Academic Year 2014/15





School of Industrial and Information Engineering



Degree Programme of:


Mathematical Engineering
Laurea (Equivalent To Bachelor Of Science)


Milano 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 Giovanni Gustavo Lozza
Coordinator of the Study programme Sandro Salsa
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.


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 Mathematical Engineering Program (Bachelor + Master) was inspired by a new and innovative professional profile, transversal in many ways to the other engineering courses and at the same time quite different from both the Mathematics and the Applied Mathematics programs, currently offered by the School of Sciences.

The project led in 2001 to a well defined and robust university curriculum which realizes a synergy between advanced mathematical methods and engineering mentality, capable to face complex problems from applied sciences and technology, through the construction and the analysis of mathematical models. As is the case for all engineers, also mathematical engineers must acquire a solid understanding of the problems by means of a number of courses ranging from physics to chemistry, to economics, to computer science. On the other hand, a number of courses on the basic principles of engineering provide the students with a technological insight.

Having an engineer’s “forma mentis” constitutes a fundamental element of the program. This feature marks a deep difference from the above mentioned courses in Mathematics or Applied Mathematics, whose aim is mainly focused to investigate from a more abstract point of view concepts, and principles of mathematics with a high standard of rigor. The training of an engineer student is directed towards an optimal use of those concepts and tools in a great variety of contingent and concrete situations.  A mathematical engineer must know how to interpolate between both of these attitudes in order to use the methodologies at his/her disposal choosing a level of depth and rigor adapted to the the significance and difficulty of the problem to be solved. Ideally, the mathematical engineer should know how to choose the model to be used, based on a compromise between desired accuracy and tolerated complexity, searching for a satisfactory adherence to reality whilst optimizing costs in terms of time and money.

During the program, the pure mathematics courses provide the student with the flexibility to understand and use any other mathematical topic needed to be used or analyzed;  in the applied mathematics courses the main objective is to see  how tools and algorithms, theoretically presented, work on typical model problems.


3. Learning objectives

The main objective of the Mathematical Engineering Program (MEP) is to prepare professionals able to analyze complex systems where a strong interdisciplinary knowledge is required, through the  acquisition of an engineer’s mentality and of methodologies provided by various sectors of applied mathematics. Thus, MEP is characterized by a continuous synergy between Mathematics and Engineering methods and provides the students with the skill to face problems from various scientific and/or technological sectors and concerning both artificial systems, constructed through human action as well as natural systems where human intervention is absent or  insignificant.

The Bachelor degree (in Italian: Laurea di primo livello or, simply, Laurea) constitutes the first part of the above formation process with the specific primary aim to provide a solid knowledge of the basic principles of engineering, together with an adequate spectrum of modern mathematics, physics, informatics. In this way the students have the possibility to start acquiring the necessary flexibility to analyze problems of relatively complexity. All these features will be refined and completed throughout the two years of Laurea Magistrale.


4. Organization of the study programme and further studies

4.1 Structure of the study programme and Qualifications

The Mathematical Engineering Bachelor Program has the duration of three years and is worth 180 CREDITS credits. The first and second years are common to all students.  The third year is differentiated according to the choice of program: Propedeutical for the Master of Science Program (M.Sc) 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 gives access to any of the Italian Master of Science program (Laurea di secondo livello or Laurea Magistrale, Teaching Regulation Law 270/04) according to the limitations established by each University.

The most natural step is of course the progression to a Master of Science in Mathematical Engineering, offered by the Politecnico di Milano.


5. Professional opportunities and work market

5.1 Professional status of the degree

The Teaching Regulations for the Bachelor Degree in Mathematical Engineering (Law 270/04) is classified in both categories 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 degree class according to the courses chosen within the program (see Paragraph 7.3).

Graduates of the Bachelor Degree in Mathematical Engineering can, if they are interested, take the Professional Exam, a state-run, professional qualification examination, enabling them to enroll under Section B (Junior Engineers) of the Engineers’ professional register, only in the class (respectively “Information Engineering” or “Industrial Engineering”) corresponding to their degree. For further details on the Professional Exam, see Presidential Law 328/2001 "Amendments and supplements to requisites for admission to the Professional Exam and corresponding tests for practicing certain professions, as well as the regulations of the corresponding Orders.

http://www.miur.it/regolame/2001/professioniregolam/AgrArch/DPR328_2001.htm orwww.tuttoingegnere.it

5.2 Careers options and profiles

The following competences are required to a junior mathematical engineer:

  • the knowledge of large diffusion codes to treat mathematical objects and structures (such as, for example, Matlab® for numerical linear algebra and the development of algorithms; the statistics package “R” for the analysis and the statistic handling of data; Mathematica or Maple for symbolic calculus);
  • the ability of exploiting and using information obtained from experimental data both for the heuristic construction of mathematical models and for estimation, checking and adaptation of these models in inferential terms;
  • the knowledge of modern techniques of scientific programming (e.g. object programming) and of industrial codes.

