Mathematics

Portico
Mathematics
Course sheet
A.Y. 2021/2022
Master programme
LM-40 - Mathematics
Master programme
120
ECTS
Access
Open with entry requirements examination
2
Years
Course location
Milano
Language
Italian
International title
Double Degree
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)
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.

Attendance is strongly recommended for each course.

Enrollment

Qualifications and knowledge required for admission

- 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 2021, 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 committee of the Mathematics Academic Board, which will meet at least twice a year. Though the committee may just assess the documentation submitted by the candidate, as a rule it will invite applicants to an interview. (Candidates must show up with a valid ID with photo.)
Only students who have already obtained their Bachelor's degree may sit the interview.
The interviews are scheduled on the following dates:
18 June 2021 - Board Room, Department of Mathematics (or possibly online)
11 October 2021 - Board Room, Department of Mathematics (or possibly online)
15 November 2021 - Board Room, Department of Mathematics (or possibly online)
10 January 2022 - Board Room, Department of Mathematics
The timetable will be published later.

The committee 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 their study plan. Any such requirements will count toward the total 120 CFU requirement for earning the degree, and will not constitute an additional requirement for the applicant;
c) not to admit the applicant.

Admission

Application for admission: from 12/03/2021 to 27/08/2021

Application for matriculation: from 01/04/2021 to 15/01/2022

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
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 Stochastics Calculus 6 47 Italian MAT/06
Algebraic Combinatorics 6 42 Italian MAT/02
Algebraic Topology 9 73 Italian MAT/03
Biomathematics 1 6 42 Italian MAT/07
Calcolabilità e complessità computazionale 6 42 Italian INF/01
Category Theory 6 42 Italian MAT/01 MAT/02 MAT/03 MAT/04
Commutative Algebra 9 73 Italian MAT/02
Complex manifolds 9 73 Italian MAT/03
Didattica della matematica 6 42 Italian MAT/04
Differential geometry (first part) 6 42 Italian MAT/03
Dynamical System 2 6 42 Italian MAT/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian MAT/04
Elements of Functional Analysis 6 42 Italian MAT/05
Fourier Analysis 6 42 Italian MAT/05
Geometry 5 9 78 Italian MAT/03
Geometry of schemes (first part) 6 42 Italian MAT/03
Hamiltonian Systems 1 9 73 Italian MAT/07
Mathematical Logic 1 9 63 Italian MAT/01
Mathematical Methods in Quantum Mechanics 6 42 Italian MAT/07
Non Linear Partial Differential Equations 6 42 Italian MAT/05
Numerical Methods for Partial Differential Equations 1 9 78 Italian MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian MAT/08
Preparation of didactical experiences 1 6 52 Italian FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08
Projective Algebraic Geometry 6 47 Italian MAT/03
Real Analysis 9 73 Italian MAT/05
Representation theory 9 73 Italian MAT/02
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities ECTS Total hours Language SSD
Optional
Advanced Topics in Complex 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
Analytic Number Theory 6 42 English MAT/05
Automated Reasoning 6 52 Italian MAT/01
Avanced Partial Differential Equations 6 42 Italian MAT/05
Calculus of Variations 6 42 Italian MAT/05
Celestial Mechanics 6 42 Italian MAT/07
Complements of Mathematics 1 6 42 Italian MAT/04
Complex Analysis 9 73 Italian MAT/05
Complex geometry(first part) 6 42 Italian MAT/03
Didattica del calcolo infinitesimale (prima parte) 6 42 Italian MAT/04
Didattica della geometria (prima parte) 6 47 Italian MAT/04
Dynamical Systems 1 6 42 Italian MAT/07
Economia matematica 1 6 42 Italian SECS-S/06
Epistemology of the Mathematical processes 6 42 Italian MAT/01 MAT/04
Geometria superiore 1 6 47 Italian MAT/03
History of Mathematics 1 6 42 Italian MAT/04
Homological Algebra 6 42 Italian MAT/02
Homotopical Algebra 6 42 English 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
Numerical Optimization 6 52 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
Riemannian Geometry 6 47 Italian MAT/03
Scientific Computing 6 60 Italian MAT/08
Sistemi operativi e reti di calcolatori 6 47 Italian INF/01
Stochastic Calculus and Applications 9 73 Italian MAT/06
