School of Industrial and Information Engineering
Degree Programme of:
Mathematical Engineering
Laurea (Equivalent To Bachelor Of Science)
Milano Campus
1. General Information
(¹) The student belongs to one or the other Degree class depending on the education chose.
School School of Industrial and Information Engineering Code Reference Law 365 Name Mathematical Engineering Reference Law Ordinamento 270/04 Class of degree (¹) L-8 - Information Technology
L-9 - Industrial EngineeringDegree 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 Lorenzo Dozio Coordinator of the Study programme Daniele Marazzina Website of the School http://www.ingindinf.polimi.it Website of the Study programme
http://www.mate.polimi.it/im
Central Student Office - Milano Leonardo
Address VIA C. GOLGI, 42 (MI)
2. General presentation of the study programme
The study programme in Mathematical Engineering, started at Politecnico di Milano in 2001, aims at giving graduates the knowledge of appropriate mathematical methods and the ability to use them in an effective way in the context of technological and management applications. This corresponds to a professional profile having basic engineering skills joined to a deep expertise in modern mathematical, numerical and statistical methods for the modelling, the analysis and the solution of various engineering problems.
This profile is different from other engineering educational profiles, and at the same time very different from the ones acquired in study programmes in Mathematics (pure or applied) since it includes education in Physics, Chemistry, Economics, Computer Science and many other technological disciplines typical of Engineering, which turns out to give the graduates adequate ability in solving practical problems and the mental 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 Bachelor of Science programme has the final goal of promoting the education of young laureates to approach the analysis of complex systems through the combined adoption of scientific knowledge and advanced mathematical tools. To this purpose, three are the main education targets for a bachelor in Mathematical Engineering:
1) To know and understand the scientific principles and the foundations of Engineering.
2) To identify solutions by the application of the approach of science and engineering (understanding, elaborating and modeling by relying on a solid multidisciplinary education).
3) To interact in a professional and effective manner with partners from different backgounds or disciplines.
Achieving objective nr. 1 yields the laureate competences that are transversal across diverse disciplines, an adequate level of knowledge of the basic subjects of engineering, together with a skill on modern mathematical, numerical and statistical approaches. In particular, besides gaining a basic scientific education, a bachelor in Mathematical Engineering acquires the ability to master the modern scientific programming techniques and a number of computer codes widely employed in industrial applications; an adequate knowledge to understand a large class of mathematical models (of differential, discrete or other kind); the knowledge of mathematical modeling for the analysis of random phenomena or characterized by variability and/or uncertainty; the knowledge of statical modeling for the treatment and analysis of data.
The continuous synergy between education in Mathematics (mainly in its applications) and in disciplines of marked engineering nature is propedeutical and essential to the subsequent phase of modeling, analysis and solution of real problems in design and management (objective nr. 2). As a matter of fact, a sound knowledge of engineering subjects indicates the bachelor in Mathematical Engineering which are the areas where methodological competences can be applied, and allows him/her to access (objective nr. 3) employment contexts in traditional engineering as well as in other disciplines (economics, life sciences, etc.), by contributing with specific professional skills.
Fulfilling the three above objectives requires knowledge and methods in the area of Information Engineering (class L-8) as well as in the area of Industrial Engineering (class L-9). In what follows, the educational targets of both classes are described in detail.
Qualifying educational targets of the class: L-8 Information Engineering
Bachelors in this class must:
- adequately know the methodological and operative aspects of mathematics and other basic sciences, and should be able to employ such knowledge to interpret and describe problems in Engineering applications;
- adequately know the methodological and operative aspects of engineering sciences, in general terms as well as specifically targeted to areas of Information Engineering in which they should be able to identify, formulate and solve problems by employing up-to-date methods, techniques and tools;
- be able to employ techniques and tools for the design of components, systems and processes;
- be able to conduct experiments and analyze/interpret results and data;
- be able to understand the impact of engineering solutions in the social, physical and environmental context;
- be aware of their professional and ethical responsabilities;
- have a detailed knowledge of corporates and enteprises in all of their economical, management and organization aspects;
- have a detailed knowledge of the contexts of our contemporary society;
- have good skills in relations and decision-making
- be able to communicate in an effective manner in at least one language of EU (written and oral), besides Italian;
- manage the basic cognitive tools for a continuous updating of their level of knowledge.
