1. General Information

School	School of Industrial and Information Engineering
Code Reference Law	487
Name	Mathematical Engineering
Reference Law	Ordinamento 270/04
Class of degree	LM-44 - Mathematical modelling for engineering
Degree level	Laurea Magistrale (Equivalent To Master Of Science)
First year of activation	2009/2010
Official length of the programme	2
Years of the programme already activated	1,2
Official language(s)	English
Campus	Milano
Dean of the School	Giovanni Gustavo Lozza
Coordinator of the Study programme	Maurizio Verri
Website of the School	http://www.ingindinf.polimi.it
Website of the Study programme	http://www.mate.polimi.it

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 intensive university curriculum which realizes a synergy between advanced mathematical methods and engineering mentality, and allows 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 problems by means of a number of courses ranging from physics to chemistry, to economics, to computer science. In addition, 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 he standard 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, on the contrary, 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 these attitudes in order to use the methodologies at his/her disposal choosing a level of depth and rigor adapted to the  significance and difficulty of the problem to be solved. Ideally, the mathematical engineer must 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

In coherence with the education objectives as of art. 3 of DM n. 270/2004, the distinction between BSc and MSc graduates relies in the acquirement of "an adequate mastership of methods and scientific general contents" (the B. Sc.) and of "an advanced education level to be employed in professional activities of a highly qualified level in specific contexts" (the M. Sc.).

The main objective of the Mathematical Engineering Program (MEP) is to prepare professionals able to analyze complex systems where it is required a strong interdisciplinary knowledge, 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 possibility 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. Clearly, during the program, the students can only be exposed to a limited number of such problems. However, the opportunity to examine a number of problems in depth, chosen among different sectors of Engineering, together with a solid mathematical and scientific grounding, gives future graduates a flexibility sufficient to deal professionally also with problems that are quite different from those studied.

In conclusion, the master of science mathematical engineer constitutes an innovative and flexible professional profile, endowed with a wide spectrum of basic scientific notions and engineering principles, together with a deep knowledge of modern pure and applied mathematical techniques oriented to the modeling, the analysis and the solution of complex systems, planning, control and management  problems.

4. Organization of the study programme and further studies

4.1 Structure of the study programme and Qualifications

The Master’s degree in Mathematical Engineering (reference Law DM 270/04) has a duration of  two years and requires 120 credits.  The Study Course Committee (CCS) proposes inside the teaching framework a number of Study Plans (PSPA) conferring a specialization track (Major) to a student. The following PSPAs are currently available:

• Computational Science and Engineering
• Applied Statistics
• Quantitative Finance

 

 

Inside each PSPA’s, the student may choose possible specific Applied Plans (PAA) proposed by the CCS and having the following characteristics:

• Each PAA is part of one of the three Majors tracks, but is more focused on a selected applied field and gives to the student a further specialization level 
• The PAAs are not officially inserted into the general teaching framework but their approval is guaranteed by the CCS.

 

 

The PAAs currently available can be found on the website http://www.mate.polimi.it/im 

The CCS may also take in consideration specific proposals of applied plans that lie outside the general indications of the CCS itself upon condition that such proposals are adequately motivated and that the basic rules of the CCS are fulfilled. The student interested in exploiting the above mentioned possibility is invited to contact the Commitee of Study Plans of the CCS (email: piani-LM-ingegneria-matematica@polimi.it).

 

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)

For the best students enrolled in BSc/MSc Programs, it is possible to be admitted to the Alta Scuola Politecnica, an advanced joint educational program organised by the Politecnico di Milano and Politecnico di Torino. For further information see: www.altascuolapolitecnica.it 

Achievement of Master Degree in Mathematical Engineering allows the access to the 3rd university education level, that is, the PhD (Dottorato di Ricerca). In this direction, a possible choice is represented by the Dottorato di Ricerca in Modelli e Metodi Matematici of Politecnico di Milano, that is activated at the Department of Mathematics. For further information, consult: www.mate.polimi.it/dottorato/.

A Second Master Degree

• A student having obtained the Master Degree in Mathematical Engineering can obtain also the  Master Degree in Mathematics at Università degli Studi di Milano-Bicocca by passing, as a basic rule, three exams (8 CFUs  each), to be agreed with the Committee of Study Plans of that Course, plus a degree  thesis (amounting to 40 CFUs).

