Mathematics (master programme)
Mathematics (master programme)
Course sheet
A.Y. 2024/2025
Master programme
LM-40 - Mathematics
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)
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, Poland, Portugal, Romania, Slovenia, Spain, Sweden, Turkey.
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, Poland, Portugal, Romania, Slovenia, Spain, Sweden, Turkey.
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.
Enrolment
Candidates must hold a scientific Bachelor's degree consistent with the study plan of the class-40 Master's degree programme, or an equivalent qualification obtained abroad.
- They must have a good basic knowledge of mathematics, physics and computer science. As a guideline, the Mathematics Academic Board has prepared a list of contents required for enrolment on the Master's degree programme in Mathematics. This list is available on the website https://matematica-lm.cdl.unimi.it/it/iscriversi
Admission assessment:
Candidates are required to submit a specific application for admission to the Master's degree programme in Mathematics (see the link: https://www.unimi.it/en/study/bachelor-and-master-study/degree-programme-enrolment/enrolment-masters-programme/open-admission-master-programmes).
We discourage students who, as of 14 September 2023, fall short of the 180 credit (CFU) requirement for earning a Bachelor's degree by more than 40 CFU, from applying for admission.
Those who graduated from the Bachelor's degree programme in Mathematics of the University of Milan with at least 95/110 will be waived from the knowledge and curricular assessment requirement.
Applications will be reviewed by a special commission of the Mathematics Academic Board, which will meet at least twice a year. The commission may consider only the documents submitted by applicants, though as a rule it will also interview them. Interviewees must show a photo ID.
Interview dates:
21 May 2024: session reserved for non-EU students requesting visas (electronically)
20 June 2024: Board room of the Department of Mathematics (or possibly online)
12 September 2024: Board room of the Department of Mathematics (or possibly online)
25 November 2024: Board room of the Department of Mathematics (or possibly online)
10 January 2025: Board room of the Department of Mathematics
The time will be announced later on.
The Commission may decide:
a) to admit the applicant without any restrictions;
b) to admit the applicant with the requirement to include certain courses (possibly within a Bachelor's degree programme) in his/her study plan. Any requirements are included in the 120 CFU provided for by the programme and do not constitute an additional requirement for the applicant;
c) not to admit the applicant.
- They must have a good basic knowledge of mathematics, physics and computer science. As a guideline, the Mathematics Academic Board has prepared a list of contents required for enrolment on the Master's degree programme in Mathematics. This list is available on the website https://matematica-lm.cdl.unimi.it/it/iscriversi
Admission assessment:
Candidates are required to submit a specific application for admission to the Master's degree programme in Mathematics (see the link: https://www.unimi.it/en/study/bachelor-and-master-study/degree-programme-enrolment/enrolment-masters-programme/open-admission-master-programmes).
We discourage students who, as of 14 September 2023, fall short of the 180 credit (CFU) requirement for earning a Bachelor's degree by more than 40 CFU, from applying for admission.
Those who graduated from the Bachelor's degree programme in Mathematics of the University of Milan with at least 95/110 will be waived from the knowledge and curricular assessment requirement.
Applications will be reviewed by a special commission of the Mathematics Academic Board, which will meet at least twice a year. The commission may consider only the documents submitted by applicants, though as a rule it will also interview them. Interviewees must show a photo ID.
Interview dates:
21 May 2024: session reserved for non-EU students requesting visas (electronically)
20 June 2024: Board room of the Department of Mathematics (or possibly online)
12 September 2024: Board room of the Department of Mathematics (or possibly online)
25 November 2024: Board room of the Department of Mathematics (or possibly online)
10 January 2025: Board room of the Department of Mathematics
The time will be announced later on.
The Commission may decide:
a) to admit the applicant without any restrictions;
b) to admit the applicant with the requirement to include certain courses (possibly within a Bachelor's degree programme) in his/her study plan. Any requirements are included in the 120 CFU provided for by the programme and do not constitute an additional requirement for the applicant;
c) not to admit the applicant.
Admission
Application for admission: from 22/01/2024 to 25/08/2024
Application for matriculation: from 08/04/2024 to 15/01/2025
Attachments and documents
Please note
Non-EU students visa applicants are required to apply for admission no later than 30 April 2024. Applications submitted after the deadline will not be evaluated and it will in no case be possible to request the refund of the admission fee.