Qualifying educational targets of the class L-9 Industrial Engineering
Bachelors in this class must:
- adequately know the methodological and operative aspects of mathematics and other basic sciences, and should be able to employ such knowledge to interpret and describe problems in Engineering applications;
- adequately know the methodological and operative aspects of engineering sciences, in general terms as well as specifically targeted to areas of Industrial Engineering in which they should be able to identify, formulate and solve problems by employing up-to-date methods, techniques and tools;
- be able to employ techniques and tools for the design of components, systems and processes;
- be able to conduct experiments and analyze/interpret results and data;
- be able to understand the impact of engineering solutions in the social, physical and environmental context;
- be aware of their professional and ethical responsabilities;
- have a detailed knowledge of corporates and enteprises in all of their economical, management and organization aspects;
- have a detailed knowledge of the contexts of our contemporary society;
- have good skills in relations and decision-making
- be able to communicate in an effective manner in at least one language of EU (written and oral), besides Italian;
- manage the basic cognitive tools for a continuous updating of their level of knowledge.
During the Bachelor of Science students may complete their education with a period of study spent abroad thanks to the several existing partnerships with international Institutions.
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.
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.
Admission to another Master's Degree Course of the Politecnico di Milano is subject to the rules specific to that Course, which can be found in the relative Didactic Regulations.
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 different italian or 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 (https://www.careerservice.polimi.it/en-US/Home/Index/) 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.
5.3 Qualification profile
Mathematical Engineer
The function in a work context:
The Bachelor in Mathematical Engineering has an adequate spectrum of basic knowledge and the forma mentis of a traditional engineer, corresponding to a professional figure characterized by originality and flexibility, able to integrate in several diverse work contexts. Thanks to a wide knowledge of modern mathematical, numerical and statistical methodologies, he/she is able to effectively contribute to modeling, analysis and solution of real problems in design, prediction, control and management.The Bachelor Programme (law system 270/04) includes curricula that are compatible with the ministery Tables for Class L-8 (Information Enginering) and for Class L-9 (Industrial Engineering), and in both cases the title of Mathematical Engineer has a unique value. According to the law, however,the Bachelor Certificate that is delivered by the university is related to only one of the above mentioned Classes. The Bachelor will belong to one of the two classes according to the choices of exams taken during the education training. Bachelors in Mathematical Engineering will be able to participate to the state exam for professional habilitation and to subscribe to Section B of Engineering Professional Register (Junior Engineers) corresponding to the Class which the Bachelor Degree belongs to.
Competences associated with the function:
The Mathematical Engineer has specific competences to:
- analyze of complex systems involving multidisciplinary skills and elements of knowledge;
- harmonize basic scientific knowledge with the management and adoption of advanced methods and tools;
- solve problems arising in diverse scientific contexts, concerning artificial and/or man-crafted systems as well as natural systems in which the human presence is absent or negligible;
- use contemporary computer codes and software to handle and treat objects and mathematical structures;
- apply the modern techniques of scientific programming (for example, object-oriented programming);
- understand differential and discrete models or, according to the chosen professional orientation, use the information obtained from experimental data in inferential terms for the estimate, verification and adaptation of mathematical models, as well as for the heuristic constriuction of such models;
- employ simulation techniques for the study of the model and for its optimal calibration.
