Mathematics (Classe LM-40)-Enrolled from 2012/13
The main objective of the Master Degree Program in Mathematics is to furnish a solid foundation in the mathematical sciences, including the knowledge of the state of the art in at least one research area. The degree recipient will be able to comprehend future developments in the field.
The Master Degree in Mathematics enables employment in both the public and private sectors for positions which require the capacity for abstract reasoning, the formulation and/or modelling of concrete problems and their solution through the use of tools coming from the mathematical sciences.
Recipients of the Masters Degree in Mathematics find careers in: banks, insurance companies, polling and survey institutes, consulting and accrediting firms, software development companies, medical, biomedical and pharmacological institutes and companies, in the green economy, and in research and development divisions of large corporations, as well as transportation, telecommunication, and aerospace companies and in other high tech industries.
Recipients of the Masters Degree can also plan for a teaching career in the public school system, upon completion of the educational certification and selection process established by law.
Employment statistics (Almalaurea)
Recipients of the Masters Degree in Mathematics find careers in: banks, insurance companies, polling and survey institutes, consulting and accrediting firms, software development companies, medical, biomedical and pharmacological institutes and companies, in the green economy, and in research and development divisions of large corporations, as well as transportation, telecommunication, and aerospace companies and in other high tech industries.
Recipients of the Masters Degree can also plan for a teaching career in the public school system, upon completion of the educational certification and selection process established by law.
Employment statistics (Almalaurea)
Requisiti e conoscenze richieste per l'accesso
- Lo studente deve essere in possesso di un titolo di studio universitario di durata triennale conseguito in una classe di area scientifica coerente con il piano di studi della LM classe 40, ovvero di altro titolo di studio conseguito anche all'estero e riconosciuto idoneo in base alla normativa vigente.
- Lo studente deve aver maturato una buona conoscenza di base della matematica, conoscenze di base della fisica e dell'informatica. Per orientare gli studenti il CDM ha preparato una lista di contenuti la cui conoscenza è ritenuta opportuna per l'iscrizione al corso di Laurea Magistrale in Matematica. Tale lista è disponibile sul sito https://matematica-lm.cdl.unimi.it/it/iscriversi
Modalità di verifica delle conoscenze e della preparazione personale:
Per essere ammessi al corso di laurea magistrale in Matematica è necessario presentare apposita domanda di ammissione (consultare il link: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/iscriversi/corsi-magistrali-biennali/magistrali-ad-accesso-libero).
Si sconsiglia la presentazione della domanda di ammissione a quegli studenti che alla data del 14 settembre 2021 siano in difetto di più di 40 CFU rispetto ai 180 richiesti per il conseguimento della Laurea triennale.
Gli studenti del corso di Laurea Triennale in Matematica dell'Università degli Studi di Milano che avranno conseguito un punteggio di laurea di almeno 95/110 saranno esonerati dalla verifica del possesso dei requisiti curriculari e dell'adeguatezza della preparazione personale.
Le domande d'accesso saranno vagliate da un'apposita Commissione del Collegio Didattico di Matematica (CDM), che si riunirà almeno due volte all'anno. La commissione potrà basarsi anche solo sulla documentazione presentata dai candidati, ma di norma convocherà gli studenti (che dovranno presentarsi con un documento d' identità valido con foto).
Le date del colloquio saranno:
18 giugno 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
17 settembre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
11 ottobre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica) 15 novembre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
10 gennaio 2022 Sala Rappresentanza Dipartimento di Matematica
L'orario verrà pubblicato in seguito.
Tale Commissione, potrà decidere:
a) di ammettere il richiedente senza alcun vincolo;
b) di ammettere il richiedente con prescrizioni sull'inserimento nel suo piano degli studi di determinati insegnamenti (eventualmente afferenti ad una laurea triennale). Tali eventuali prescrizioni sono sempre nell'ambito dei 120 CFU per il conseguimento del titolo e non costituiscono un debito formativo per il richiedente;
c) di non ammettere il richiedente.
- Lo studente deve essere in possesso di un titolo di studio universitario di durata triennale conseguito in una classe di area scientifica coerente con il piano di studi della LM classe 40, ovvero di altro titolo di studio conseguito anche all'estero e riconosciuto idoneo in base alla normativa vigente.