• It is possible to obtain after a further year of study the Master Degree in Nuclear Engineering at Politecnico di Milano. In this degree project, it is assumed that the student obtained a Master Degree in Mathematical Engineering with PAA in Mathematical-Physical Modeling in Nuclear Applications (see Paragraph 4.1) and a thesis in the area of Nuclear Engineering. In such a case, the student needs to acquire an extra amount of 55 CFUs from courses within a time duration of a sixth year of study. In the Final Work (amounting to 15 CFUs) the student may avail him/herself of the thesis already discussed to obtain the Master Degree in Mathematical Engineering.

• It is possible to obtain after a further year of study the Master Degree in Civil Engineering at Politecnico di Milano. To this purpose, it is required that:
• The student has obtained a LM in Mathematical Engineering with a PAA in Structure Mechanics (see Paragraph 4.1) and a thesis in the area of Structural Analysis. In such a case, the student needs to acquire an extra amount of 57 CFUs from courses within a time duration of a sixth year of study. In the Final Work (amounting to 14 CFUs) the student may avail him/herself of the thesis already discussed to obtain the Master Degree in Mathematical Engineering.
• The student has obtained a Master Degree in Mathematical Engineering  with a PAA in Hydraulics (see  Paragraph 4.1) and a thesis in the area of Hydraulics/Fluid Mechanics. In such a case, the student needs to acquire an extra amount of 58 CFUs from courses within a time duration of a sixth year of study. In the Final Work (amounting to 14 CFUs) the student may avail him/herself of the thesis already discussed to obtain the Master Degree in Mathematical Engineering.

 

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.

5.2 Careers options and profiles

The flexibility and training to study different type of problems and to develop models carrying out both a priori analysis (physical, geometric or statistical)  and  a posteriori analysis oriented to graphical visualization and to results validation, as well as to implement mathematical algorithm with modern computing techniques, facilitate the Master of Science mathematical engineers the access also to  companies not requiring an initial  particular specialization level.

On the other hand there are also specialized professional sectors in  which a mathematical engineer could play a central role:

• Engineering firms with expertise in the treatment of complex computational problems, requiring a multidisciplinary knowledge, finalized to the discrete or continuous modelling and to the solution of the related numerical questions.
• Industrial companies, consultancy and/or management societies, whose activities require deep analysis, based on advanced mathematical methods.
• Service societies, banks, insurance companies, finance or consultant agencies  for the statistical interpretation  and the simulation of complex situations related to the analysis of large number of data (e.g. management and optimization of services, data mining, information retrieval)  or for handling  financial products and risk management.
• Public and private research centers.

 

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 to graduation.

For a statistical analysis of the professional employment relative of the mathematical engineers in the past years it is possible to consult the website (see also paragraph 13 below http://www.polimi.it/ateneo/organi-centrali/nucleo-di-valutazione

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

6. Enrolment

6.1 Access requirements

First cycle degree (level 6 EQF) or comparable qualification

In order to be admitted to the Master of Science Program in Mathematical Engineering candidates must meet precise  requirements, that is a preparation consistent with the above Degree’s study Program.  The BSc in Mathematical Engineering is used as a reference model to define this background knowledge. It may therefore be requested to the students to supplement their curriculum if the Bachelor Degree Program from which they have graduated is not sufficiently “consistent” with the study Program in Mathematical Engineering.

Thus, admission to the Master’s Degree (MSc) is subject to a process of evaluation of candidates’ career. This process, in accordance with the existing regulation (D.M. 22/10/2004 n. 270 art. 6 par. 2 and D.M. 16/3/2007, art.6 par. 1), verifies possession of required curriculum qualifications and adequacy of personal preparation. Admission to the MSc Program is decided by an Evaluation  Board appointed by the CCS.