Job opportunities:
Flexibility and capacity of studying problems of diverse nature promote the access of Bachelors 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:
- Research & Development centers or computing laboratories in large and medium-size enterprises;
- production companies of industrial goods requiring a level of knowledge based on the use of advanced mathematical procedures;
- 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
Italian secondary school leaving qualification or other comparable foreign qualification (level 4 EQF)
To optimize the use of available resources across different locations, the total number of places for first-year enrollment in each degree program at the University is set by the Academic Senate during the definition of the educational offer, based on the indications provided by the relevant School. Enrollment in the first year of the degree course is conditional upon passing a test aimed at verifying the possession of the knowledge required for admission and the aptitude for study. The verification of the possession of the required knowledge for admission is carried out through a common test for all Engineering courses activated by the University (TOL – Test Online). The TOL can be taken by students in the penultimate and final year of high school, and by graduates. The Engineering test has a minimum threshold. Even if there are available places, students who do not achieve a score of 30,00/100 or higher cannot enroll. The ranking position of the candidates is established based on the score, available places for each test session, and the order of preferences expressed. There are two phases of enrollment. The first phase of early enrollment is reserved for students who have passed the TOL in their penultimate year of high school with a score of 75,00/100 or higher. The second phase of standard enrollment is reserved for students who passed the TOL in their penultimate year of high school with a score lower than 75,00/100, students who passed the TOL in their last year of high school, graduates, or students who passed the TOL in the penultimate year of high school but did not enroll in the first enrollment window.Those who have achieved the minimum score set annually by the University in one of the following internationally recognized tests: SAT, GRE, GMAT, and TOLC-I (CISIA Test), may be exempted from the admission test. The test is conducted remotely, using the candidate's personal computer and smartphone/tablet, with a connection in a Zoom Room supervised by a responsible person.The attribution of Additional Educational Obligations (OFA TENG) occurs when, considering only the English section, the number of correct answers is less than 24.For the fulfillment of the OFA TENG, it is possible to present a certification of English language knowledge accepted by the University or, alternatively, take specific tests at external entities to the Polytechnic.All details about the admission procedures, including the updated dates of the sessions scheduled for the TOL, are available on the University's website at: https://www.polimi.it/en/futuri-studenti/admission-to-laurea-programmes/engineering6.2 Requested knowledge
Adequate preparation and attitude to scientific study is required. As explained above, this is assessed by the admission test.6.3 Deadlines for admission and number of places available
For the current academic year the number of enrolments to the Mathematical Engineering Bachelor of Science is equal to 340.6.4 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
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.
https://www.ingindinf.polimi.it/en/1/translate-to-english-studenti/services/tutoring
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.)
According to Law No. 33 of April 12, 2022, simultaneous enrollment in two programs is allowed. Enrollment in two programs is possible only if they are of different degree classes (classi di laurea) and differ in at least two-thirds of their educational activities regarding academic credits.
Consistent with what is defined by Law No. 33, at the student's instance, the maximum number of CFUs already taken in the other program and validatable is 60 CFUs for BSc programmes.
Please note that courses belonging to programs of a different level or type from the program you are enrolled in cannot be validated.
Full details on when to apply for validation and the administrative fees to be paid are available on the Polimi website: https://www.polimi.it/contemporanea-iscrizione
7.2 Mode of study
This programme requires a full time attendance. Educational activities include lectures, exercise classes, and possibly computer and experimental laboratories.
The study program is organized on a full-time basis, divided into student participation to classes and laboratory activities.