- Lo studente deve aver maturato una buona conoscenza di base della matematica, conoscenze di base della fisica e dell'informatica. Per orientare gli studenti il CDM ha preparato una lista di contenuti la cui conoscenza è ritenuta opportuna per l'iscrizione al corso di Laurea Magistrale in Matematica. Tale lista è disponibile sul sito https://matematica-lm.cdl.unimi.it/it/iscriversi
Modalità di verifica delle conoscenze e della preparazione personale:
Per essere ammessi al corso di laurea magistrale in Matematica è necessario presentare apposita domanda di ammissione (consultare il link: https://www.unimi.it/it/studiare/frequentare-un-corso-di-laurea/iscriversi/corsi-magistrali-biennali/magistrali-ad-accesso-libero).
Si sconsiglia la presentazione della domanda di ammissione a quegli studenti che alla data del 14 settembre 2021 siano in difetto di più di 40 CFU rispetto ai 180 richiesti per il conseguimento della Laurea triennale.
Gli studenti del corso di Laurea Triennale in Matematica dell'Università degli Studi di Milano che avranno conseguito un punteggio di laurea di almeno 95/110 saranno esonerati dalla verifica del possesso dei requisiti curriculari e dell'adeguatezza della preparazione personale.
Le domande d'accesso saranno vagliate da un'apposita Commissione del Collegio Didattico di Matematica (CDM), che si riunirà almeno due volte all'anno. La commissione potrà basarsi anche solo sulla documentazione presentata dai candidati, ma di norma convocherà gli studenti (che dovranno presentarsi con un documento d' identità valido con foto).
Le date del colloquio saranno:
18 giugno 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
17 settembre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
11 ottobre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica) 15 novembre 2021: Sala Rappresentanza Dipartimento di Matematica (o eventualmente in modalità telematica)
10 gennaio 2022 Sala Rappresentanza Dipartimento di Matematica
L'orario verrà pubblicato in seguito.
Tale Commissione, potrà decidere:
a) di ammettere il richiedente senza alcun vincolo;
b) di ammettere il richiedente con prescrizioni sull'inserimento nel suo piano degli studi di determinati insegnamenti (eventualmente afferenti ad una laurea triennale). Tali eventuali prescrizioni sono sempre nell'ambito dei 120 CFU per il conseguimento del titolo e non costituiscono un debito formativo per il richiedente;
c) di non ammettere il richiedente.
The Master of Science in Mathematics has long been committed to insert its educational activities in an international framework through integrated programs of study. We activated several international cooperation agreements with other universities in Europe and in the world (in Canada, South Africa and India).
The programs ALGANT, Master in Algebra, Geometry and Number Theory, and ECMI, Master in Industrial Mathematics, programs are unique in Europe for pure and industrial mathematics.
These programs are supported by international university consortia and are targeted to the conferment of academic value recognized abroad (that is double degrees) and to the promotion of European higher education. For more information see the institutional web pages
http://www.algant.eu/
http://www.ecmi-indmath.org/
Moreover, in the Erasmus program, we have exchange agreements with universities Austria, Britain, Czech Blind, Denmark , Finland, France, Germany, Holland , Norway, Polonia, Portugal, Romania, Slovenia, Spain, Sweden.
See the website http://users.unimi.it/erasmusmat/ for information collected on the various programs of internationalization and the activities carried out abroad.
The programs ALGANT, Master in Algebra, Geometry and Number Theory, and ECMI, Master in Industrial Mathematics, programs are unique in Europe for pure and industrial mathematics.
These programs are supported by international university consortia and are targeted to the conferment of academic value recognized abroad (that is double degrees) and to the promotion of European higher education. For more information see the institutional web pages
http://www.algant.eu/
http://www.ecmi-indmath.org/
Moreover, in the Erasmus program, we have exchange agreements with universities Austria, Britain, Czech Blind, Denmark , Finland, France, Germany, Holland , Norway, Polonia, Portugal, Romania, Slovenia, Spain, Sweden.
See the website http://users.unimi.it/erasmusmat/ for information collected on the various programs of internationalization and the activities carried out abroad.