In case of admission, possible limitations and/or curriculum integration (see Paragraph 6.2) will be communicated before enrolment in order to provide the necessary information to the student to make a rational 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

Bachelor Degree in Mathematical Engineering at the Politecnico di Milano

The curriculum requirements are automatically fulfilled for B. Sc. graduates with PSPA MFO-Propedeutic. In case of admission to the LM, and in order to recover the CFUs devoted to stage activity, the B. Sc. graduates with PSPA MAP-Applied will have to provide a curriculum integration of 15 CFU by choosing courses for a total amount of 15 CFUs (see § 6.1.1.1). Also for B. Sc. graduates with an autonomous study plan, the fulfillment of curriculum requirements may result in a possible course integration. CFUs of courses of LM that have been acquired during the B. Sc. and exceeding the minimum amount of 180 or that have been acquired through “single courses” of university level may be validated as well up to a maximum amount of 30 CFUs.

Bachelor degree in Mathematical Engineering obtained by 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 up to a maximum of 30 credits.

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

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

 

6.1.1.1 Curricula integrations.

In the case of curriculum integration assigned to a student, during the period between the Bachelor degree acquisition and the enrolment into the M. Sc Program, the student can:

• A1)  acquire credits by registering to single courses from the M. Sc program and passing the relative 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 M. Sc program.
• A3)  earn credits from courses assigned as curriculum integration by the Evaluation Board: these credits must be added to the regular 120 credits needed for the M. Sc degree.

 

The following limitations are to be taken into consideration:

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) 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.

6.1.2 Preparation level

For students possessing:

• a) a Bachelor Degree in Mathematical Engineering at the Politecnico di Milano:
  Admission to the MSc program, is automatic without any other requirement, if at the time of enrolling into the third year of the Bachelor the candidate has acquired at least 110 credits with an average score greater than equal to 25/30 and if the Bachelor degree has been obtained within 4 academic years from the initial enrolment (see note box).
  
  
• b)  any of the other categories of Bachelor degrees:
  Admission is possible only if the candidate has achieved a final score greater than equal to 85/110 in the final Bachelor exam. If this score is greater than equal to 85/110, the Evaluation Board will examine the candidate’s curriculum and her/his attitude also through  a possible individual colloquium.
  
  
• c) another MSc or equivalent degree:
  The Evaluation Board will examine the complete candidate’s. Job experience are not valid for acquisition of credits.

 

Note

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

 

6.2 Requested knowledge

To access the Master of Science in Mathematical Engineering, the candidate must possess specific curricular requirements, as detailed in the previous paragraph, or a knowledge  background consistent with the educational program of the  Bachelor of Science in Mathematical Engineering. Therefore, curricular supplements may be necessary if the Bachelor of Science obtained by the candidate does not present a sufficient degree of "consistency" with the educational program of the Master of Science in Mathematical Engineering.

In all cases in which it is necessary, an ad hoc examination of curricula will take place to ensure that candidates are admitted only if they meet the requirements of "consistency" with the educational program of the Bachelor of Science, possibly achieved through a curricular supplement plan.

6.2.1 Educational obligations

Admission to the Master of Science can be resolved with the assignment of educational obligations in the choice of curricula, that is, assigning obligations or prohibitions concerning the study plan to be presented. Any obligations imposed will be communicated together with the positive assessment of admission and before enrolment, so as to provide students with the necessary information for the preparation of their study plan.

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

6.3 Deadlines for admission and number of places available

At the Politecnico di Milano, admission to the Master of Science Program is possible in both the first and second semester.

The career evaluation application must be submitted within the established time limits even by those who are automatically admitted on the basis of the criteria explained in Paragraph 6.1.2.  Positive evaluation of the application is only valid for the semester in which it has been submitted.

Specific information on admission to the Master’s Degree in Mathematical Engineering must be submitted to the following e-mail address ammissioni-LM-ingegneria-matematica@polimi.it

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

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.

As specified in the Academic Regulation, 120 credits are required to obtain the MSc degree.

 The LM-44 Degree Class sets the following restrictions on the Program-specific modules:

• no less than 18 credits in mathematics, physics and computer science studies (modules MAT/02, 03, 05, 06, 07, 08 , 09; FIS/01, 02, 03, 04; INF/01)
• no less than 27 credits in the engineering subjects (modules ICAR/01, 08; ING-IND/06, 10, 13, 18, 22, 31; ING-INF/01, 02, 04, 05)
  
  

For further details on the Class LM-44, consult the following website

http://www.cun.it/media/77608/lauree_magistrali.pdf

7.2 Mode of study

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

Full time Program includes participation in courses with lessons and exercises, compulsory Laboratory activity, Seminars and visits.

