Academic Year 2018/19





School of Industrial and Information Engineering



Degree Programme of:


Mathematical Engineering
Laurea Magistrale (Equivalent To Master Of Science)


Milano Leonardo 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 Capone Antonio
Coordinator of the Study programme Anna Maria Paganoni
Website of the School http://www.ingindinf.polimi.it
Website of the Study programme
http://www.mate.polimi.it/im/


Central Student Office - Milano
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 receives 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 Master of Science (LM) in Mathematical Engineering is structured according to the following three education tracks (shortly denoted as PSPA):

  • Computational Science and Engineering
  • Applied Statistics
  • Quantitative Finance

and allows the student to acquire a specific degree in one of them. Students are allowed to modify their plan of studies in a rather flexible manner according to theachievement of specific professional skills. Duringthe Master of Science students may also improve their education level by a study abroad experience within one of the numerous existing international partnerships and agreements.


The Master of Science in Mathematical Engineering aims at educating professionals able to address the analysis of complex systems that require a deep modeling scrutiny in conjunction with the need of merging the use of advanced mathematical knowledge with the usual techniques and methodologies of engineering. To this purpose, the LM proposes an education programme pursuing two complementary objectives:

- to develop (through a common background of knowledge and methodologies) a unified figure characterizing the Mathematical Engineer;

- to form and promote professionals with specific competences, able to satisfy the most diverse requests from companies and institutions in which the Mathematical Engineers are going to operate, by performing highly innovative tasks.

The professional contexts for a graduate in Mathematical Engineering are quite diverse: research and development divisions in big companies, research centers in enterprises as well as service companies and industrial consulting, engineering companies and scientific computing laboratories for the treatment of highly complex design problems, banking, financial or insurance institutions, as well as institutions devoted to scientific and technological research. Also, the graduate in Mathematical Engineering is opened to the possibility of taking a doctoral degree in Mathematics as well as in other technical and scientific disciplines. The excellent level of job placement of graduates in Mathematical Engineering is a witness of the very high consideration that such a professional figure is nowadays receiving from work and research environment.


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 designed for students admitted without constraints in curricular choices to the Master of Science in Mathematical Engineering;
  • if the above-mentioned case occurs, 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.


Autonomous Study Plans, other than PSPAs and PAAs, may also be taken into consideration by the CCS, but only in exceptional cases (e.g., Erasmus programmes). Students interested in submitting specific Study Plan proposals have 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.

As for the "free movers" (students aiming to attend a course offered by other universities outside the official exchange programmes of Politecnico di Milano), in the case where the offering university requires the Faculty of the Study Programme (CCS) to produce a "nomination", such a document will be delivered only if the requiring university belongs to the top international ranking (within the first 150 in the QS ranking). Upon request of the student, the course in object, if approved, will be considered as "additional exam" and qualified as "Generic Credit" in the pertinent Academic Fields and Disciplines List (SSD, from the Italian acronym). The Faculty will not consider any request of validation of the exam within the official Study Plan of the student.


Internal Double Master of Science Degree

The Internal Double Master of Science degree programmes are joint programmes developed in cooperation with another Study Course with the aim of integrating the mathematical engineer competence profile with different disciplines, in order to answer to the needs of some specific sectors through a new professional profile. In the 2018-2019 academic year, the following Internal Double Master of Science degree programmes will be run:


International Double Master of Science Degree

The International Double Master of Science degree programmes are joint programmes developed in cooperation with foreign Universities. The student will get both the Master of Science Degree in Mathematical Engineering at the Politecnico di Milano and the foreign Degree. For more information see Paragraph 12.

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.
  • 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).

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 is not 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.

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. 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

5.3 Qualification profile

Mathematical Engineer

Function in a work environment:
The Graduate in Mathematical Engineering is a professional able to address the treatment of complex systems involving competences from different disciplines, and is able to combine in a harmonic manner a solid knowledge of basic science with advanced methodologies and techniques. The Graduate in Mathematical Engineering has an original and flexible personality, with a significant spectrum of basic knowledge and the typical forma mentis of an engineer, combined with a wide knowledge of modern mathematical, numerical and statistical methodologies to modeling, analysis and solution of complex problems in design, control and management.

The Master of Science Programme in Mathematical Engineering (law system 270/04) belongs to Class LM-44 (mathematica-physical modeling in Engineering). This Class corresponds to a new professional figure within the reform of University which, because of its recent formulation, has not been yet included in the Master Degree Classes of Engineering (those preexisting to the “3+2 reform”). The Master of Science degree, as a consequence, does not presently provide automatic access to State Exam of Professional Registers for Section A. This does not constitute a limitation to job placement or career progression of graduates in Mathematical Engineering. As a matter of fact, according to the present law, for the above cited sectors there is no explicit indication of any professional activity accessible to subjects belonging to Section B. This is consistent with the fact that recent tariffs published in the professional register do not show any significant difference between the two Sections.