 

Career prospects of a Mathematical Engineering graduate include

  • Research and Development centers of large companies,
  • calculus labs of  medium-sized companies,
  • industrial consulting societies,
  • banks and finance companies,
  • software houses
  • public and private research institutes.

The Career Service of the Politecnico (http://www.careerservice.polimi.it) informs on job opportunities and organizes periodic presentations to interested companies for students near graduation.


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

Italian secondary school leaving qualification or other comparable foreign qualification (level 4 EQF)


For admission to the Mathematical Engineering Bachelor Program, the test, that is the same for all Politecnico di Milano Engineering Bachelor degrees, must be taken to ascertain students’ aptitude and preparation. For further information:
http://www.polimi.it/orientamento


Students who are already enrolled on other degree programs or at other Universities and wish to transfer to the Mathematical Engineering Program can request he validity of any CREDITS credits they have already earned. For information refer to the Transfers and Exam Recognition Commission of the Program Board:

(e-mail: trasferimenti@mate.polimi.it).

6.2 Requested knowledge

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 for admission and number of places available

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  Tutoring service has the objective of assisting students during their studies, especially in the first three years. This activity involves a reference student-tutor and a professor-tutor. Student-tutors provide information to students concerning practical organization of studies and support structures offered by the Politecnico. Furthermore, they help students who need to fill basic gaps (for example, students with mandatory supplementary education). Student-tutor activity is organized through meetings in fixed appointment periods or via e-mail. The service is organized as part of the Program of studies to which students should refer for all necessary information to contact tutors and services .

Moreover, the tutoring service provides professors, on request, with PhD students to support laboratory activities, to provide additional support to foreign students or to organize teaching material provided by professors.

Guidance site https://www.ingindinf.polimi.it


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

As specified in the teaching regulations, 180 credits are required to obtain the degree (first level). In particular, 87 credits are due to basic scientific topics (mathematics, statistics, computer science, physics, chemistry); 50 to characterizing courses (fundamentals of automatic control, electrical engineering, business  economics and organization, energy, safety and industrial protection engineering); 20 to related and supplementary activities (scientific culture, other engineering disciplines) are 20; 23 for other educational activities (choice of the student, final exam, stages, etc.).

7.2 Mode of study

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

7.3 Detailed learning objectives

1 Year courses


Code Educational activities SSD Course Title Language Sem CFU CFU Group
083215AMAT/05ANALISI MATEMATICA I110.010.0
061202B,CING-INF/05INFORMATICA A110.010.0
083217ACHIM/07CHIMICA17.07.0
083214AMAT/03ALGEBRA LINEARE E GEOMETRIA25.05.0
083024AFIS/01FISICA SPERIMENTALE I210.010.0
061204BING-IND/35ECONOMIA E ORGANIZZAZIONE AZIENDALE D210.010.0
083229CSECS-S/01STATISTICA25.05.0

2 Year courses


Code Educational activities SSD Course Title Language Sem CFU CFU Group
096350AMAT/05ANALISI MATEMATICA II110.010.0
083224AFIS/01FISICA SPERIMENTALE II110.010.0
083223BING-IND/31ELETTROTECNICA110.010.0
083216AMAT/08MATEMATICA NUMERICA210.010.0
085924AMAT/06PROBABILITA'210.010.0
083225BING-INF/04FONDAMENTI DI AUTOMATICA210.010.0

3 Year courses - Track: MAP - Applicativo


Code Educational activities SSD Course Title Language Sem CFU CFU Group
085925AMAT/05ANALISI MATEMATICA III15.05.0
083220CMAT/09FONDAMENTI DI RICERCA OPERATIVA15.0
085928AMAT/07MECCANICA RAZIONALE E DEI CONTINUI [C.I.]110.010.0
085930BING-INF/01ELETTRONICA (a)110.010.0
085929CING-IND/10FISICA TECNICA (b)110.0
073469CICAR/08SCIENZA DELLE COSTRUZIONI210.010.0
085932A,CMAT/06
SECS-S/01
MODELLI E METODI DELL'INFERENZA STATISTICA210.010.0
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 - Propedeutico


Code Educational activities SSD Course Title Language Sem CFU CFU Group
085925AMAT/05ANALISI MATEMATICA III15.05.0
085928AMAT/07MECCANICA RAZIONALE E DEI CONTINUI [C.I.]110.010.0
085930BING-INF/01ELETTRONICA (a)110.010.0
085929CING-IND/10FISICA TECNICA (b)110.0
083220CMAT/09FONDAMENTI DI RICERCA OPERATIVA15.05.0
073469CICAR/08SCIENZA DELLE COSTRUZIONI210.010.0
078246CSECS-S/06FINANZA MATEMATICA I210.020.0
085932A,CMAT/06
SECS-S/01
MODELLI E METODI DELL'INFERENZA STATISTICA210.0
078047AMAT/05
MAT/08
METODI ANALITICI E NUMERICI DELLE E.D.P.210.0
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)

7.3.1 Request of Special Study Plans


The Committee of the Course  (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 inside the CCS.

In particular, the student interested in accessing the Laurea Magistrale 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 [I.C.]