7.3 Detailed learning objectives

The next pages  describe the Major Study Plans (PSPA) for the academic year 2014/15.

 As already mentioned in Par. 4.1, the CCS offers a certain amount of PSPAs, which characterize the specialization (Major).

In each Major the 120 credits are divided according to the following courses categories:

 

Code	Category of course	CREDITS
OB	Mandatory for all students	18
MA	Mandatory  for a specific major	30
MA	Major courses	30
ING	Engineering	20
MTM	Choice from table MTM (Mathematics)	24
SC	Choice from table SC	16
	subtotal CREDITS	108
	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
095958	B	MAT/05	REAL AND FUNCTIONAL ANALYSIS			1	8,0	8,0
095959	B	ING-INF/05	ALGORITHMS AND PARALLEL COMPUTING			1	10,0	10,0
--	--	--	Courses to be chosen from Group ING		--	--	--	10,0
095963	B	MAT/05	ADVANCED PARTIAL DIFFERENTIAL EQUATIONS			2	8,0	8,0
095964	B,C	MAT/08	NUMERICAL ANALYSIS FOR PARTIAL DIFFERENTIAL EQUATIONS			2	10,0	10,0
--	--	--	Courses to be chosen from Group MOX		--	--	--	10,0

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

Code	Educational activities	SSD	Course Title		Language	Sem	CFU	CFU Group
097634	B,C	MAT/07 MAT/08	COMPUTATIONAL FLUID DYNAMICS [C.I.]			1	10,0	10,0
095962	B	ICAR/01	FLUIDS LABS			1	10,0	10,0
--	--	--	Courses to be chosen from Group MTM		--	--	--	8,0
--	--	--	Courses to be chosen from Group MTM		--	--	--	8,0
--	--	--	Courses to be chosen from Group FREE		--	--	--	8,0
--	--	--	Courses to be chosen from Group FREE		--	--	--	8,0
097690	--	--	FINAL WORK		--	1	12,0	12,0
097690	--	--	FINAL WORK		--	2	12,0

1 Year courses - Track: MMF - Quantitative Finance

Code	Educational activities	SSD	Course Title		Language	Sem	CFU	CFU Group
095958	B	MAT/05	REAL AND FUNCTIONAL ANALYSIS			1	8,0	8,0
095959	B	ING-INF/05	ALGORITHMS AND PARALLEL COMPUTING			1	10,0	10,0
095975	B	MAT/06	STOCHASTIC DIFFERENTIAL EQUATIONS			1	8,0	8,0
095981	C	SECS-S/06	MATHEMATICAL FINANCE II			2	10,0	10,0
095982	C	SECS-S/06	FINANCIAL ENGINEERING			2	10,0	10,0
096297	B	ING-INF/04	MODEL IDENTIFICATION AND DATA ANALYSIS			1	10,0	10,0
089234	B	ING-INF/04	IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI			2	10,0
--	--	--	Courses to be chosen from Group FREE		--	--	--	8,0

2 Year courses - Track: MMF - Quantitative Finance

Code	Educational activities	SSD	Course Title		Language	Sem	CFU	CFU Group
097658	B,C	MAT/08 SECS-S/06	COMPUTATIONAL FINANCE			1	10,0	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 MTM		--	--	--	8,0
--	--	--	Courses to be chosen from Group FREE		--	--	--	8,0
097690	--	--	FINAL WORK		--	1	12,0	12,0
097690	--	--	FINAL WORK		--	2	12,0

