Mathematics (master programme)

Portico
Mathematics (master programme)
Course sheet
A.Y. 2025/2026
Master programme
LM-40 R - Matematica
Master programme
120
ECTS
Access
Open with entry requirements examination
2
Years
Course location
Milan
Language
Italian
International title
Double Degree
The core objectives of the Master's degree in Mathematics are:
- to provide a solid and in-depth mathematical understanding, allowing students to specialise in a branch of mathematics and to get acquainted with some of its latest developments;
- to equip students with the mathematical tools necessary for contextualising, analysing and solving complex theoretical as well as practical problems, including problems related to other scientific fields;
- to provide students with an adequate knowledge base to build upon, allowing them to assimilate future advancements in the field of mathematics.
For the Master's degree in Mathematics there are two graduate profiles: MATHEMATICIAN and APPLIED MATHEMATICIAN.

MATHEMATICIAN
Job function
Typical job functions for this profile include: analysing phenomena that require a high degree of abstraction and logical rigour; managing and analysing large amounts of complex data; personnel training; disseminating knowledge about STEM subjects (with different degrees of details).

Professional skills
This graduate profile shows a remarkable aptitude for abstract reasoning and logical rigour and is able to use mathematical models, also in innovative ways, to solve the above-mentioned problems. This translates into strong problem-solving skills applicable to a wide range of scientific as well as socio-cultural situations.
Graduates falling under this profile have a solid grounding in mathematical modelling and computational mathematics, as well as advanced theoretical knowledge in at least one of the following fields: mathematical logic, algebra, geometry, didactics of mathematics, mathematical analysis.

Career opportunities
Typical career prospects for this graduate profile include high-level roles in private and public organisations, particularly:
- banks and financial companies
- insurance companies
- universities and other research institutions
- consulting firms
- the aerospace industry.
Graduates who have earned enough credits in certain subject areas, as provided for by the laws in force, may take admission tests for training courses for secondary school teaching.

APPLIED MATHEMATICIAN
Job function
Typical job functions for this profile include: analysing any phenomena (in the field of physics, biology, medicine, etc.) whose understanding requires accurate mathematical modelling; managing and analysing large amounts of complex data; using sophisticated scientific and management software programmes in business settings; disseminating knowledge about STEM subjects (with different degrees of details).

Professional skills
This graduate profile shows a remarkable aptitude for the formalisation and modelling of real-life problems, including highly complex ones, and is able to use mathematical models, also in innovative ways, to solve these problems. This translates into strong problem-solving skills applicable to a wide range of scientific as well as socio-cultural situations.
Graduates falling under this profile have a solid grounding in theoretical mathematics, as well as advanced knowledge of mathematical modelling and computational mathematics in at least one of the following fields: mathematical probability and statistics, mathematical physics, numerical analysis.

Career opportunities
Typical career prospects for this graduate profile include high-level roles in private and public organisations, particularly:
- banks and financial companies
- insurance companies
- universities and other research institutions
- survey institutes
- software development companies
- the aerospace industry.
Graduates who have earned enough credits in certain subject areas, as provided for by the laws in force, may take admission tests for training courses for secondary school teaching.

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, Czech Republic, Denmark, Finland, France, Germany, Holland, Norway, Poland, 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.
Enrolment
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 9 September 2025, 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:
20 May 2025: session reserved for non-EU students requesting visas (electronically)
20 June 2025: (or possibly online)
17 September 2025: (or possibly online)
24 November 2025: (or possibly online)
9 January 2026: 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 22/01/2025 to 25/08/2025

