Academic Year 2017/18





School of Industrial and Information Engineering



Degree Programme of:


Mathematical Engineering
Laurea (Equivalent To Bachelor Of Science)


Milano Leonardo Campus

1. General Information

School School of Industrial and Information Engineering
Code Reference Law365
NameMathematical Engineering
Reference LawOrdinamento 270/04
Class of degree ()L-8 - Information Technology
L-9 - Industrial Engineering
Degree level Laurea (Equivalent To Bachelor Of Science)
First year of activation 2008/2009
Official length of the programme 3
Years of the programme already activated 1,2,3
Official language(s) Italian
Campus Milano
Dean of the School Lozza Giovanni
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
() The student belongs to one or the other Degree class depending on the education chose.

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 attitude 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 aim of the 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 Engineers 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.

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 Bachelor of Science in Mathematical Engineering lasts three years. The first and second year are common to all students. At the third year students choose between two tracks:

  • Propedeutical
  • Applied

The Propedeutical track is designed for students who wish to continue their study in a Master programme, the Applied track leads to professional work and includes a professional stage.

During their career, students are given the opportunity to spend a period in a foreign university, within one of the many international exchange agreements.


4. Organization of the study programme and further studies

4.1 Structure of the study programme and Qualifications

The Bachelor programme in Mathematical Engineering has a three-year duration, corresponding to 180 credits. The first and second years are common to all students.  The third year is differentiated according to the choice of a track: Propedeutical for the Master of Science programme or Applied which requires a professional stage.


4.2 Further Studies

The qualification grants access to "Laurea Magistrale" (2nd degree), "Corso di Specializzazione di primo livello" (1st level Specialization Course) and "Master Universitario di primo livello" (1st level University Master)


The Bachelor Degree qualification in Mathematical Engineering grants access to any of the Italian Master of Science programmes (Laurea Magistrale) according to the limitations established by each University.

The most natural continuation is of course the Master of Science in Mathematical Engineering run at Politecnico di Milano since the academic year 2009/10. Admission to this course is also subordinated to specific conditions.


5. Professional opportunities and work market

5.1 Professional status of the degree

Bachelor graduates in Mathematical Engineering have a sound engineering education joined with 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 Bachelor degrees made by the Italian Ministry of University and Research under the educational system 270/04, the Bachelor in Mathematical Engineering belongs to the Class L 8 - Information Technology Engineering, and L 9 - Industrial Engineering. According to the law, however, the Degree issued by the University will refer to only one of the above mentioned Classes. The graduate student will belong to one or the other class according to the courses chosen within his study program (see paragraph 7.3).

Graduates with a Bachelor Degree in Mathematical Engineering can take the State Examination, a state-run, professional qualification examination enabling them to enroll under Section B (Junior Engineers) of the Engineers’ professional register. The Exam and the enrolment depend on the Class mentioned above (“Information Technology Engineering” or “Industrial Engineering”).

5.2 Careers options and profiles

The large majority of Bachelor graduates in Mathematical Engineering continue their study in a Master of Science programme. Most of them enroll in the Master of Science in Mathematical Engineering at Politecnico di Milano, but a fraction of them gets a Master degree in a foreign university.

Bachelor graduates that start a professional activity may find a job in Research and Development divisions of big firms, in study centers of industrial  or consultancy companies, in engineering firms and computing laboratories, in banks, insurance and financial companies, in public or private institutions involved in scientific or technological research.

We mention that Politecnico di Milano runs the Career Service  (http://www.careerservice.polimi.it) which 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=4140

6. Enrolment

6.1 Access requirements

Secondary school leaving qualification, or foreign comparable qualifications


Admission to the Mathematical Engineering Bachelor programme requires passing a test. The admission test is the same for all the engineering Bachelor programmes at Politecnico di Milano. It is required in order to assess prospective students’ attitude and preparation. We mention that it is possible, and often convenient, to pass the test much time before the beginning of the course, and that repetition upon failure is admitted several times. Detailed information is available at http://www.polinternational.polimi.it/


Students who are already enrolled in other degree programs or at other Universities and wish to transfer to the Mathematical Engineering Bachelor programme can request the validity of any credits they have already earned. To this end they must apply  to the Transfers and Exam Recognition Committee (e-mail: trasferimenti-l-ingegneria-matematica@polimi.it).

6.2 Requested knowledge

Adequate preparation and attitude to scientific study is required. As explained above, this is assessed by the admission test.
The educational offer at the Politecnico di Milano
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=4943

6.3 Deadlines

How to become a student at Politecnico di Milano
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=2984

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=2184

7. Contents of the study Program

7.1 Programme requirements

180 credits are required to obtain the Bachelor degree. They correspond to all the educational activities, a final work and possibly a stage.


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

The study program is organized on a full-time basis, divided into student participation to classes and laboratory activities.