La frequenza alle attività didattiche di ogni singolo insegnamento è fortemente consigliata.
Courses list
Conclusive activities
There are no specific sessions for these activities (e.g. open online courses).
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
First semester
Second semester
Optional activities and study plan rules
a1 - CHARACTERIZING ACTIVITIES: 57 ECTS
Students must obtain at least 18 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 1A.
Students must obtain at least 18 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 1A.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Algebraic Number Theory | 9 | 73 | Italian | Second semester | MAT/02 |
| Algebraic Topology | 9 | 73 | Italian | First semester | MAT/03 |
| Commutative Algebra | 9 | 73 | Italian | First semester | MAT/02 |
| Complements of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Complex Geometry(FIRST PART) | 6 | 42 | Italian | Second semester | MAT/03 |
| Complex Manifolds | 9 | 73 | Italian | First semester | MAT/03 |
| Didactics of Geometry (first part) | 6 | 47 | Italian | Second semester | MAT/04 |
| Didactics of Infinitesimal Calculus (first part) | 6 | 42 | Italian | Second semester | MAT/04 |
| Differential Geometry (FIRST PART) | 6 | 42 | Italian | First semester | MAT/03 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| Mathematical Logic 1 | 9 | 63 | Italian | First semester | MAT/01 |
| Mathematical Methods in Quantum Mechanics | 6 | 42 | Italian | First semester | MAT/07 |
| Numerical Methods for Partial Differential Equations 1 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Relativity 1 | 9 | 78 | Italian | Second semester | MAT/07 |
| Representation Theory | 9 | 73 | Italian | First semester | MAT/02 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | Second semester | MAT/06 |
a2 - Students must obtain at least 12 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 2A.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Mathematical Statistics | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Complex Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Stochastics Calculus | 6 | 47 | Italian | First semester | MAT/06 |
| Algebra 4 | 6 | 60 | Italian | Second semester | MAT/02 |
| Algebraic Combinatorics | 6 | 42 | Italian | First semester | MAT/02 |
| Algebraic Surfaces | 6 | 42 | Italian | Second semester | MAT/03 |
| Analytic Number Theory | 6 | 42 | English | Second semester | MAT/05 |
| Automated Reasoning | 6 | 52 | Italian | Second semester | MAT/01 |
| Biomathematics 1 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Category Theory | 6 | 42 | Italian | First semester | MAT/01 MAT/02 MAT/03 MAT/04 |
| Celestial Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Computability and Computational Complexity | 6 | 42 | Italian | First semester | INF/01 |
| Differential Topology | 6 | 42 | Italian | Second semester | MAT/03 |
| Dynamical System 2 | 6 | 42 | Italian | First semester | MAT/07 |
| Elementary Mathematics from an Advanced Standpoint 1 | 6 | 42 | Italian | First semester | MAT/04 |
| Epistemology of the Mathematical Processes | 6 | 42 | Italian | Second semester | MAT/01 MAT/04 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry 5 | 9 | 78 | Italian | First semester | MAT/03 |
| Geometry of Schemes (first part) | 6 | 42 | Italian | First semester | MAT/03 |
| Higher Geometry 1 | 6 | 42 | Italian | Second semester | MAT/03 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Homological Algebra | 6 | 42 | Italian | Second semester | MAT/02 |
| Homotopical Algebra | 6 | 42 | English | Second semester | MAT/02 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Mathematical Economics 1 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Mathematical Logic 2 | 6 | 42 | Italian | Second semester | MAT/01 |
| Mathematics Education | 6 | 42 | Italian | First semester | MAT/04 |
| Non Linear Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 3 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Optimization | 6 | 52 | Italian | Second semester | MAT/08 |
| Operating Systems and Computer Networks. | 6 | 47 | Italian | Second semester | INF/01 |
| Point Processes and Random Sets | 6 | 42 | Italian | Second semester | MAT/06 |
| Preparation of Didactical Experiences 1 | 6 | 52 | Italian | First semester | FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08 |
| Preparation of Future Teachers 2 | 6 | 52 | Italian | Second semester | FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08 |
| Projective Algebraic Geometry | 6 | 42 | Italian | First semester | MAT/03 |
| Riemannian Geometry | 6 | 47 | Italian | Second semester | MAT/03 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
a3 - Students must obtain at least 6 ects in the sectors Mat/06-07-08-09, by choosing courses that appear in Tables 1A and 2A.
a4 - Students must obtain the ects remaining to reach the total of 57 by choosing courses in any sector Mat/xx among those appearing in Tables 1A,2A,1B,2B,1C,2C.
a5 - COMPLEMENTARY ACTIVITIES: 12 ECTS
Students must take at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf. The choice must be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx. The choice must be approved by the CDM.