Online services
Learn more:
Programme description and courses list
Conclusive activities
There are no specific sessions for these activities (e.g. open online courses).
| Courses or activities | 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 | ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Algebraic Number Theory | 6 | 42 | Italian | First semester | MAT/02 |
| Algebraic Topology (FIRST PART) | 6 | 47 | Italian | First semester | MAT/03 |
| Commutative Algebra | 6 | 42 | Italian | First semester | MAT/02 |
| 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 | 52 | Italian | Second semester | MAT/04 |
| Didactics of Infinitesimal Calculus (first part) | 6 | 42 | Italian | First 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 | 73 | Italian | First semester | MAT/01 |
| Mathematical Logic 2 | 6 | 42 | Italian | Second 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 | 6 | 42 | 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 | ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Mathematical Statistics | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Advanced Topics in Analytic Number Theory | 6 | 42 | English | Second semester | MAT/05 |
| Advanced Topics in Probability Theory | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Stochastics Calculus | 6 | 47 | Italian | Second 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 |
| Automated Reasoning | 6 | 52 | Italian | Second semester | MAT/01 |
| Biomathematics 2 | 6 | 52 | Italian | First semester | MAT/08 |
| Biomathematics 3 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Categorical Dualities in Logic and Algebra | 6 | 42 | Italian | First semester | MAT/01 |
| Category Theory | 9 | 73 | Italian | First semester | MAT/01 MAT/02 MAT/03 MAT/04 |
| Computability and Computational Complexity | 6 | 42 | Italian | First semester | INF/01 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| Differential Topology | 6 | 42 | Italian | Second semester | MAT/03 |
| Dynamical System 2 | 6 | 42 | Italian | First semester | MAT/07 |
| Epistemology of the Mathematical Processes | 6 | 42 | Italian | Second semester | MAT/01 MAT/04 |
| Foundations of Mathematics I | 6 | 42 | Italian | Second semester | MAT/04 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Geometry 5 | 9 | 78 | Italian | First semester | MAT/03 |
| Geometry of Schemes | 9 | 73 | Italian | First semester | MAT/03 |
| Harmonic Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Higher Algebra | 6 | 42 | Italian | Second semester | MAT/02 |
| Higher Geometry 1 | 6 | 42 | Italian | Second semester | MAT/03 |
| Higher Geometry 2 | 6 | 42 | Italian | First semester | MAT/03 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Homological Algebra | 6 | 42 | Italian | Second semester | MAT/02 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Mathematical Fluid-Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Mathematics Education | 6 | 47 | 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 |
| Operating Systems and Computer Networks. | 6 | 47 | Italian | Second semester | INF/01 |
| Point Processes and Random Sets | 6 | 47 | 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 | 47 | Italian | First semester | MAT/03 |
| Riemannian Geometry | 6 | 42 | Italian | Second semester | MAT/03 |
| Scientific Computing | 6 | 60 | Italian | First 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 | 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 | 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 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Didactics of Geometry (first part) | 6 | 52 | Italian | Second semester | MAT/04 |
| Didactics of Infinitesimal Calculus (first part) | 6 | 42 | Italian | First 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 | ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Probability Theory | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Advanced Topics in Stochastics Calculus | 6 | 47 | Italian | Second semester | MAT/06 |
| Algebra 4 | 6 | 60 | Italian | Second semester | MAT/02 |
| Biomathematics 2 | 6 | 52 | Italian | First semester | MAT/08 |
| Biomathematics 3 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Combinatorial Optimization | 6 | 48 | Italian | First semester | MAT/09 |
| Complements of Operating Research | 6 | 48 | Italian | First semester | MAT/09 |
| Computability and Computational Complexity | 6 | 42 | Italian | First semester | INF/01 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| 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 |
| Foundations of Mathematics I | 6 | 42 | Italian | Second 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 |
| Harmonic Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| History of Mathematics 1 | 6 | 42 | Italian | Second semester | MAT/04 |
| Lie Groups | 6 | 42 | Italian | Second semester | MAT/03 |
| Logistics | 6 | 48 | Italian | First 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 Fluid-Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Mathematical Modelling Laboratory | 6 | 72 | Italian | Second semester | MAT/06 MAT/07 MAT/08 MAT/09 |
| Mathematics Education | 6 | 47 | 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 |
| 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 | 47 | Italian | Second semester | MAT/06 |
| Scientific Computing | 6 | 60 | Italian | First 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 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 by 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).