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

7.3 Detailed learning objectives

1 Year courses - Track: MND - Non Diversificato


Code Educational activities SSD Course Title Language Sem Credits (CFU) CFU Group
083215AMAT/05MATHEMATICAL ANALYSIS I110.010.0
061202B,CING-INF/05COMPUTER SCIENCE A110.010.0
083217ACHIM/07CHEMISTRY17.07.0
083214AMAT/03LINEAR ALGEBRA AND GEOMETRY25.05.0
083024AFIS/01EXPERIMENTAL PHYSICS I210.010.0
061204BING-IND/35BUSINESS ECONOMICS AND ORGANIZATION D210.010.0
083229CSECS-S/01STATISTICS25.05.0

2 Year courses - Track: MND - Non Diversificato


Code Educational activities SSD Course Title Language Sem Credits (CFU) CFU Group
096350AMAT/05MATHEMATICAL ANALYSIS II110.010.0
083224AFIS/01EXPERIMENTAL PHYSICS II110.010.0
083223BING-IND/31ELECTRICAL ENGINEERING110.010.0
083216AMAT/08NUMERICAL MATHEMATICS210.010.0
085924AMAT/06PROBABILITY210.010.0
083225BING-INF/04FUNDAMENTALS OF AUTOMATIC CONTROL210.010.0

3 Year courses - Track: MAP - Applicativo


Code Educational activities SSD Course Title Language Sem Credits (CFU) CFU Group
085925AMAT/05MATHEMATICAL ANALYSIS III15.05.0
083220CMAT/09INTRODUCTION TO OPERATIONS RESEARCH15.0
099989AMAT/07RATIONAL AND CONTINUUM MECHANICS110.010.0
085930BING-INF/01ELECTRONICS (a)110.010.0
097575--ING-IND/10THERMODYNAMICS AND ENERGETIC PROCESSES (b)110.0
073469CICAR/08MECHANICS OF ELASTIC STRUCTURES210.010.0
085932A,CMAT/06
SECS-S/01
MODELS AND METHODS FOR STATISTICAL INFERENCE210.010.0
086286----STAGE (LP MTM)--115.015.0
086286----STAGE (LP MTM)--215.0
086285----FINAL WORK--13.03.0
086285----FINAL WORK--23.0

(a) Distinctive for the class L-8 (Information Technology).
(b) Distinctive for the class L-9 (Industrial Engineering).

3 Year courses - Track: MFO - Formativo


Code Educational activities SSD Course Title Language Sem Credits (CFU) CFU Group
085925AMAT/05MATHEMATICAL ANALYSIS III15.05.0
099989AMAT/07RATIONAL AND CONTINUUM MECHANICS110.010.0
085930BING-INF/01ELECTRONICS (a)110.010.0
097575--ING-IND/10THERMODYNAMICS AND ENERGETIC PROCESSES (b)110.0
083220CMAT/09INTRODUCTION TO OPERATIONS RESEARCH15.05.0
073469CICAR/08MECHANICS OF ELASTIC STRUCTURES210.010.0
078246--SECS-S/06MATHEMATICAL FINANCE I210.020.0
085932A,CMAT/06
SECS-S/01
MODELS AND METHODS FOR STATISTICAL INFERENCE210.0
078047AMAT/05
MAT/08
P.D.E. ANALITICAL AND NUMERICAL METHODS210.0
094892AMAT/05ANALITICAL METHODS FOR P.D.E.25.0
094891CSECS-S/01STATISTICAL INFERENCE25.0
086285----FINAL WORK--13.03.0
086285----FINAL WORK--23.0

(a) Distinctive for the class L-8 (Information Technology).
(b) Distintctive for the class L-9 (Industrial Engineering).

7.3.1 Request of Special Study Plans


The Faculty of the Bachelor programme  (CCS)  will examine proposals of study plans different from the ones indicated above (paragraph 7.3) only in the following exceptional cases:

  • students whose study plan has been specifically tailored ("autonomous" study plan) as a consequence of modifications of the General Structure of the Courses;
  • students who need a special adaptation to participate to international exchange programs. In this case the new plan has to be examined by the International Exchange Committee of the CCS.

In particular, students wishing to apply for admission to the Master of Science in Nuclear Engineering at Politecnico di Milano can submit at the 3rd year an autonomous study plan including the following courses:

 

Codice

Attività formative

SSD

Denominazione Insegnamento

Sem

Crediti (CFU)

CFU Gruppo

085925

A

MAT/05

MATHEMATICAL ANALYSIS III

1

5.0

5.0

085928

A

MAT/07

RATIONAL AND CONTINUUM MECHANICS

1

10.0

10.0

085929

B

ING-IND/10

THERMODYNAMICS AND HEAT TRANSFER (a)

1

10.0

10.0

089540

--

FIS/03

ATOMIC PHYSICS

1

10.0

10.0

073469

C

ICAR/08

MECHANICS OF ELASTIC STRUCTURES

2

10.0

10.0

094893

--

ING-IND/20

PHYSICS OF NUCLEUS

2

5.0

5.0

094891

C

SECS-S/01

STATISTICAL INFERENCE

2

5.0

5.0

094892

A

MAT/05

ANALYTICAL METHODS FOR P.D.E. 