Students must take at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf. The choice must be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx. The choice must be approved by the CDM.
a6 - ADDITIONAL TRAINING ACTIVITIES: 3 ECTS
Students must obtain 3 ects preparing a seminar on a topic assigned by a staff member chosen by the student or by participating in other activities such as those provided for curriculum C or by doing the exam of the course "Mathematical Modelling Laboratory"or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python"(Contact Prof. Paleari); students can also obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
Students must obtain 3 ects preparing a seminar on a topic assigned by a staff member chosen by the student or by participating in other activities such as those provided for curriculum C or by doing the exam of the course "Mathematical Modelling Laboratory"or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python"(Contact Prof. Paleari); students can also obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
a7 - FREE CHOICE ECTS : students must take the missing ects to reach 90 ects, by following free choice courses.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
Non ci sono propedeuticità.
First semester
Second semester
Conclusive activities
There are no specific sessions for these activities (e.g. open online courses).
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
Optional activities and study plan rules
b1 - CHARACTERIZING ACTIVITIES: 57 ECTS
Students must obtain at least 9 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 1B.
Students must obtain at least 9 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 1B.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Mathematical Statistics | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Complements of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Didactics of Geometry (first part) | 6 | 47 | Italian | Second semester | MAT/04 |
| Didactics of Infinitesimal Calculus (first part) | 6 | 42 | Italian | Second semester | MAT/04 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| Mathematical Finance 1 | 9 | 73 | English | First semester | SECS-S/06 |
| Mathematical Methods in Quantum Mechanics | 6 | 42 | Italian | First semester | MAT/07 |
| Numerical Methods for Partial Differential Equations 1 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Relativity 1 | 9 | 78 | Italian | Second semester | MAT/07 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | Second semester | MAT/06 |
b2 - Students must obtain at least 6 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 2B, or in the previous table 1B.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Complex Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Stochastics Calculus | 6 | 47 | Italian | First semester | MAT/06 |
| Algebra 4 | 6 | 60 | Italian | Second semester | MAT/02 |
| Biomathematics 1 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Celestial Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Computability and Computational Complexity | 6 | 42 | Italian | First semester | INF/01 |
| Cytology and Histology | 9 | 78 | Italian | First semester | BIO/06 |
| Decision Methods and Models | 6 | 48 | English | First semester | MAT/09 |
| Dynamical System 2 | 6 | 42 | Italian | First semester | MAT/07 |
| Ecology | 9 | 80 | Italian | First semester | BIO/07 |
| Elementary Mathematics from an Advanced Standpoint 1 | 6 | 42 | Italian | First semester | MAT/04 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| General Physiology and Animal Physiology | 9 | 80 | Italian | Second semester | BIO/09 |
| Genetics | 9 | 80 | English | First semester | BIO/18 |
| Geometry 5 | 9 | 78 | Italian | First semester | MAT/03 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Logistics | 6 | 48 | English | Second semester | MAT/09 |
| Mathematical Economics 1 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Mathematical Finance 2 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Mathematical Modelling Laboratory | 6 | 72 | Italian | Second semester | MAT/06 MAT/07 MAT/08 MAT/09 |
| Mathematics Education | 6 | 42 | Italian | First semester | MAT/04 |
| Molecular Biology and Bioinformatics | 12 | 96 | Italian | Second semester | BIO/11 |
| Non Linear Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 3 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Optimization | 6 | 52 | Italian | Second semester | MAT/08 |
| Operating Systems and Computer Networks. | 6 | 47 | Italian | Second semester | INF/01 |
| Operations Research | 6 | 48 | Italian | Second semester | MAT/09 |
| Point Processes and Random Sets | 6 | 42 | Italian | Second semester | MAT/06 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
b3 - Students must obtain at least 12 ects in the sectors Mat/06-07-08-09, by inserting in their curriculum courses that appear in Table 1B.
