Mathematics
Master programme
A.Y. 2020/2021
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)
Candidates must have a scientific Bachelor's degree consistent with the study plan of the class-40 MDP, or an equivalent qualification obtained abroad.
They must have a good basic knowledge of mathematics, physics and computer science. As a guideline, we have prepared a list of contents required for enrolment in the Master's degree programme in Mathematics. This list is available on the website: http://files.ccdmat.unimi.it/modulo/formati/formati012171.rtf
Skills assessment
To be admitted to the Master's degree programme in Mathematics, you will have to pre-apply from 10 March to 28 August 2020.
If you graduated from the Bachelor's degree programme in Mathematics of the University of Milan with at least 100/110, you will be exempted from the assessment of knowledge and curricular requirements.
Applications will be reviewed by a special Commission of the Mathematics Academic Board, which will meet at least twice a year. As a rule, applicants will have an interview with the Commission (an ID will be required).
Interview dates:
June 18, 2020, 11.30 am, Mathematics Department, Board Room
October 6, 2020, 11.30 am, Mathematics Department, Board Room
November 12, 2020, 1.30 pm, Mathematics Department, Board Room
February 9, 2021, 11.30 am, Mathematics Department, Board Room
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 from 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.
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.
Highly recommended, not mandatory
Courses list
Conclusive activities
| 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 Analytic Number Theory | 6 | 42 | English | MAT/05 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | MAT/05 |
| Algebra 4 | 6 | 60 | Italian | MAT/02 |
| Algebraic Number Theory | 9 | 73 | Italian | MAT/02 |
| Algebraic Surfaces | 6 | 42 | Italian | MAT/03 |
| Automated Reasoning | 6 | 52 | Italian | MAT/01 |
| Calculus of Variations | 6 | 42 | Italian | MAT/05 |
| Celestial Mechanics | 6 | 42 | Italian | MAT/07 |
| Complex Analysis | 9 | 73 | Italian | MAT/05 |
| Complex geometry(first part) | 6 | 42 | Italian | MAT/03 |
| Constructive Approximation | 6 | 60 | Italian | MAT/08 |
| Dynamical Systems 1 | 6 | 42 | Italian | MAT/07 |
| History and didactics of calculus (first part) | 6 | 52 | Italian | MAT/04 |
| History of Mathematics 1 | 6 | 42 | Italian | MAT/04 |
| Homological Algebra | 6 | 42 | Italian | MAT/02 |
| Lie Groups | 6 | 42 | Italian | MAT/03 |
| Mathematical Logic 2 | 6 | 42 | Italian | MAT/01 |
| Numerical Linear Algebra | 6 | 60 | English | MAT/08 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Point Processes and Random Sets | 6 | 42 | Italian | MAT/06 |
| 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 | 78 | 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 |
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 Topology | 9 | 73 | Italian | First semester | MAT/03 |
| Commutative Algebra | 9 | 73 | Italian | First semester | MAT/02 |
| Complex Manifolds | 6 | 42 | Italian | First semester | MAT/03 |
| Differential geometry (first part) | 6 | 42 | Italian | First semester | MAT/03 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| History and Teaching of Geometry (First Part) | 6 | 47 | Italian | First semester | MAT/04 |
| 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 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Representation theory | 9 | 73 | Italian | First semester | MAT/02 |
| Algebraic Number Theory | 9 | 73 | Italian | Second semester | MAT/02 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Complex geometry(first part) | 6 | 42 | Italian | Second semester | MAT/03 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| History and didactics of calculus (first part) | 6 | 52 | Italian | Second semester | MAT/04 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second semester | MAT/05 |
| Relativity 1 | 9 | 78 | Italian | Second semester | MAT/07 |
| 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 Topics in Stochastics Calculus | 6 | 47 | Italian | First semester | MAT/06 |
| Algebraic Combinatorics | 6 | 42 | Italian | First semester | MAT/02 |
| Avanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Biomathematics 2 | 6 | 52 | Italian | First semester | MAT/08 |
| 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 |
| Foundations of Computer Science 1 | 6 | 42 | Italian | First semester | INF/01 |
| 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 |
| Group Theory | 6 | 42 | Italian | First semester | MAT/02 |
| 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 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Analytic Number Theory | 6 | 42 | English | Second semester | MAT/05 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Algebra 4 | 6 | 60 | Italian | Second semester | MAT/02 |
| Algebraic Surfaces | 6 | 42 | Italian | Second semester | MAT/03 |
| Automated Reasoning | 6 | 52 | Italian | Second semester | MAT/01 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Celestial Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| 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 Logic 2 | 6 | 42 | Italian | Second semester | MAT/01 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| Point Processes and Random Sets | 6 | 42 | Italian | Second semester | MAT/06 |
| 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 |
| Scientific Computing | 6 | 60 | Italian | Second semester | MAT/08 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
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
| Courses or activities | ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
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 |
| Elements of Functional Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Hamiltonian Systems 1 | 9 | 73 | Italian | First semester | MAT/07 |
| History and Teaching of Geometry (First Part) | 6 | 47 | Italian | First semester | MAT/04 |
