Industrial and Applied Mathematics.

Analogously, education projects in statistics and mathematics, oriented towards the modelling of stochastic phenomena and to the analysis of complex data finalized to engineering, physics and biology applications characterize curricula of several university in the Anglo-Saxon area. A prestigious example is provided by the program in Mathematical and Computational Science of the Statistics Department of Stanford University at Palo Alto, California; other analogous  programs are offered, for instance, by the Johns Hopkins University at Baltimora, by the University of Minnesota and by the Warwick University in U.K.

Finally, educational programs oriented to the modelling and to the quantitative aspects of Finance are present in curricula of several European engineering schools. We mention the Master of Science in Quantitative Finance at the ETH  and the University of Zürich, the programme Mathématiques Financières of the École Polytechnique and other Universities in Paris, the Master in Mathematical Finance and Acutarial Science at the TU in Münich, the Finanz und Versicherung Mathematik at the TU of Vienna; a program of Mathematical Statistics and Financial Mathematics is offered at the KTH of Stockholm; one of Mathematics and Finance at the Imperial College of London.

 

These educational projects show how the mathematical engineer is already a well established professional profile in Europe and in the world.


12. Internationalization

As a useful completion of studies by an international experience promoted by the Politecnico, the Master programme Faculty welcomes proposals by students who intend to spend a period in a foreign University, taking advantage of conditions and facilities of one of the various international agreements. An overview can be found at

http://www.polimi.it/en/students/experience-abroad/

while a detailed list of partner universities for exchange programmes may be found at

https://www4.ceda.polimi.it/manifesti/manifesti/controller/extra/ScambiInternazionaliPublic.do?evn_default=EVENTO&aa=2013&k_cf=10&k_corso_la=1119&ac_ins=1&k_indir=***&lang=EN&tipoFac=I&tipoCorso=ALL_TIPO_CORSO&semestre=2&codDescr=089383&c_accordo=-1&jaf_currentWFID=main

To access international exchange programs, and obtain the corresponding grant if available, students must usually apply to admission calls, generally opened annually. For the majority of exchange programmes applicants are evaluated and ranked. It is important that the activity abroad is clearly planned, so that it can easily validated as a part of the student's career. Foreign exchange proposals put forward by students are examined and approved by a Committee of the CCS: erasmus-dmat@polimi.it A detailed guide has been prepared by the School of Industrial and Information Engineering (in Italian):

http://www.ingindinf.polimi.it/uploads/media/Regole_mobilita_Scuola.pdf

We mention that a large number of possible activities abroad can be planned: attendance of short courses, regular courses and corresponding exams for one semester (typical of the ERASMUS program), preparation of the Master thesis etc.

A double degree programme is available with some Universities abroad. Students completing these programmes get the Master degree of Politecnico as well as the foreign degree title. Generally, double degrees require three years of study, to be spent partly in Italy and partly abroad. The Master of Science in Mathematical Engineering offers several double degree programmes, in particular one with EPFL (École Polytechnique Fédérale de Lausanne) and one with ENSIIE (École Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - Évry - Université Paris-Saclay), focused on computational science, and on statistical and financial science respectively: further information is available at the Master programme web site:

https://www.mate.polimi.it/im/


Information on exchange programmes, double degree projects and international internships, European research and international relations projects are available at
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4689

13. Quantitative data


The University Assessment Commission performs periodic analysis on the overall results and on the quality of teaching degree programs, by monitoring teaching activities and the integration of graduates into the job market. Reports and studies are available on the website of the Politecnico di Milano.
http://www.polimi.it/ateneo/organi/nucleo-di-valutazione/

14. Further information

We recall that Politecnico di Milano fixes a maximum duration for each study programme: see the web site

http://www.polimi.it/en/students/from-enrolment-to-degree/loss-of-student-status/

For any further information, please visit the website of the School of Industrial and Information Engineering
http://www.ingindinf.polimi.it

Updates to the information given above will be made available on this School web site as well as on the Master programme web site (http://www.mate.polimi.it/im).


15. Errata corrige