7.3 Detailed learning objectives
1 Year courses - Track: MTM - Ingegneria Matematica
Code Educational activities SSD Course Title Language Sem CFU CFU Group 083215 A MAT/05 ANALISI MATEMATICA I 1 10.0 10.0 061202 B,C ING-INF/05 INFORMATICA A 1 10.0 10.0 083217 A CHIM/07 CHIMICA 1 7.0 7.0 056951 A MAT/03 ALGEBRA LINEARE E GEOMETRIA 2 8.0 8.0 083024 A FIS/01 FISICA SPERIMENTALE I 2 10.0 10.0 056937 B ING-IND/35 ECONOMIA E ORGANIZZAZIONE AZIENDALE 2 7.0 7.0 083229 C SECS-S/01 STATISTICA 2 5.0 5.0 2 Year courses - Track: MTM - Ingegneria Matematica
Code Educational activities SSD Course Title Language Sem CFU CFU Group 096350 A MAT/05 ANALISI MATEMATICA II 1 10.0 10.0 083224 A FIS/01 FISICA SPERIMENTALE II 1 10.0 10.0 083223 B ING-IND/31 ELETTROTECNICA 1 10.0 10.0 052488 A,C MAT/08 MATEMATICA NUMERICA 2 10.0 [2.0]
10.0 085924 A MAT/06 PROBABILITA' 2 10.0 10.0 083225 B ING-INF/04 FONDAMENTI DI AUTOMATICA 2 10.0 10.0 3 Year courses - Track: MTM - Ingegneria Matematica
Code Educational activities SSD Course Title Language Sem CFU CFU Group 085925 A MAT/05 ANALISI MATEMATICA III 1 5.0 5.0 083220 C MAT/09 FONDAMENTI DI RICERCA OPERATIVA 1 5.0 5.0 052490 A MAT/07 MECCANICA RAZIONALE E DEI CONTINUI 1 10.0 [1.010.0 085930 B ING-INF/01 ELETTRONICA (a) 1 10.0 10.0 097575 C ING-IND/10 TERMODINAMICA E PROCESSI ENERGETICI (b) 1 10.0 -- -- -- Courses to be chosen from Group GRUPPO 1 -- -- -- 10.0 -- -- -- Courses to be chosen from Group GRUPPO 2 -- -- -- 20.0(c) 054068 -- -- PROVA FINALE (LP MTM) 1 3.0 [3.03.0 054068 -- -- PROVA FINALE (LP MTM) 2 3.0 [3.0(a) Distinctive for the class L-8 (Information Technology).
(b) Distinctive for the class L-9 (Industrial Engineering).
(c) Students who intend to continue in the MSc in Mathematical Engineering must select from GROUP 2 at least 20 ECTS of courses of the following SSDs: ICAR / 08, MAT / 05, MAT / 08, SEC-S / 01, SEC-S / 06, ING-IND / 17 and / or the subject Algoritmi e progetti per il calcolo ad alte prestazioni. Furthermore, the courses GESTIONE DEI SISTEMI LOGISTICI E PRODUTTIVI and Algoritmi e progetti per il calcolo ad alte prestazioni are mutually exclusive.Courses of the Group GRUPPO 1
Code Educational activities SSD Course Title Language Sem CFU 052491 C SECS-S/06 FINANZA MATEMATICA I 2 10.0 [2.0081076 A FIS/01 INTRODUZIONE ALLA FISICA DEI QUANTI 2 10.0 054067 A,C MAT/06
SECS-S/01MODELLI E METODI DELL'INFERENZA STATISTICA 2 10.0 [2.0078047 A,C MAT/05
MAT/08METODI ANALITICI E NUMERICI DELLE E.D.P. 2 10.0 Courses of the Group GRUPPO 2
Code Educational activities SSD Course Title Language Sem CFU 056978 -- -- STAGE (LP MTM) 1 10.0 056978 -- -- STAGE (LP MTM) 2 10.0 056974 B,C ING-INF/05 ALGORITMI E ARCHITETTURE PER IL CALCOLO AD ALTE PRESTAZIONI 2 10.0 052512 B,C ING-INF/05 BIOINFORMATICS ALGORITHMS 2 5.0 056338 B ING-INF/04 COMPLEMENTI DI CONTROLLI AUTOMATICI 2 5.0 052491 C SECS-S/06 FINANZA MATEMATICA I 2 10.0 [2.0086224 -- ING-IND/06 FLUIDODINAMICA 2 10.0 072363 B ING-IND/17 GESTIONE DEI SISTEMI LOGISTICI E PRODUTTIVI 2 10.0 081076 A FIS/01 INTRODUZIONE ALLA FISICA DEI QUANTI 2 10.0 088713 -- ING-IND/32 MACCHINE ELETTRICHE 2 5.0 062337 C ICAR/08 MECCANICA DEI SOLIDI E DELLE STRUTTURE 2 10.0 054076 B ING-INF/01 MICROCONTROLLORI 2 5.0 [3.0054067 A,C MAT/06
SECS-S/01MODELLI E METODI DELL'INFERENZA STATISTICA 2 10.0 [2.0088712 B ING-INF/01 OPTOELETTRONICA 2 5.0 099322 -- ING-INF/03 SEGNALI PER LE COMUNICAZIONI 2 10.0 086067 B,C ING-INF/05 ALGORITMI E PRINCIPI DELL'INFORMATICA 2 10.0 054293 B ING-INF/06 BIOMEDICAL SIGNAL PROCESSING AND MEDICAL IMAGES - BIOE 540-421 [I.C.] 2 10.0 [1.0078047 A,C MAT/05
MAT/08METODI ANALITICI E NUMERICI DELLE E.D.P. 2 10.0 It should be noted that students who opt for the L-8 degree class (Ingegneria dell'Informazione) in the second semester of the third year must include in their study plan at least 10 credits of one of the following SSD:
ICAR/08, ING-INF/05, SECS-S/01, SECS-S/06It should be noted that students who opt for the L-9 degree class (Ingegneria Industriale) in the second semester of the third year must include in their study plan one of the following two courses:
Scienza delle costruzioni (ICAR/08)
Gestione dei sistemi logistici e produttivi (ING-IND/17)7.3.1 Innovative education
Within the framework of the Innovative Education Programme promoted by the University 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
052488 – Numerical Mathematics
Obligatory
II Year
10 CFU
MND
2 CFU
052490 – Rational and Continuum Mechanics
Obligatory
III Year
10 CFU
MAP, MFO
1 CFU
052491 – Mathematical Finance I
Optional
III Year
10 CFU
MFO
2 CFU
054067 - Models and Methods for Statistical Inference Optional
III Year
10 CFU
MFO
2 CFU
054068 - Final Work 3 CFU
MAP, MFO
3 CFU
7.3.2 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:
Code
Educational activities
SSD
Course Title
Sem
CFU
CFU Group
085925
A
MAT/05
MATHEMATICAL ANALYSIS III
1
5.0
5.0
052490
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:
https://www.polimi.it/futuri-studenti/corsi-di-laurea-magistrale/nuclear-engineering-ingegneria-nucleare
7.3.3 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.
7.3.4 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:
- 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.
- 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.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:
https://www.ingindinf.polimi.it/en/1/teaching/lectures-and-exams/degree-examinations
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.
Students have the choice between two graduation exam procedures:
- Thesis (or final exam of type A) 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.
- Project (or final exam of type B): the student agrees with the teacher in charge of the final exam the activities to be followed (moos, seminars, ...) and the topic on ewhich the final project will be focused. The project will have to respond the requirements defined by the teacher in charge of the final examination and delivered to the same reference teacher within 30 days from the date of the graduation session to which the student inteds to participate. The maximum score is 5 points.
If the student's study plan includes an stage, the student must also send a short written report describing the activity carried out during the stage to the e-mail address tirocini-ingegneria-matematica@polimi.it within 30 days from the date of before the date graduation.
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 the following rules are enforced:
- 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).
- 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.
- Detailed rules to determine the final grade, possibily cum laude, will be made available to students in due time.
8. Academic calendar
On the web site of the School of Industrial and Information Engineering (https://www.ingindinf.polimi.it/en/) the Calendar of the current academic year can be downloaded. The general Academic Calendar of Politecnico is available at the following web site:
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: https://www.ingindinf.polimi.it/en/
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
https://www.polimi.it/en/campuses-and-services/international-mobility/study-abroad
while a detailed list of partner universities for exchange programmes may be found at
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):https://www.polimi.it/en/campuses-and-services/international-mobility/study-abroad
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.
13. Quantitative data
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
For any further information, please visit the website of the School of Industrial and Information Engineering
https://www.ingindinf.polimi.it/en/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/