Topologia differenziale 6 42 Italian MAT/03
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.
Courses or activities ECTS Total hours Language Lesson period SSD
Advanced Probability 9 78 Italian First semester MAT/06
Algebraic Number Theory 9 73 Italian Second semester MAT/02
Algebraic Topology 9 73 Italian First semester MAT/03
Commutative Algebra 9 73 Italian First semester MAT/02
Complements of Mathematics 1 6 42 Italian Second semester MAT/04
Complex Analysis 9 73 Italian Second semester MAT/05
Complex geometry(first part) 6 42 Italian Second semester MAT/03
Complex manifolds 9 73 Italian First semester MAT/03
Didattica del calcolo infinitesimale (prima parte) 6 42 Italian Second semester MAT/04
Didattica della geometria (prima parte) 6 47 Italian Second semester MAT/04
Differential geometry (first part) 6 42 Italian First semester MAT/03
Dynamical Systems 1 6 42 Italian Second semester MAT/07
Elements of Functional Analysis 6 42 Italian First semester MAT/05
Hamiltonian Systems 1 9 73 Italian First semester MAT/07
Mathematical Logic 1 9 63 Italian First semester MAT/01
Mathematical Methods in Quantum Mechanics 6 42 Italian First semester MAT/07
Numerical Methods for Partial Differential Equations 1 9 78 Italian First semester MAT/08
Numerical Methods for Partial Differential Equations 2 9 78 Italian Second semester MAT/08
Partial Differential Equations 6 42 Italian Second semester MAT/05
Real Analysis 9 73 Italian First semester MAT/05
Relativity 1 9 78 Italian Second semester MAT/07
Representation theory 9 73 Italian First semester MAT/02
Stochastic Calculus and Applications 9 73 Italian Second semester MAT/06
a2 - Students must obtain at least 12 ects in the sectors Mat/01-02-03-04-05, by choosing courses that appear in the following table 2A.
Courses or activities ECTS Total hours Language Lesson period SSD
Advanced Mathematical Statistics 9 78 Italian First semester MAT/06
Advanced Topics in Complex Analysis 6 42 Italian Second semester MAT/05
Advanced Topics in Stochastics Calculus 6 47 Italian First semester MAT/06
Algebra 4 6 60 Italian Second semester MAT/02
Algebraic Combinatorics 6 42 Italian First semester MAT/02
Algebraic Surfaces 6 42 Italian Second semester MAT/03
Analytic Number Theory 6 42 English Second semester MAT/05
Automated Reasoning 6 52 Italian Second semester MAT/01
Avanced Partial Differential Equations 6 42 Italian Second semester MAT/05
Biomathematics 1 6 42 Italian First semester MAT/07
Calcolabilità e complessità computazionale 6 42 Italian First semester INF/01
Calculus of Variations 6 42 Italian Second semester MAT/05
Category Theory 6 42 Italian First semester MAT/01 MAT/02 MAT/03 MAT/04
Celestial Mechanics 6 42 Italian Second semester MAT/07
Didattica della matematica 6 42 Italian First semester MAT/04
Dynamical System 2 6 42 Italian First semester MAT/07
Economia matematica 1 6 42 Italian Second semester SECS-S/06
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian First semester MAT/04
Epistemology of the Mathematical processes 6 42 Italian Second semester MAT/01 MAT/04
Fourier Analysis 6 42 Italian First semester MAT/05
Geometria superiore 1 6 47 Italian Second semester MAT/03
Geometry 5 9 78 Italian First semester MAT/03
Geometry of schemes (first part) 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
Homotopical Algebra 6 42 English Second semester MAT/02
Lie Groups 6 42 Italian Second semester MAT/03
Mathematical Logic 2 6 42 Italian Second semester MAT/01
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
Point Processes and Random Sets 6 42 Italian Second semester MAT/06
Preparation of didactical experiences 1 6 52 Italian First semester FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08
Preparation of future teachers 2 6 52 Italian Second semester FIS/01 FIS/02 FIS/03 FIS/04 FIS/05 FIS/06 FIS/07 FIS/08
Projective Algebraic Geometry 6 47 Italian First semester MAT/03
Riemannian Geometry 6 47 Italian Second semester MAT/03
Scientific Computing 6 60 Italian Second semester MAT/08
Sistemi operativi e reti di calcolatori 6 47 Italian Second semester INF/01
Stochastic Control Optimization 6 47 Italian First semester MAT/06
Topologia differenziale 6 42 Italian Second semester MAT/03
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.
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).
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.
Non ci sono propedeuticità.
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