1 Year courses - Track: MST - Applied Statistics

Code	Educational activities	SSD	Course Title		Language	Sem	CFU	CFU Group
095958	B	MAT/05	REAL AND FUNCTIONAL ANALYSIS			1	8,0	8,0
095959	B	ING-INF/05	ALGORITHMS AND PARALLEL COMPUTING			1	10,0	10,0
095966	B	MAT/06	STOCHASTIC DYNAMICAL MODELS			1	8,0	8,0
095967	C	SECS-S/01	APPLIED STATISTICS			2	10,0	10,0
096297	B	ING-INF/04	MODEL IDENTIFICATION AND DATA ANALYSIS			1	10,0	10,0
089234	B	ING-INF/04	IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI			2	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
097659	B,C	MAT/06 SECS-S/01	BAYESIAN STATISTICS			1	10,0	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		--	1	12,0	12,0
097690	--	--	FINAL WORK		--	2	12,0

Courses of the Group FREE

Code	Educational activities	SSD	Course Title	Language	Sem	CFU
095978	--	ING-INF/03	AUDIO AND VIDEO SIGNALS		1	8,0
097667	B,C	MAT/08 SECS-S/06	COMPUTATIONAL FINANCE		1	8,0
097482	C	ING-IND/16	DESIGN AND ANALYSIS OF EXPERIMENTS A		1	8,0
095973	B	MAT/05	DISCRETE DYNAMICAL MODELS		1	8,0
095974	B	MAT/05	GAME THEORY		1	8,0
098637	--	GEO/11	GEOPHYSICAL DATA PROCESSING		1	8,0
097660	B,C	MAT/07	METHODS AND MODELS FOR STATISTICAL MECHANICS		1	8,0
097670	B	FIS/03	PLASMA PHYSICS		1	8,0
098516	B,C	MAT/08 SECS-S/01	NUMERICAL AND STATISTICAL METHODS IN GEOSCIENCES		1	10,0
095976	B,C	MAT/08	ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING		2	8,0
095977	C	SECS-S/01	APPLIED STATISTICS		2	8,0
097661	B,C	MAT/07	BIOMATHEMATICAL MODELING		2	8,0
097673	B	MAT/05	CALCULUS OF VARIATIONS(a)		2	8,0
096659	B,C	MAT/08	COMPUTATIONAL MODELING IN ELECTRONICS AND BIOMATHEMATICS		2	8,0
097676	B	ING-INF/05	ECONOMICS AND COMPUTATION		2	6,0
098512	--	ICAR/09	ENGINEERING SEISMOLOGY		2	8,0
088933	B	FIS/01	FISICA QUANTISTICA		2	8,0
098513	B	ICAR/01	GROUNDWATER HYDRAULICS		2	8,0
095980	C	SECS-S/06	MATHEMATICAL FINANCE II		2	8,0
098388	C	SECS-S/06	MATHEMATICAL MODELS AND METHODS FOR FINANCIAL AND INSURANCE MARKETS		2	8,0
095972	B,C	MAT/09	OPTIMIZATION		2	8,0
097662	B	MAT/06	STOCHASTIC OPTIMAL CONTROL		2	8,0

^(a) Course offered every other year, active for the Academic Year 2015/2016

Courses of the Group ING

Code	Educational activities	SSD	Course Title	Language	Sem	CFU
085930	B	ING-INF/01	ELETTRONICA		1	10,0
096297	B	ING-INF/04	MODEL IDENTIFICATION AND DATA ANALYSIS		1	10,0
097575	B	ING-IND/10	TERMODINAMICA E PROCESSI ENERGETICI		1	10,0
089195	B	ING-INF/04	DINAMICA DEI SISTEMI COMPLESSI		1	10,0
095962	B	ICAR/01	FLUIDS LABS		1	10,0
089234	B	ING-INF/04	IDENTIFICAZIONE DEI MODELLI E ANALISI DEI DATI		2	10,0

Courses of the Group MOX

Code	Educational activities	SSD	Course Title	Language	Sem	CFU
095965	B,C	MAT/08	ADVANCED PROGRAMMING FOR SCIENTIFIC COMPUTING		2	10,0
097725	B,C	MAT/07	MATHEMATICAL AND PHYSICAL MODELING IN ENGINEERING [C.I.]		2	10,0