Application for matriculation: from 02/04/2025 to 15/01/2026


Attachments and documents

Admission notice

Learn more:
Programme description and courses list
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
English Proficiency B2 (3 ECTS) 3 0 English NN
be activated by the A.Y. 2026/2027
Conclusive activities
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
Final Exam 27 0 Italian NN
First semester
Courses or activities Max ECTS Total hours Language SSD
Optional
Advanced Mathematical Statistics 9 78 Italian MAT/06
Advanced Partial Differential Equations 6 42 Italian MAT/05
Advanced Probability 9 78 Italian MAT/06
Algebraic and Categorical Logic 6 42 Italian MAT/01
Algebraic Combinatorics 6 42 Italian MAT/02
Algebraic Topology 6 47 Italian MAT/03
Biomathematics 1 6 42 Italian MAT/07
Categorical Dualities in Logic and Algebra 6 42 Italian MAT/01
Category Theory 9 73 Italian MAT/02
Category Theory 6 47 Italian MAT/02
Commutative Algebra 6 42 Italian MAT/02
Complex Manifolds 6 47 Italian MAT/03
Complex Manifolds 9 73 Italian MAT/03
Computability and Computational Complexity 6 42 Italian INF/01
Didactics of Infinitesimal Calculus 6 42 Italian MAT/04
Didactics of Mathematic 6 47 Italian MAT/04
Didactics of Mathematic 9 73 Italian MAT/04
Differential Geometry 6 42 Italian MAT/03
Dynamical System 2 6 42 Italian MAT/07
Fourier Analysis 6 42 Italian MAT/05
Functional Analysis 6 42 Italian MAT/05
Geometry 5 9 78 Italian MAT/03
Geometry of Schemes 9 73 Italian MAT/03
Geometry of Schemes 6 47 Italian MAT/03
Hamiltonian System 1 6 47 Italian MAT/07
Hamiltonian System 1 9 73 Italian MAT/07
Higher Geometry 1 6 42 Italian MAT/03
Higher Geometry 2 6 52 Italian MAT/03
Mathematical Analysis 5 6 60 Italian MAT/05
Mathematical Logic 1 9 73 Italian MAT/01
Mathematical Logic 1 6 47 Italian MAT/01
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
Optimal Transport and Applications. 6 42 Italian MAT/05
Preparation of Didactical Experiences 1 6 52 Italian FIS/08
Projective Algebraic Geometry 6 47 Italian MAT/03
Real Analysis 9 73 Italian MAT/05
Representation Theory 6 42 Italian MAT/02
Scientific Computing 6 60 Italian MAT/08
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities Max ECTS Total hours Language SSD
Optional
Advanced Topics in Real Analysis 6 42 Italian MAT/05
Algebra 4 9 78 Italian MAT/02
Algebraic Number Theory 6 42 Italian MAT/02
Algebraic Surfaces 6 42 Italian MAT/03
Analytic Number Theory 6 42 Italian MAT/05
Automated Reasoning 6 52 Italian MAT/01
Calculus of Variations 6 42 Italian MAT/05
Complex Analysis 9 73 Italian MAT/05
Complex Analysis 6 47 Italian MAT/05
Complex Geometry 6 42 Italian MAT/03
Didactics of Geometry 6 52 Italian MAT/04
Differential Topology 6 42 Italian MAT/03
Dynamical Systems 1 6 42 Italian MAT/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian MAT/04
Foundations of Mathematics I 6 42 Italian MAT/04
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 Fluid-Mechanics 6 42 Italian MAT/07
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
Operating Systems and Computer Networks 6 47 Italian INF/01
Partial Differential Equations 6 42 Italian MAT/05
Point Processes and Random Sets 6 47 Italian MAT/06
Preparation of Future Teachers 2 6 52 Italian FIS/08
Relativity 1 9 78 Italian MAT/07
Riemannian Geometry 6 42 Italian MAT/03
Stochastic Calculus and Applications 9 73 Italian MAT/06
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Optional
Financial Technologies 3 20 Italian NN
Laboratory of Education and Public Engagement 3 0 Italian NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian NN
Optional activities and study plan rules
a1 - ATTIVITA' CARATTERIZZANTI: 45 CREDITI
Gli studenti devono conseguire almeno 18 crediti nei settori Mat/01-02-03-04-05 scegliendo corsi che compaiono nella seguente tabella 1A.
Courses or activities Max ECTS Total hours Language Lesson period SSD
Advanced Probability 9 78 Italian First semester MAT/06
Algebraic Number Theory 6 42 Italian Second semester MAT/02
