Mathematics (Classe LM-40)-Enrolled from 2012/13 A.y.
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)
Per essere ammessi al corso di laurea magistrale in Matematica è necessario presentare apposita domanda di pre-iscrizione dal 1 marzo al 13 settembre 2019 ore 12.00.
Gli studenti del corso di Laurea Triennale in Matematica dell'Università degli Studi di Milano che avranno conseguito un punteggio di laurea di almeno 100/110 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 CDM, che si riunirà almeno due volte all'anno. Di norma gli aspiranti dovranno sostenere un colloquio con tale commissione presentando un documento d'identità con foto valido.
Le date del colloquio saranno:
17 giugno 2019 h. 14.00, Sala Rappresentanza Dipartimento di Matematica
4 ottobre 2019 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
8 novembre 2019 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
10 gennaio 2020 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
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);
c) di non ammettere il richiedente.
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 http://files.ccdmat.unimi.it/modulo/formati/formati012171.rtf
Gli studenti del corso di Laurea Triennale in Matematica dell'Università degli Studi di Milano che avranno conseguito un punteggio di laurea di almeno 100/110 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 CDM, che si riunirà almeno due volte all'anno. Di norma gli aspiranti dovranno sostenere un colloquio con tale commissione presentando un documento d'identità con foto valido.
Le date del colloquio saranno:
17 giugno 2019 h. 14.00, Sala Rappresentanza Dipartimento di Matematica
4 ottobre 2019 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
8 novembre 2019 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
10 gennaio 2020 h. 10.00, Sala Rappresentanza Dipartimento di Matematica
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);
c) di non ammettere il richiedente.
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 http://files.ccdmat.unimi.it/modulo/formati/formati012171.rtf
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.
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
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Algebra 4 | 6 | 58 | Italian | MAT/02 |
| Algebraic Number Theory | 6 | 42 | Italian | MAT/02 |
| Algebraic Surfaces | 6 | 42 | Italian | MAT/03 |
| Automated Reasoning | 6 | 50 | Italian | MAT/01 |
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Complex Analysis | 9 | 64 | Italian | MAT/05 |
| Complex Geometry(FIRST PART) | 6 | 42 | Italian | MAT/03 |
| Differential Geometry (FIRST PART) | 6 | 42 | Italian | MAT/03 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| Epistemology of the Mathematical Processes | 6 | 42 | Italian | MAT/01 MAT/04 |
| Evolutions Equations | 6 | 42 | Italian | MAT/05 |
| Harmonic Analysis | 6 | 42 | Italian | MAT/05 |
| History of Mathematics 1 | 6 | 42 | Italian | MAT/04 |
| Homotopical Algebra | 6 | 42 | English | MAT/02 |
| Lie Groups | 6 | 42 | Italian | MAT/03 |
| Mathematical Statistics | 9 | 78 | Italian | MAT/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 |
| Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Preparation of Future Teachers 2 | 6 | 52 | Italian | FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08 |
| Relativity 1 | 9 | 72 | Italian | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | MAT/07 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | MAT/06 |
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 |
|---|---|---|---|---|---|
| Algebraic Number Theory | 6 | 42 | Italian | Second semester | MAT/02 |
| Algebraic Topology | 9 | 69 | Italian | First semester | MAT/03 |
| Commutative Algebra | 9 | 69 | English | First semester | MAT/02 |
| Complex Analysis | 9 | 64 | Italian | Second semester | MAT/05 |
| Complex Geometry(FIRST PART) | 6 | 42 | Italian | Second semester | MAT/03 |
| Complex Manifolds | 9 | 69 | Italian | First semester | MAT/03 |
| Differential Geometry (FIRST PART) | 6 | 42 | Italian | Second semester | MAT/03 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry History and Education | 9 | 73 | Italian | First semester | MAT/04 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Mathematical Logic 1 | 6 | 42 | Italian | First semester | MAT/01 |
| 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 |
| Probability Theory | 9 | 72 | Italian | First semester | MAT/06 |
| Real Analysis | 9 | 64 | Italian | First semester | MAT/05 |
| Relativity 1 | 9 | 72 | Italian | Second semester | MAT/07 |
| Representation Theory | 9 | 69 | 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 Topics in Probability Theory | 6 | 42 | Italian | First semester | MAT/06 |
| Algebra 4 | 6 | 58 | 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 | First semester | MAT/05 |
| Automated Reasoning | 6 | 50 | 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 |
| 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 |
| Evolutions Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Foundations of Computer Science 1 | 6 | 42 | Italian | First semester | INF/01 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry 5 | 9 | 77 | Italian | First semester | MAT/03 |
| Geometry of Schemes (first part) | 6 | 42 | Italian | First semester | MAT/03 |
| Group Theory | 6 | 42 | Italian | First semester | MAT/02 |
| Harmonic Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Homotopical Algebra | 6 | 42 | English | Second semester | MAT/02 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Mathematical Statistics | 9 | 78 | Italian | Second semester | MAT/06 |
| 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 |
| 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 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Stochastic Geometry (first part) | 6 | 42 | 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 obbligatorie.