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 | ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
First semester
Second semester
| Courses or activities | ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Optional | ||||
| Advanced Topics in Real Analysis | 6 | 42 | Italian | MAT/05 |
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Complex Analysis | 9 | 73 | Italian | MAT/05 |
| Constructive Approximation | 6 | 60 | Italian | MAT/08 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| Mathematical Economics 1 | 6 | 42 | Italian | SECS-S/06 |
| Mathematical Finance 2 | 6 | 42 | Italian | SECS-S/06 |
| Mathematical Fluid-Mechanics | 6 | 42 | Italian | MAT/07 |
| Numerical Linear Algebra | 6 | 60 | English | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | 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 | 47 | Italian | MAT/06 |
| Relativity 1 | 9 | 78 | 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 | 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 | ECTS | Total hours | Language | Lesson period | SSD |
|---|---|---|---|---|---|
| Advanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Advanced Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Probability Theory | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Biomathematics 2 | 6 | 52 | Italian | First semester | MAT/08 |
| Biomathematics 3 | 6 | 42 | Italian | First semester | MAT/07 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Combinatorial Optimization | 6 | 48 | Italian | First semester | MAT/09 |
| Complements of Operating Research | 6 | 48 | Italian | First semester | MAT/09 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| 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 | Italian | First 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 Fluid-Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| 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 |
| 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 | 47 | Italian | Second semester | MAT/06 |
| Relativity 1 | 9 | 78 | Italian | Second semester | MAT/07 |
| Scientific Computing | 6 | 60 | Italian | First 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 - 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 2025 (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 d'étude et de recherche) 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 2025 (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 d'étude et de recherche) 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).
c6 - 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.
Learn more
Location
Milan
Head of study programme
Academic guidance tutor
Quality Assurance Delegate
Reference structures
Contacts
- Degree programme administration
via Cesare Saldini 50
https://informastudenti.unimi.it/saw/ess?AUTH=SAML
+390250316107
09.30-11.30 - Master's Degree Study Plan Board
COLOMBO Elisabetta (Presidente), PIZZOCCHERO Livio, PAYNE Kevin, UGOLINI Stefania - Other Activities and Credit Award Board
SCACCHI Simone (Presidente), MOLTENI Giuseppe, TORTORA Alfonso - Master's Degree Organization Board
CALANCHI Marta (Presidente), PELOSO Marco, GHILARDI Silvio, VIGNATI Marco - Socrates-Erasmus Board
GAETA Giuseppe (Presidente), GORI Anna, MATESSI Diego, SCACCHI Simone, PAYNE Kevin - Programme Transfer and International Qualifications Recognition Board
ZAMPIERI Elena (Presidente), REGGIO Luca - Orientation and Internship Board
TORTORA Alfonso (Presidente), MAGGIS Marco, MICHELETTI Alessandra, NALDI Giovanni, COZZI Matteo, BRANCHETTI Laura - Timetables Board
ZAMPIERI Elena (Presidente), LOVADINA Carlo, ZANOTTI Pietro - Master's Degree Admission Board
VIGNATI Marco (Presidente), ALZATI Alberto, SCACCHI Simone, MAZZA Carlo - Web pages and website academic tutors
PALEARI Simone, TURRINI Cristina - ALGANT academic tutor
MAZZA Carlo - Piano Lauree Scientifiche" academic tutor
CAUSIN Paola - ECMI academic tutor
CAUSIN Paola - Student registrar
CONTATTI, SEDI E ORARI
https://www.unimi.it/it/node/359
+390250325032
https://www.unimi.it/it/node/360 - Disability academic tutor
Scacchi Simone - Secondary school teacher training activities
BRANCHETTI Laura (Presidente), RIZZO Ottavio, TURRINI Cristina
The tuition fees for students enrolled in Bachelor's, Master's and single-cycle degree programmes are divided into two instalments with different calculation methods and payment schedules:
- The amount of the first instalment is the same for all students
- The amount of the second instalment varies according to the ISEE University value, the degree programme and the student status (on track / off track for one year or off track for more than a year)
- An additional fee is due for online programmes
The University also offers:
- Concessions for students meeting high merit requirements
- Diversified tuition fees according to the student's home country for international students with assets/income abroad
- Concessions for international students with refugee status
Scholarships and benefits
The University provides a range of financial benefits to students meeting special requirements (merit, financial or personal conditions, international students).
Learn more
Guidance:
Admission, ranking and enrolment
Official documents