b4 - Students must obtain at least 12 ects in the sectors Mat/06-07-08-09, by choosing courses that appear in Table 2B.
b5 - Students must obtain the remaining ects for the achievement of 57 ects by choosing courses in any sector Mat/xx through the entries in Tables 1A,2A,1B,2B,1C,2C.
b6 - COMPLEMENTARY ACTIVITIES: 12 ECTS
Students must obtain at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf. The choice must be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx. The choice must be approved by the CDM.
Students must obtain at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf. The choice must be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx. The choice must be approved by the CDM.
b7 - ADDITIONAL TRAINING ACTIVITIES: 3 ECTS
Students must obtain 3 ects by preparing a seminar on a topic assigned by a staff member chosen by the student or by partecipating in other activities such as those provided for curriculum C or by doing the exam of the course "Mathematical Modelling Laboratory" or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python" (Contact Prof. Paleari); students can also obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
Students must obtain 3 ects by preparing a seminar on a topic assigned by a staff member chosen by the student or by partecipating in other activities such as those provided for curriculum C or by doing the exam of the course "Mathematical Modelling Laboratory" or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python" (Contact Prof. Paleari); students can also obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
b8 - FREE CHOICE ECTS: students must take the missing ects to reach 90 ects, by following free choice courses.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
Non ci sono propedeuticità.
Conclusive activities
There are no specific sessions for these activities (e.g. open online courses).
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
First semester
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Advanced Mathematical Statistics | 9 | 78 | Italian | MAT/06 |
| Advanced Probability | 9 | 78 | Italian | MAT/06 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | SECS-S/06 |
| Biomathematics 1 | 6 | 42 | Italian | MAT/07 |
| Combinatorial Optimization | 6 | 48 | English | MAT/09 |
| Decision Methods and Models | 6 | 48 | English | MAT/09 |
| Dynamical System 2 | 6 | 42 | Italian | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | MAT/05 |
| Fourier Analysis | 6 | 42 | Italian | MAT/05 |
| Geometry 5 | 9 | 78 | Italian | MAT/03 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | MAT/07 |
| Mathematical Finance 1 | 9 | 73 | English | SECS-S/06 |
| Mathematical Methods in Quantum Mechanics | 6 | 42 | Italian | MAT/07 |
| Non Linear Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Numerical Methods for Partial Differential Equations 1 | 9 | 78 | Italian | MAT/08 |
| Numerical Methods for Partial Differential Equations 3 | 9 | 78 | Italian | MAT/08 |
| Real Analysis | 9 | 73 | Italian | MAT/05 |
| Stochastic Control Optimization | 6 | 47 | Italian | MAT/06 |
Second semester
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Advanced Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Advanced Topics in Complex Analysis | 6 | 42 | Italian | MAT/05 |
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Complex Analysis | 9 | 73 | Italian | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| General Physiology and Animal Physiology | 9 | 80 | Italian | BIO/09 |
| Logistics | 6 | 48 | English | MAT/09 |
| Mathematical Economics 1 | 6 | 42 | Italian | SECS-S/06 |
| Mathematical Finance 2 | 6 | 42 | Italian | SECS-S/06 |
| Numerical Linear Algebra | 6 | 60 | English | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | MAT/08 |
| Numerical Optimization | 6 | 52 | Italian | MAT/08 |
| Operating Systems and Computer Networks. | 6 | 47 | Italian | INF/01 |
| Operations Research | 6 | 48 | Italian | MAT/09 |
| Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Point Processes and Random Sets | 6 | 42 | Italian | MAT/06 |
| Relativity 1 | 9 | 78 | Italian | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | MAT/08 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | MAT/06 |
Optional activities and study plan rules
c1 - CHARACTERIZING ACTIVITIES: 45 ECTS
Students must obtain at least 15 ects in Mat/05 sector, 9 ects in Mat/06, 9 in Mat/08, by inserting in their curriculum those courses that appear in the table 1C below. If this is not possible for some SSD (eg. when the examination of some of these teachings had already been claimed during a previous undergraduate course) the student must include in his study plan all teachings remaining in table 1C (for that SSD) and, if necessary, add the teachings of that SSD to obtain the expected ects, choosing among those activated and shown in Table 2C.