First semester
Second semester
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Algebra 4 | 6 | 58 | Italian | MAT/02 |
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Complex Analysis | 9 | 64 | Italian | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| Epistemology of the Mathematical Processes | 6 | 42 | Italian | MAT/01 MAT/04 |
| Evolutions Equations | 6 | 42 | Italian | MAT/05 |
| Harmonic Analysis | 6 | 42 | Italian | MAT/05 |
| History of Mathematics 1 | 6 | 42 | Italian | MAT/04 |
| Lie Groups | 6 | 42 | Italian | MAT/03 |
| Logistics | 6 | 48 | English | MAT/09 |
| Mathematical Finance 2 | 6 | 42 | Italian | SECS-S/06 |
| Mathematical Modelling Laboratory | 6 | 72 | Italian | MAT/06 MAT/07 MAT/08 MAT/09 |
| Mathematical Statistics | 9 | 78 | Italian | MAT/06 |
| Molecular Biology and Bioinformatics | 12 | 96 | Italian | BIO/11 |
| 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 |
| Operations Research | 6 | 48 | Italian | MAT/09 |
| Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Relativity 1 | 9 | 72 | Italian | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | MAT/07 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | MAT/06 |
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 |
|---|---|---|---|---|---|
| Complex Analysis | 9 | 64 | Italian | Second semester | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry History and Education | 9 | 73 | Italian | First semester | MAT/04 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Mathematical Finance 1 | 9 | 69 | English | First semester | SECS-S/06 |
| Mathematical Statistics | 9 | 78 | Italian | Second semester | MAT/06 |
| 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 |
| Probability Theory | 9 | 72 | Italian | First semester | MAT/06 |
| Real Analysis | 9 | 64 | Italian | First semester | MAT/05 |
| Relativity 1 | 9 | 72 | 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 Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Probability Theory | 6 | 42 | Italian | First semester | MAT/06 |
| Algebra 4 | 6 | 58 | Italian | Second semester | MAT/02 |
| 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 |
| Complements of Operating Research | 6 | 48 | Italian | First semester | MAT/09 |
| 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 |
| Evolutions Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Foundations of Computer Science 1 | 6 | 42 | Italian | First semester | INF/01 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| General Physiology and Animal Physiology | 9 | 80 | Italian | First semester | BIO/09 |
| Genetics | 9 | 80 | English | First semester | BIO/18 |
| Geometry 5 | 9 | 77 | Italian | First semester | MAT/03 |
| Harmonic Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Logistics | 6 | 48 | English | Second semester | MAT/09 |
| 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 |
| 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 |
| Operations Research | 6 | 48 | Italian | Second semester | MAT/09 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Stochastic Geometry (first part) | 6 | 42 | 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 obbligatorie.
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
| Courses or activities | Max ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Complex Analysis | 9 | 64 | Italian | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| Evolutions Equations | 6 | 42 | Italian | MAT/05 |
| Harmonic Analysis | 6 | 42 | Italian | MAT/05 |
| Logistics | 6 | 48 | English | MAT/09 |
| Mathematical Finance 2 | 6 | 42 | Italian | SECS-S/06 |
| Mathematical Statistics | 9 | 78 | Italian | MAT/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 |
| Operations Research | 6 | 48 | Italian | MAT/09 |
| Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Relativity 1 | 9 | 72 | Italian | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | MAT/07 |
| 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 |
|---|---|---|---|---|---|
| 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 Statistics | 9 | 78 | Italian | Second semester | MAT/06 |
| 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 | 64 | 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 Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Probability Theory | 6 | 42 | Italian | First semester | MAT/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 |
| Complements of Operating Research | 6 | 48 | Italian | First semester | MAT/09 |
| Complex Analysis | 9 | 64 | 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 |
| Evolutions Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry 5 | 9 | 77 | Italian | First semester | MAT/03 |
| Harmonic Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Logistics | 6 | 48 | English | Second semester | MAT/09 |
| Mathematical Finance 1 | 9 | 69 | English | First semester | SECS-S/06 |
| Mathematical Finance 2 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| 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 |
| Operations Research | 6 | 48 | Italian | Second semester | MAT/09 |
| Probability Theory | 9 | 72 | Italian | First semester | MAT/06 |
| Relativity 1 | 9 | 72 | Italian | Second semester | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Stochastic Geometry (first part) | 6 | 42 | 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 obbligatorie.
Course location
Milano
Laboratories locations
Il corso di laurea si avvale principalmente dei laboratori presenti presso il dipartimento di Matematica, via Saldini 50.
Si veda http://www.matematica.unimi.it/ecm/home/organizzazione/laboratori
Si veda http://www.matematica.unimi.it/ecm/home/organizzazione/laboratori
Presidente del Collegio Didattico
Prof. Lovadina Carlo
Tutors professors
Bianchi Mariagrazia
Bressan Nicoletta
Pacifici Emanuele
Zanco Clemente
Reference structures
Contacts
- registrations and admissions
via Cesare Saldini 50
http://www.unimi.it/studenti/matricole/77648.htm - secretariat of the course of study
via Cesare Saldini 50
[email protected]
+390250316107
09.30-11.30
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