Advanced Topics in Stochastics Calculus 6 47 Italian MAT/06
Biomathematics 1 6 42 Italian MAT/07
Calcolabilità e complessità computazionale 6 42 Italian INF/01
Cytology and histology 9 78 Italian BIO/06
Decision methods and models 6 48 English MAT/09
Didattica della matematica 6 42 Italian MAT/04
Dynamical System 2 6 42 Italian MAT/07
Ecology 9 80 Italian BIO/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian MAT/04
Elements of Functional Analysis 6 42 Italian MAT/05
Fourier Analysis 6 42 Italian MAT/05
Genetics 9 80 English BIO/18
Geometry 5 9 78 Italian MAT/03
Hamiltonian Systems 1 9 73 Italian MAT/07
Mathematical Finance 1 9 63 English SECS-S/06
Mathematical Methods in Quantum Mechanics 6 42 Italian MAT/07
Non Linear Partial Differential Equations 6 42 Italian MAT/05
Numerical Methods for Partial Differential Equations 1 9 78 Italian MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian MAT/08
Real Analysis 9 73 Italian MAT/05
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities ECTS Total hours Language SSD
Optional
Advanced Topics in Complex Analysis 6 42 Italian MAT/05
Algebra 4 6 60 Italian MAT/02
Avanced Partial Differential Equations 6 42 Italian MAT/05
Calculus of Variations 6 42 Italian MAT/05
Celestial Mechanics 6 42 Italian MAT/07
Complements of Mathematics 1 6 42 Italian MAT/04
Complex Analysis 9 73 Italian MAT/05
Didattica del calcolo infinitesimale (prima parte) 6 42 Italian MAT/04
Didattica della geometria (prima parte) 6 47 Italian MAT/04
Dynamical Systems 1 6 42 Italian MAT/07
Economia matematica 1 6 42 Italian SECS-S/06
General physiology and animal physiology 9 80 Italian BIO/09
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
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
Point Processes and Random Sets 6 42 Italian MAT/06
Relativity 1 9 78 Italian MAT/07
Scientific Computing 6 60 Italian MAT/08
Sistemi operativi e reti di calcolatori 6 47 Italian INF/01
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 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.
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
Complements of Mathematics 1 6 42 Italian Second semester MAT/04
Complex Analysis 9 73 Italian Second semester MAT/05
Didattica del calcolo infinitesimale (prima parte) 6 42 Italian Second semester MAT/04
Didattica della geometria (prima parte) 6 47 Italian Second semester MAT/04
Dynamical Systems 1 6 42 Italian Second semester MAT/07
Elements of Functional Analysis 6 42 Italian First semester MAT/05
Hamiltonian Systems 1 9 73 Italian First semester MAT/07
Mathematical Finance 1 9 63 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 Topics in Complex Analysis 6 42 Italian Second semester MAT/05
Advanced Topics in Financial Mathematics 6 42 Italian First semester SECS-S/06
Advanced Topics in Stochastics Calculus 6 47 Italian First semester MAT/06
Algebra 4 6 60 Italian Second semester MAT/02
Avanced Partial Differential Equations 6 42 Italian Second semester MAT/05
Biomathematics 1 6 42 Italian First semester MAT/07
Calcolabilità e complessità computazionale 6 42 Italian First semester INF/01
Calculus of Variations 6 42 Italian Second semester MAT/05
Celestial Mechanics 6 42 Italian Second semester MAT/07
Cytology and histology 9 78 Italian First semester BIO/06
Decision methods and models 6 48 English First semester MAT/09
Didattica della matematica 6 42 Italian First semester MAT/04
Dynamical System 2 6 42 Italian First semester MAT/07
Ecology 9 80 Italian First semester BIO/07
Economia matematica 1 6 42 Italian Second semester SECS-S/06
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian First semester MAT/04
Fourier Analysis 6 42 Italian First semester MAT/05
General physiology and animal physiology 9 80 Italian Second semester BIO/09
Genetics 9 80 English First semester BIO/18
Geometry 5 9 78 Italian First semester MAT/03
History of Mathematics 1 6 42 Italian Second semester MAT/04
Lie Groups 6 42 Italian Second semester MAT/03
Logistics 6 48 English Second semester MAT/09
Mathematical 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
Point Processes and Random Sets 6 42 Italian Second semester MAT/06
Scientific Computing 6 60 Italian Second semester MAT/08
Sistemi operativi e reti di calcolatori 6 47 Italian Second semester INF/01
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.
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).
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.