Courses of the Group MTM

Code	Educational activities	SSD	Course Title	Language	Sem	CFU
095973	B	MAT/05	DISCRETE DYNAMICAL MODELS		1	8,0
095974	B	MAT/05	GAME THEORY		1	8,0
097660	B,C	MAT/07	METHODS AND MODELS FOR STATISTICAL MECHANICS		1	8,0
095975	B	MAT/06	STOCHASTIC DIFFERENTIAL EQUATIONS		1	8,0
095966	B	MAT/06	STOCHASTIC DYNAMICAL MODELS		1	8,0
095963	B	MAT/05	ADVANCED PARTIAL DIFFERENTIAL EQUATIONS		2	8,0
097661	B,C	MAT/07	BIOMATHEMATICAL MODELING		2	8,0
095972	B,C	MAT/09	OPTIMIZATION		2	8,0
097662	B	MAT/06	STOCHASTIC OPTIMAL CONTROL		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
089167	B	ING-INF/05	DATA MINING AND TEXT MINING (UIC 583)		2	5,0
097683	B	ING-INF/05	MACHINE LEARNING		2	5,0
091754	C	ING-IND/19	COMPUTATIONAL METHODS FOR SAFETY AND RISK ANALYSIS A+B		2	10,0

7.3.1 Correspondences relating to courses available in previous years

code	Deleted course	CFU	code	Equivalent course	CFU
089038	Digital Signal Processing  2	10	093267	Digital Signal Processing	10

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/studenti/guide/.

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 Regulations for final graduation exams  approved by the Executive Committee of the School in  the  meeting of 09/10/2013: .

http://www.ingindinf.polimi.it/cms/file/12396/RegolamentoProvaFinale.pdf

In relation to these norms and, according to the specific needs and peculiarities of the Master Degree Program, the Mathematical Engineering Program Board has introduced a number of integrations, approved by the School, that are contained in the document:

http://www.ingindinf.polimi.it/cms/file/12396/Reg-Int_L-LM-MTM.pdf

A synthesis of such regulations is reported below:

1. The subject of the Master Degree Thesis is chosen by the student upon agreement with a teacher of Politecnico who acts as Supervisor.
2. If the student intends to conduct the work on the dissertation at another University or external Institution, he/she must obtain prior consensus from the President of the Study Program Board, who will appoint an internal supervisor within the Politecnico. The 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 discussion during the graduation dissertation.
3. The dissertation may not have more than 2 authors. In the event of presentation at separate sessions, the work must be discussed by the second candidate within the next two sessions successive to that of the first discussion.
4. As a basic rule, dissertations do not require an external critical report. Upon request of the Supervisor, who recognizes that the thesis is of particular significance, the President of the Study Program will appoint an external Examiner. The Examiner is required to send a written report to the secretary of the graduation board, unless he/she will be present at the graduation dissertation.
5. A copy of the dissertation must be submitted to the Mathematics Department Student Office one day prior to the graduation session.
6. The maximum score attributed to the final examination during graduation is of 4 points (5 points in exceptional cases) in the case of a dissertation without Examiner, while it is of 7 points (8 points in exceptional cases) in the case of a dissertation with Examiner.

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

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 professors for each Course, will be available on the degree program, yearly published on the website of the 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:
Master of Science Admissions	ammissioni-LM-ingegneria-matematica@polimi.it
Study Plans (Master of Science degree)	piani-LM-ingegneria-matematica@polimi.it
Erasmus program and international exchanges	erasmus-dmat@polimi.it
Stages	tirocini-ingegneria-matematica@polimi.it
Final Exam Secretary	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 into 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. 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 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 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 modelling and to the quantitative aspects of Finance are present in curricula of several European engineering schools. We mention the Finanz Mathematik 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.

 

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 through an international experience promoted by the Politecnico, the M.Sc. Program favourably considers proposals by students who intend to spend a period by a foreign University (normally one semester), as part of the various international agreements. Foreign exchange proposals put forward by students are submitted for preliminary approval to a special committee of the Study Program Board.

The international exchange programs 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).

Details regarding international exchange in which the Mathematical Engineering Program is involved can be found at http://www.mate.polimi.it/im/

For further information, contact erasmus-dmat@polimi.it

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

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 of Industrial and Information Engineering website (http://www.ingindinf.polimi.it) and on the Degree Program website (http://www.mate.polimi.it/im/).

15. Errata corrige