| 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 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| History and didactics of calculus (first part) | 6 | 52 | Italian | Second semester | MAT/04 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second 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 Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Advanced Topics in Stochastics Calculus | 6 | 47 | Italian | First semester | MAT/06 |
| Avanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Biomathematics 2 | 6 | 52 | Italian | First 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 |
| Elementary Mathematics from an Advanced Standpoint 1 | 6 | 42 | Italian | First semester | MAT/04 |
| Foundations of Computer Science 1 | 6 | 42 | Italian | First semester | INF/01 |
| Fourier Analysis | 6 | 42 | Italian | First semester | MAT/05 |
| Genetics | 9 | 80 | English | First semester | BIO/18 |
| Geometry 5 | 9 | 78 | Italian | First semester | MAT/03 |
| Operational research complements | 6 | 48 | English | First semester | MAT/09 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Algebra 4 | 6 | 60 | Italian | Second semester | MAT/02 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Celestial Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| General physiology and animal physiology | 9 | 80 | Italian | Second semester | BIO/09 |
| 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 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 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| 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 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
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
| Courses or activities | ECTS | Total hours | Language | SSD |
|---|---|---|---|---|
| Compulsory | ||||
| Final Exam | 30 | 0 | Italian | |
First semester
| Courses or activities | 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 |
| Avanced Partial Differential Equations | 6 | 42 | Italian | MAT/05 |
| Biomathematics 2 | 6 | 52 | Italian | MAT/08 |
| 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 |
| Numerical Methods for Partial Differential Equations 1 | 9 | 78 | Italian | MAT/08 |
| Operational research complements | 6 | 48 | English | MAT/09 |
| Real Analysis | 9 | 73 | Italian | MAT/05 |
| Stochastic Control Optimization | 6 | 47 | Italian | MAT/06 |
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 |
| General physiology and animal physiology | 9 | 80 | Italian | BIO/09 |
| Logistics | 6 | 48 | English | MAT/09 |
| 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 |
| 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 |
| Statistical Mechanics | 6 | 42 | Italian | MAT/07 |
| Stochastic Calculus and Applications | 9 | 73 | Italian | MAT/06 |
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 |
| 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 |
| Real Analysis | 9 | 73 | Italian | First semester | MAT/05 |
| Dynamical Systems 1 | 6 | 42 | Italian | Second semester | MAT/07 |
| Numerical Methods for Partial Differential Equations 2 | 9 | 78 | Italian | Second semester | MAT/08 |
| Partial Differential Equations | 6 | 42 | Italian | Second 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 Probability | 9 | 78 | Italian | First semester | MAT/06 |
| Advanced Topics in Financial Mathematics | 6 | 42 | Italian | First semester | SECS-S/06 |
| Avanced Partial Differential Equations | 6 | 42 | Italian | First semester | MAT/05 |
| Biomathematics 2 | 6 | 52 | Italian | First 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 |
| Mathematical Finance 1 | 9 | 73 | English | First semester | SECS-S/06 |
| Mathematical Methods in Quantum Mechanics | 6 | 42 | Italian | First semester | MAT/07 |
| Operational research complements | 6 | 48 | English | First semester | MAT/09 |
| Stochastic Control Optimization | 6 | 47 | Italian | First semester | MAT/06 |
| Advanced Topics in Real Analysis | 6 | 42 | Italian | Second semester | MAT/05 |
| Calculus of Variations | 6 | 42 | Italian | Second semester | MAT/05 |
| Complex Analysis | 9 | 73 | Italian | Second semester | MAT/05 |
| Constructive Approximation | 6 | 60 | Italian | Second semester | MAT/08 |
| Logistics | 6 | 48 | English | Second semester | MAT/09 |
| Mathematical Finance 2 | 6 | 42 | Italian | Second semester | SECS-S/06 |
| Numerical Linear Algebra | 6 | 60 | English | Second semester | MAT/08 |
| 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 |
| Statistical Mechanics | 6 | 42 | Italian | Second semester | MAT/07 |
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.
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Location
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Head of study programme
Tutors professors
Quality Assurance Delegate
Reference structures
Contacts
- 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, MASTROLIA Paolo, 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 - Commissione Piani di studio laurea Magistrale
COLOMBO Elisabetta (Presidente), FUHRMAN Marco, PALEARI Simone, PAYNE Kevin - Commissione Altre Attività e Conferimento Crediti
SCACCHI Simone (Presidente), MOLTENI Giuseppe, TORTORA Alfonso - Commissione Organizzazione Lauree Magistrali
CALANCHI Marta (Presidente), BERTOLINI Marina, LOVADINA Carlo - Segreteria studenti
CONTATTI
https://www.unimi.it/it/node/359
+390250325032 - Segreteria studenti
SEDI E ORARI
https://www.unimi.it/it/node/360 - Docente responsabile ALGANT
MAZZA Carlo - Docente responsabile ECMI
CAUSIN Paola - Docente responsabile Piano Lauree Scientifiche
CAUSIN Paola - secretariat of the course of study
via Cesare Saldini 50
segrccd.mat@unimi.it
+390250316107
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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).
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Enrollment
First year enrolment: ✔
Admission
Open with entry requirements examination
Admission
Application for admission: from 10/03/2020 to 28/08/2020
Application for matriculation: from 17/06/2020 to 15/01/2021
A.Y. 2020/2021
A.Y. 2019/2020
A.Y. 2018/2019
A.Y. 2017/2018
A.Y. 2016/2017
A.Y. 2015/2016
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