Students must obtain at least 15 ects in Mat/05 sector, 9 ects in Mat/06, 9 in Mat/08, by inserting in their curriculum those courses that appear in the table 1C below. If this is not possible for some SSD (eg. when the examination of some of these teachings had already been claimed during a previous undergraduate course) the student must include in his study plan all teachings remaining in table 1C (for that SSD) and, if necessary, add the teachings of that SSD to obtain the expected ects, choosing among those activated and shown in Table 2C.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Mathematical Statistics | 9 | 78 | Italian | First semester | MAT/06 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| Numerical Methods for Partial Differential Equations 1 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | Second semester | MAT/06 |
c2 - Students must obtain at least 6 ects in the sectors mat/06-07-08-09, by inserting in their syllabus courses that appear in the table below 2C.
| Courses or activities | Max ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Topics in Complex Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Biomathematics 1 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Combinatorial Optimization | 6 | 48 | English | First semester | MAT/09 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Decision Methods and Models | 6 | 48 | English | First semester | MAT/09 |
| Dynamical System 2 | 6 | 42 | Italian | First semester | MAT/07 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry 5 | 9 | 78 | Italian | First semester | MAT/03 |
| Logistics | 6 | 48 | English | Second semester | MAT/09 |
| Mathematical Economics 1 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Mathematical Finance 1 | 9 | 73 | English | First semester | SECS-S/06 |
| Mathematical Finance 2 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Mathematical Methods in Quantum Mechanics | 6 | 42 | Italian | First semester | MAT/07 |
| Non Linear Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| Numerical Methods for Partial Differential Equations 3 | 9 | 78 | Italian | First semester | MAT/08 |
| Numerical Optimization | 6 | 52 | Italian | Second semester | MAT/08 |
| Operating Systems and Computer Networks. | 6 | 47 | Italian | Second semester | INF/01 |
| Operations Research | 6 | 48 | Italian | Second semester | MAT/09 |
| Point Processes and Random Sets | 6 | 42 | Italian | Second semester | MAT/06 |
| Relativity 1 | 9 | 78 | Italian | Second semester | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
c3 - Students must obtain 45 ects by choosing courses in any sector mat/xx through the entries in Tables 1C,2C.
c4 - COMPLEMENTARY ACTIVITIES: 18 ECTS
Students must obtain at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx , as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf . The choice must be approved by the CDM.
Students must obtain at least 12 ects in a sector different from Mat/xx, by inserting in their curriculum those courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx , as long as these sectors are included in the list in the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/OrdinamentoMagistrale.pdf . The choice must be approved by the CDM.
c5 - Students must obtain additional 6 ects in a section different from Mat/xx, by inserting in their curriculum courses that appear in Tables 1A,2A,1B,2B,1C,2C.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list on the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/ordinamento.doc . The choice will be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx.
The choice must be approved by the CDM.
Students also have the opportunity to enter courses in sectors different from Mat/xx, as long as these sectors are included in the list on the "Ordinamento" del CDL degree in Mathematics, http://www.mat.unimi.it/users/ccd_mat/ordinamento.doc . The choice will be approved by the CDM.
Students also have the opportunity to replace the courses mentioned above with others in the sectors Mat/xx.
The choice must be approved by the CDM.
c6 - ADDITIONAL TRAINING ACTIVITIES: 12 ECTS
Students can obtain 12 ects through an internship/industrial training (6 ects) or by doing the exam of the course "Mathematical Modelling Laboratory" (6 ects) or through participation in the activities of the ECMI Modelling Week which are going to be held in San Pietroburgo (Russia) in the summer of 2020 (6 ects; for information please contact Prof. Causin.
Alternatively, they can be achieved by:
Activity "Criptovalute and Blockchain " (3 CFU), please contact Prof. Maggis or the "Laboratory of mathematical methods and models in Python ".