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) Characterizing course for the L-9 class of Industrial Engineering Laurea.
 
For further information on Laurea Magistrale in Nuclear Engineering one can consult the web-page: http://info-corsi.cesnef.polimi.it/.


7.3.2 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 Board; 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 considered:

  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 30. Thus any additional credit earned exceeding 30 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

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 Board on 09.10.2013 (http://www.ingindinf.polimi.it/cms/file/12396/RegolamentoProvaFinale.pdf).

Compared to these rules and, according to the specific requirements and peculiarities of the degree, the Program in Mathematical Engineering introduces the following supplements according to the Propedeutic/Applied choice and to the participation to a T.I.M.E. program.

 

Propedeutic

Choice between two graduation exam procedures:

  1. Reading course: the student chooses a topic in agreement with a Professor of the University (part of a book, a scientific paper,…); the final exam consists in an oral presentation of the chosen topic in front of a CCS committee. Alternatively, the student attends an intensive course inside ATHENS project and has to pass the final exam. The maximum score is 5 points.
  2. Written Thesis on a subject chosen in agreement with a Professor of the University. Two students (at most) may agree to work together on the same subject. The final exam consists in a presentation of its (or their) work in front of a CCS committee. The maximum score is 8 points.

 

Applied

An ad hoc CCS Stage Committee (e-mail: tirocini@mate.polimi.it) assigns to the student a stage in agreement with a Professor of the University (internal-tutor) and a company-tutor. The final exam consists in a discussion of a written report of the stage activity in front of a CCS committee, with the possible participation of the company-tutor; a report from the company-tutor must be attached. The maximum score is 8 points.

 

T.I.M.E. Program.

The final exam consists of a written report on the activity developed abroad. The document may be compiled in the language of the country where the activity was carried out with an ample summary in Italian.

The report, which must be accompanied by the opinion of the tutor who supervised the work abroad, is discussed in front of a CCS committee. The maximum score is 8 points.

 

For all the final exam typologies the following rules apply:

  • the studentmust communicate the start of the final exam activity to the Secretary of  the Bachelor Committee (e-mail: lauree@mate.polimi.it)
  • a copy of the document thesis or the stage report must be delivered to the Student Office (of the Study program) by the Math Department, at least two days before the final exam day.

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

The Calendar of the School of Industrial and Information Engineering for the A. Y. 2014/15 is available on the School website, at the section "Teaching" (http://www.ingindinf.polimi.it/).


Academic calendar
https://aunicalogin.polimi.it/aunicalogin/getservizio.xml?id_servizio=204&idApp=1&idLink=3224

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.

10. Infrastructures and laboratories

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

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 Program  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:
Transfers and recognition of credits (Bachelor degree) trasferimenti@mate.polimi.it
Study Plans (Bachelor degree) pianiLT@mate.polimi.it
Master of Science Admissions ammissioneLM@mate.polimi.it
Study Plans (Master of Science degree) pianiLM@mate.polimi.it
Erasmus program and international exchanges erasmus@mate.polimi.it
Stages tirocini@mate.polimi.it
Coordinator of the Study Program Board (CCS) ccs@mate.polimi.it
Final Exam Secretary lauree@mate.polimi.it
Student-elected representatives of the Study Program Board studenticcs@mate.polimi.it

 


11. International context

The international context, relative to European countries with an economy and cultural level comparable to the Italian one, 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 access educational projects characterized by mathematically oriented professional profiles.

Examples are the EPFL at Lausanne, the ETHZ at Zurich, 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 are available. 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,  Austin, at the Santa Barbara U. in California, at the Institute of Math and its Applications (U. of Minnesota), sponsored by Society for Industrial and Applied Math.

Similarly, education projects in statistics and mathematics, oriented towards the modeling 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 Statistic Department of Stanford U. at Palo Alto, California; other analogous  programs are offered, for instance, by the Johns Hopkins U. at Baltimora, by the U. of Minnesota and by the Warwick U. in U.K.

Finally, educational programs oriented to the modeling and to the quantitative aspects of Finance are present in curricula of several European engineering schools. We mention the Finanz Mathematic Program  at the ETHZ (Zurich) and at the TUM (Munich), the Finanz und Versicherung Mathematik at the TU of Vienna; a program of Statistical and Math Finance is offered at the KTH of Stockholm; one of Mathematics and Finance at the Imperial College of London.

The above educational projects clearly demonstrate show how the mathematical engineer is already a well established professional profile in Europe and in the world.


12. Internationalization

The Mathematical Engineering student has the possibility to carry out part of its Program by a foreign university, enriching its preparation with a professional and human experience of significant value. The international exchange programs (Erasmus, Time) are managed by the International Relations Centre  (CRI) of the  Politecnico di Milano, to which one should refer for any general information (http://www.polimi.it/studenti/fai-unesperienza-allestero).


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

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

Any updates to the information hereafter will be made available on the School website (http://www.ingindinf.polimi.it) and on the degree program website (http://www.mate.polimi.it/im/).


15. Errata corrige