2

5.0

5.0

086285

--

--

FINAL WORK (LP MTM)

1

3.0

3.0

086285

--

--

FINAL WORK (LP MTM)

2

3.0

(a) Distinctive course for the Degree class L-9 (Industrial Engineering).

 

For further information on the Master programme in Nuclear Engineering one can consult the web page: http://www.energia.polimi.it/english/education/l_nucleare.php.


7.3.2 Free movers


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.


7.3.3 Possibility of acquiring credits for the Master of Science degree (Laurea Magistrale)


During the Bachelor program, students interested in future admission into Master of Science program may:

  • A1) earn credits form extra MSc courses, included in their personal study plan. These credits  are considered excess credits and  recognized as part of the 120 credits needed to acquire the MSc degree.
  • A2) acquire attendance status in MSc courses.  This gives the possibility to anticipate the examination in the chosen courses.
  • A3) Earn credits from courses added to the regular study plan, established by an ad hoc Master of Science Admissions Committee; these credits are considered “in addition” to the 120 needed to be awarded the Master of Science.

 

In the period between the award of the Bachelor Degree and the enrolment into the MSc program,  it is possible to:

  • B1) earn credits by registering and pass the relative exam, in single courses of the MSc These credits are considered as part of the 120 credits needed to acquire the MSc degree.
  • B2) acquire attendance status only in MSc courses as in A2).
  • B3) Earn credits in A3).

 

The following limitations must 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 MSc degree (A1+A2+B1+B2) 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 and B3 .

7.4 Foreign language

We refer to the following web site of Politecnico di Milano.
Language courses
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=3064

7.5 Degree examination

The general rules for graduation exams are established in the Regulations for graduation examinations approved by the School of Industrial and Information Engineering.

According to its specific requirements and peculiarities, the Faculty of the programme in Mathematical Engineering has introduced supplementary rules. See:

http://www.ingindinf.polimi.it/en/didactics/bachelors-and-masters-degree-exams/

Below we report the main information on those rules, that also depend on the choice between the Propedeutic or Applied track and on possible participation in an international exchange program.

 

Propedeutical track

Students have the choice between two graduation exam procedures:

  1. Reading course: the student chooses a topic, in agreement with a Professor of Politecnico (part of a book, a scientific paper etc.); the final exam consists in an oral exposition of the chosen topic in front of a Faculty Committee. The maximum score is 5 points.
  2. Written Thesis on a subject chosen in agreement with a Professor of Politecnico. Two students (at most) may agree to work together on the same subject. The final exam consists in a defense of her/his/their work in front of a Faculty committee. The maximum score is 7 points (8 in exceptional cases).

 

Applied track

An ad hoc Faculty Stage Committee (e-mail: tirocini-ingegneria-matematica@polimi.it) assigns a stage to the student, in agreement with a Professor of Politecnico (official Supervisor, or Academic Tutor) and under the supervision of an External Tutor, a member of the company where the stage takes place. The final exam consists in a discussion of a written report of the stage activity, that takes into account a written report of the External Tutor. The discussion takes place in front of a Faculty Committee, with the possible participation of the External Tutor. The maximum score is 7 points (8 in exceptional cases).

Upon request by the student, instead of a discussion of the stage activity, the graduation exam may consist in a Reading course as described above. In this case, a written report on the stage activity is still required, but it will not be discussed by the Graduation Committee.

 

International exchange programs and special cases

Special procedures are prepared for students who have attended an intensive course within the ATHENS program, or who are enrolled in a TIME double degree programme, or who carry our the work on the Bachelor thesis abroad or in another university or research center.

For all kind of graduation exams (reading course, written thesis, stage activity report etc.) the following rules are enforced:

  1. Students starting to prepare their graduation work are required to inform the Secretary of the Graduation Board (e-mail: lauree-l-ingegneria-matematica@polimi.it) reporting the planned graduation exam, the subject, the name of the Supervisor and of the second author (if any).
  2. A copy of the written work (if any) must be submitted to the Mathematics Department Student Office at least one day prior to the graduation session.
  3. 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=3144

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=3224

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 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 study 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:

Study Plans (Bachelor degree): piani-l-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-l-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?k_corso_la=365&lang=EN


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, double degree programmes (typically the TIME program) etc.


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=4653

13. Quantitative data


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 study programme web site http://www.mate.polimi.it/im/


15. Errata corrige