Competences associated with function:
Specific competences to: 
- address problems arising in diverse scientific contexts, involving artificial and/or man-crafted systems (typical of Technology or Finance) as well as natural systems (for example biological systems in medical sciences) n which the human presence is absent or negligible;
- utilize differential or discrete modeling and other advanced mathematical procedures to obtain the solution of numerical problems;
- perform advanced design by leveraging on the use of advanced mathematical approaches;
- provide a statistical interpretation and the simulation of possible scenarios for the treatment of data in situations of large complexity (management and optimization for call centers, data mining, information retrieval) orthe management of financial products and risk management.

Job opportunities:

Flexibility and training to solving problems of diverse nature, developing models that are able to interface with the a priori analysis of data (physical, geometrical or statistical) as well as the a posteriori analysis for the interpretation of results, promotes and favors the access of the graduate in Mathematical Engineering to companies or industries that do not require specific sectorial competences. On the other hand, there exist valid job opportunities in markedly specialized contexts such as:
- engineering companies specialized in the treatment of complex computational problems;
- production companies of industrial goods requiring a level of knowledge based on the use of advanced mathematical procedures;
-
companies for the design and/or management of complex problems in Civil Engineering;
- service companies, banks, insurance, financial and consulting companies;
- engineering enterprises or companies devoted to the development of computational software; 
- public or private institutions and research laboratories.


6. Enrolment

6.1 Access requirements

Laurea (First degree), or foreign comparable degree


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 Paragraph 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 Italian Bachelor degrees

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.


Foreign country Bachelor degree.

The curriculum requirements are considered fulfilled only if the candidate has a BSc with at least 45 ECTS credits (= 25% of the overall credits) in different areas of Engineering (Informatics, Economics & Business Organization, Theory of electrical circuits, Automation, Electronics, Applied Physics, Civil Engineering), as well as with at least 60 ECTS credits (= 33% of the overall credits) in different areas of Mathematics (Mathematical Analysis, Linear Algebra, Geometry, Probability, Statistics, Numerical Analysis, Optimization). The Evaluation Commitee may take into account possible correspondences among courses in programs different from the program in Mathematical Engineering. For more information see https://www.mate.polimi.it/im/index.php?settore=magistrale&id_link=97&#an.


Master degree

The Evaluation Committee will examine the complete applicant’s curriculum. Job experiences are not valid for acquisition of credits.

 

 

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 Bachelor Degree in Engineering at the Politecnico di Milano
    They will not be admitted to attend to the MSc in Mathematical Engineering if they earned their BSc degree with a score M lower than the admission threshold S. The score M is the average of the exams’ grades, weighted by the credits of each exam. The threshold is: S=21.50 for the AY 2018/19, S=22.00 from the AY 2019/20 onwards.

  • a Bachelor Degree in Architecture or Design at the Politecnico di Milano
    They will not be admitted to attend to the MSc in Mathematical Engineering if they earned their BSc degree with a score M lower than the admission threshold S. The score M is the average of the exams’ grades, weighted by the credits of each exam. The threshold is S=23.50.

  • any of the other categories of Italian Bachelor degrees
    Admission is possible only if the applicant has achieved a final score greater than or equal to 90/110 in the final Bachelor exam. In this case the Evaluation Committee will examine the applicant’s curriculum and her/his attitude.

  • any foreign Bachelor degree
    The Evaluation Committee will examine the complete applicant’s curriculum.

  • 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.


The number of years spent to get the Bachelor Degree plays no role in the admission procedure.

 

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

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.

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, 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 2018/19.

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:

 

Category of course

  Credits

 

 

Mandatory for all students

18

Mandatory for a specific major

30

Engineering courses

20

Mathematics courses

24

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
052496BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.0
[1.0Innovative teaching]
10.0
------Courses to be chosen from Group ING------10.0
095963BMAT/05ADVANCED PARTIAL DIFFERENTIAL EQUATIONS28.08.0
052497B,CMAT/08NUMERICAL ANALYSIS FOR PARTIAL DIFFERENTIAL EQUATIONS210.0
[2.0Innovative teaching]
10.0
------Courses to be chosen from Group MOX------10.0
------Courses to be chosen from Group MTM------8.0

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 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
095975BMAT/06STOCHASTIC DIFFERENTIAL EQUATIONS18.08.0
095981CSECS-S/06MATHEMATICAL FINANCE II110.010.0
096297BING-INF/04MODEL IDENTIFICATION AND DATA ANALYSIS210.010.0
052500CSECS-S/06FINANCIAL ENGINEERING210.0
[2.0Innovative teaching]
10.0
------Courses to be chosen from Group FREE------8.0
------Courses to be chosen from Group MTM------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
052496BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.0
[1.0Innovative teaching]
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