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
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
Biomathematics 1 6 42 Italian MAT/07
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 63 English SECS-S/06
Mathematical Methods in Quantum Mechanics 6 42 Italian MAT/07
Non Linear Partial Differential Equations 6 42 Italian MAT/05
Numerical Methods for Partial Differential Equations 1 9 78 Italian MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian MAT/08
Real Analysis 9 73 Italian MAT/05
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities ECTS Total hours Language SSD
Optional
Advanced Topics in Complex Analysis 6 42 Italian MAT/05
Avanced Partial Differential Equations 6 42 Italian MAT/05
Calculus of Variations 6 42 Italian MAT/05
Complex Analysis 9 73 Italian MAT/05
Dynamical Systems 1 6 42 Italian MAT/07
Economia matematica 1 6 42 Italian SECS-S/06
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
Numerical Optimization 6 52 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
Sistemi operativi e reti di calcolatori 6 47 Italian INF/01
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.
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 Probability 9 78 Italian First semester MAT/06
Advanced Topics in Complex Analysis 6 42 Italian Second semester MAT/05
Advanced Topics in Financial Mathematics 6 42 Italian First semester SECS-S/06
Avanced Partial Differential Equations 6 42 Italian Second semester MAT/05
Biomathematics 1 6 42 Italian First semester MAT/07
Calculus of Variations 6 42 Italian Second semester MAT/05
Complex Analysis 9 73 Italian Second semester MAT/05
Decision methods and models 6 48 English First semester MAT/09
Dynamical System 2 6 42 Italian First semester MAT/07
Economia matematica 1 6 42 Italian Second semester SECS-S/06
Fourier Analysis 6 42 Italian First semester MAT/05
Geometry 5 9 78 Italian First semester MAT/03
Logistics 6 48 English Second semester MAT/09
Mathematical Finance 1 9 63 English First semester SECS-S/06
Mathematical Finance 2 6 42 Italian Second semester SECS-S/06
Mathematical Methods in Quantum Mechanics 6 42 Italian First semester MAT/07
Non Linear Partial Differential Equations 6 42 Italian First semester MAT/05
Numerical Linear Algebra 6 60 English Second semester MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian First semester MAT/08
Numerical Optimization 6 52 Italian Second semester MAT/08
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
Sistemi operativi e reti di calcolatori 6 47 Italian Second semester INF/01
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.
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.
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).
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.
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Location
Milano
Head of study programme
Quality Assurance Delegate
Contacts
  • secretariat of the course of study
    via Cesare Saldini 50
    [email protected]
    +390250316107
    09.30-11.30
  • Commissione Piani di studio laurea Magistrale
    COLOMBO Elisabetta (Presidente), PALEARI Simone, PAYNE Kevin, UGOLINI Stefania
  • Commissione Altre Attività e Conferimento Crediti
    SCACCHI Simone (Presidente), MOLTENI Giuseppe, TORTORA Alfonso
  • Commissione Organizzazione Lauree Magistrali
    CALANCHI Marta (Presidente), BERTOLINI Marina, LOVADINA Carlo
  • Commissione Trasferimenti e Riconoscimento Titoli Esteri
    BIANCHI Mariagrazia (Presidente), ZAMPIERI Elena
  • Commissione Orientamento e Stage
    TORTORA Alfonso (Presidente), MAGGIS Marco, MICHELETTI Alessandra, NALDI Giovanni,PENATI Tiziano
  • Commissione Orario
    ZAMPIERI Elena (Presidente), MORALE Daniela
  • Commissione Ammissione alla Laurea Magistrale
    VIGNATI Marco (Presidente), ALZATI Alberto, BIANCHI Mariagrazia, SCACCHI Simone
  • Docenti responsabili Pagine Web e Sito Internet
    PALEARI Simone, TURRINI Cristina
  • Docente responsabile ALGANT
    MAZZA Carlo
  • Docente responsabile Piano Lauree Scientifiche
    CAUSIN Paola
  • Docente responsabile ECMI
    CAUSIN Paola
  • Segreteria studenti
    CONTATTI
    https://www.unimi.it/it/node/359
    +390250325032
  • Segreteria studenti
    SEDI E ORARI
    https://www.unimi.it/it/node/360
  • Commissione Socrates-Erasmus
    GAETA Giuseppe (Presidente), CIRAOLO Giulio, GORI Anna, MATESSI Diego, SCACCHI Simone

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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