Algant students can acquire 3 ects after active participation to an Algant Summer School and / or by TER ( = Travaux de recherche et d' Actude ) certificate from a University which is an Algant French partner.
At most 3 CFU can also be acquired by preparing a seminar, on a topic assigned by a teacher or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python" (Contact Prof. Paleari).
At most 3 ects can be acquired also preparing a seminar on a topic assigned by a teacher, as long as the topic concerns a theme or industrial application, students can obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
Students can obtain 12 ects through an internship/industrial training (6 ects) or by doing the exam of the course "Mathematical Modelling Laboratory" (6 ects) or through participation in the activities of the ECMI Modelling Week which are going to be held in San Pietroburgo (Russia) in the summer of 2020 (6 ects; for information please contact Prof. Causin.
Alternatively, they can be achieved by:
Activity "Criptovalute and Blockchain " (3 CFU), please contact Prof. Maggis or the "Laboratory of mathematical methods and models in Python ".
Algant students can acquire 3 ects after active participation to an Algant Summer School and / or by TER ( = Travaux de recherche et d' Actude ) certificate from a University which is an Algant French partner.
At most 3 CFU can also be acquired by preparing a seminar, on a topic assigned by a teacher or through the "Criptovalute and Blockchain " activity (Contact Prof. Maggis) or the "Laboratory of mathematical methods and models in Python" (Contact Prof. Paleari).
At most 3 ects can be acquired also preparing a seminar on a topic assigned by a teacher, as long as the topic concerns a theme or industrial application, students can obtain 3 ects through Laboratorio Didattico and Internship (please contact Prof. Turrini).
c7 - FREE CHOICE ECTS : students must take the missing ects to reach 90 ects, by following free choice courses.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
The courses of the undergraduate programme which are not mandatory for all can be included in the study plan only among the free ects.
The courses of the undergraduate programme which are mandatory for all can only be assigned by the Admissions Committee.
Non ci sono propedeuticità.
Course location
Milano
Presidente del Collegio Didattico
Prof. Lovadina Carlo
Tutors professors
Bianchi Mariagrazia
Bressan Nicoletta
Rondi Luca
Zanco Clemente
Reference structures
Contacts
- secretariat of the course of study
via Cesare Saldini 50
[email protected]
+390250316107
09.30-11.30 - Commissione Piani di studio laurea Magistrale
COLOMBO Elisabetta (Presidente), PALEARI Simone, PAYNE Kevin, UGOLINI Stefania - Commissione Altre Attività e Conferimento Crediti
SCACCHI Simone (Presidente), MOLTENI Giuseppe, TORTORA Alfonso - Commissione Organizzazione Lauree Magistrali
CALANCHI Marta (Presidente), BERTOLINI Marina, LOVADINA Carlo - Commissione Socrates-Erasmus
GAETA Giuseppe (Presidente), CIRAOLO Giulio, GORI Anna, MATESSI Diego, SCACCHI Simone - Commissione Trasferimenti e Riconoscimento Titoli Esteri
BIANCHI Mariagrazia (Presidente), ZAMPIERI Elena - Commissione Orientamento e Stage
TORTORA Alfonso (Presidente), MAGGIS Marco, MICHELETTI Alessandra, NALDI Giovanni,PENATI Tiziano - Commissione Orario
ZAMPIERI Elena (Presidente), MORALE Daniela - Commissione Ammissione alla Laurea Magistrale
VIGNATI Marco (Presidente), ALZATI Alberto, BIANCHI Mariagrazia, SCACCHI Simone - Docenti responsabili Pagine Web e Sito Internet
PALEARI Simone, TURRINI Cristina - Docente responsabile ALGANT
MAZZA Carlo - Docente responsabile Piano Lauree Scientifiche
CAUSIN Paola - Docente responsabile ECMI
CAUSIN Paola - Segreteria studenti
CONTATTI
https://www.unimi.it/it/node/359
+390250325032 - Segreteria studenti
SEDI E ORARI
https://www.unimi.it/it/node/360
A.Y. 2025/2026
A.Y. 2024/2025
A.Y. 2023/2024
A.Y. 2022/2023
A.Y. 2021/2022
A.Y. 2020/2021
A.Y. 2019/2020
A.Y. 2018/2019
Official documents