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
052496BING-INF/05ALGORITHMS AND PARALLEL COMPUTING110.0
[1.0Innovative teaching]
10.0
095966BMAT/06STOCHASTIC DYNAMICAL MODELS18.08.0
096297BING-INF/04MODEL IDENTIFICATION AND DATA ANALYSIS210.010.0
052498CSECS-S/01APPLIED STATISTICS210.0
[3.0Innovative teaching]
10.0
------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
052499B,CMAT/06
SECS-S/01
BAYESIAN STATISTICS110.0
[2.0Innovative teaching]
10.0
------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
052502 B,C MAT/06
SECS-S/01
BAYESIAN STATISTICS 1 8.0
[2.0Innovative teaching]
097667 B,C MAT/08
SECS-S/06
COMPUTATIONAL FINANCE 1 8.0
052030 B,C MAT/07
MAT/08
COMPUTATIONAL FLUID DYNAMICS [C.I.] 1 8.0
051676 C ICAR/07
ICAR/08
COMPUTATIONAL MECHANICS FOR GEOMATERIALS 1 8.0
097482 C ING-IND/16 DESIGN AND ANALYSIS OF EXPERIMENTS A 1 8.0
093153 B MAT/03 DIFFERENTIAL GEOMETRY 1 8.0
095973 B MAT/05 DISCRETE DYNAMICAL MODELS 1 8.0
098512 -- ICAR/09 ENGINEERING SEISMOLOGY 1 8.0
052503 B MAT/05 GAME THEORY 1 8.0
[1.0Innovative teaching]
098637 -- GEO/11 GEOPHYSICAL DATA PROCESSING 1 8.0
095980 C SECS-S/06 MATHEMATICAL FINANCE II 1 8.0
098516 B,C MAT/08
SECS-S/01
NUMERICAL AND STATISTICAL METHODS IN GEOSCIENCES 1 10.0
097670 B FIS/03 PLASMA PHYSICS 1 8.0
052504 B,C MAT/08 ADVANCED NUMERICAL METHODS FOR COUPLED PROBLEMS WITH APPLICATION TO LIVING SYSTEMS 2 8.0
095976 B,C MAT/08 ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING 2 8.0
052742 C SECS-S/01 APPLIED STATISTICS 2 8.0
[3.0Innovative teaching]
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
052397 -- ING-IND/35 ENERGY AND CLIMATE CHANGE MODELING AND SCENARIOS 2 8.0
052505 C SECS-S/06 FINANCIAL ENGINEERING 2 8.0
098513 B ICAR/01 GROUNDWATER HYDRAULICS 2 8.0
052506 C SECS-S/06 INSURANCE & ECONOMETRICS 2 10.0
095972 B,C MAT/09 OPTIMIZATION 2 8.0
088933 B FIS/01 QUANTUM PHYSICS 2 8.0

Courses of the Group ING


Code Educational activities SSD Course Title Language Sem CFU
089195 B ING-INF/04 COMPLEX SYSTEMS DYNAMICS 1 10.0
085930 B ING-INF/01 ELECTRONICS 1 10.0
095962 B ICAR/01 FLUIDS LABS 1 10.0
097575 B ING-IND/10 THERMODYNAMICS AND ENERGETIC PROCESSES 1 10.0
096297 B ING-INF/04 MODEL IDENTIFICATION AND DATA ANALYSIS 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
093153 B MAT/03 DIFFERENTIAL GEOMETRY 1 8.0
095973 B MAT/05 DISCRETE DYNAMICAL MODELS 1 8.0
052503 B MAT/05 GAME THEORY 1 8.0
[1.0Innovative teaching]
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
096659 B,C MAT/08 COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS 2 8.0
095972 B,C MAT/09 OPTIMIZATION 2 8.0

Courses of the Group STAT


Code Educational activities SSD Course Title Language Sem CFU
093267 -- ING-INF/03 DIGITAL SIGNAL PROCESSING 1 10.0
091754 C ING-IND/19 COMPUTATIONAL METHODS FOR SAFETY AND RISK ANALYSIS A+B 2 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

7.3.1 Innovative education


Within the framework of the Innovative Education Programme promoted by the University, starting from the Academic Year 2018/19 a number of initiatives of innovative education will be activated for the courses listed in the Table below:

 

Code / Course title

Characteristics of the course

PSPA

Innovative CFU

052496 - Algorithms and Parallel Computing

Obligatory

Year I / II

10 CFU

MCS – MMF – MST

 

1 CFU

052498 - Applied Statistics

Obligatory

Year I

10 CFU

MST

 

3 CFU

052499 -Bayesian Statistics

Obligatory

Year II

10 CFU

MST

 

2 CFU

052500 -Financial Engineering

Obligatory

Year I

10 CFU

MMF

 

2 CFU

052497 -Numerical Analysis for PDE

Obligatory

Year I

10 CFU

MSC

 

2 CFU

052503 – Game Theory

Optional

Year I / II

8 CFU

MCS – MMF – MST

 

1 CFU

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/EsamiLaureaIntegratoAteneo3I.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 Coordinator 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 Coordinator 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 professors for each Course, together with their subject, will be available on the degree programme starting from the month of September.
The degree programme is annually published on the website of Politecnico di Milano.

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 their university e-mail, as well as information and news 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 Didactic Observation Unit and the Evaluation Nucleus perform periodic analysis on the overall results analysing the teaching activities and the integration of graduates into the work world. Reports and studies are available on the website of the Politecnico di MIlano.

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).


Only the original in Italian is valid.

15. Errata corrige