Algebraic Topology 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 Analysis 6 47 Italian Second semester MAT/05
Complex Geometry 6 42 Italian Second semester MAT/03
Complex Manifolds 9 73 Italian First semester MAT/03
Complex Manifolds 6 47 Italian First semester MAT/03
Didactics of Geometry 6 52 Italian Second semester MAT/04
Didactics of Infinitesimal Calculus 6 42 Italian First semester MAT/04
Differential Geometry 6 42 Italian First semester MAT/03
Dynamical Systems 1 6 42 Italian Second semester MAT/07
Functional Analysis 6 42 Italian First semester MAT/05
Hamiltonian System 1 9 73 Italian First semester MAT/07
Hamiltonian System 1 6 47 Italian First semester MAT/07
Mathematical Logic 1 6 47 Italian First semester MAT/01
Mathematical Logic 1 9 73 Italian First semester MAT/01
Mathematical Logic 2 6 42 Italian Second semester MAT/01
Numerical Methods for Partial Differential Equations 1 9 78 Italian First semester MAT/08
Numerical Methods for Partial Differential Equations 2 9 78 Italian Second semester MAT/08
Partial Differential Equations 6 42 Italian Second semester MAT/05
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 - Gli studenti devono conseguire almeno 12 crediti , nei settori Mat/01-02-03-04-05 scegliendo corsi che compaiono nella seguente tabella 2A.
Courses or activities Max ECTS Total hours Language Lesson period SSD
Advanced Mathematical Statistics 9 78 Italian First semester MAT/06
Advanced Partial Differential Equations 6 42 Italian First semester MAT/05
Advanced Topics in Real Analysis 6 42 Italian Second semester MAT/05
Algebra 4 9 78 Italian Second semester MAT/02
Algebraic and Categorical Logic 6 42 Italian First semester MAT/01
Algebraic Combinatorics 6 42 Italian First semester MAT/02
Algebraic Surfaces 6 42 Italian Second semester MAT/03
Analytic Number Theory 6 42 Italian Second semester MAT/05
Automated Reasoning 6 52 Italian Second semester MAT/01
Biomathematics 1 6 42 Italian First semester MAT/07
Calculus of Variations 6 42 Italian Second semester MAT/05
Categorical Dualities in Logic and Algebra 6 42 Italian First semester MAT/01
Category Theory 6 47 Italian First semester MAT/02
Category Theory 9 73 Italian First semester MAT/02
Computability and Computational Complexity 6 42 Italian First semester INF/01
Didactics of Mathematic 9 73 Italian First semester MAT/04
Didactics of Mathematic 6 47 Italian First semester MAT/04
Differential Topology 6 42 Italian Second semester MAT/03
Dynamical System 2 6 42 Italian First semester MAT/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian Second semester 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
Geometry of Schemes 6 47 Italian First semester MAT/03
Higher Geometry 1 6 42 Italian First semester MAT/03
Higher Geometry 2 6 52 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 Analysis 5 6 60 Italian First semester MAT/05
Mathematical Fluid-Mechanics 6 42 Italian Second semester MAT/07
Non Linear Partial Differential Equations 6 42 Italian First semester MAT/05
Numerical Linear Algebra 6 60 English Second semester MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian First semester MAT/08
Numerical Optimization 6 52 Italian Second semester MAT/08
Operating Systems and Computer Networks 6 47 Italian Second semester INF/01
Optimal Transport and Applications. 6 42 Italian First semester MAT/05
Point Processes and Random Sets 6 47 Italian Second semester MAT/06
Preparation of Didactical Experiences 1 6 52 Italian First semester FIS/08
Preparation of Future Teachers 2 6 52 Italian Second semester 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 - Gli studenti devono conseguire almeno 6 crediti nei settori Mat/06-07-08-09 scegliendo corsi che compaiono nelle tabelle 1A e 2A.
a4 - Gli studenti devono conseguire i crediti rimanenti per raggiungere il totale di 45 scegliendo corsi in un qualunque settore Mat/xx tra quelli che compaiono nelle tabelle 1A,2A,1B,2B,1C,2C.
a5 - ATTIVITA' AFFINI O INTEGRATIVE: 24 CREDITI
Gli studenti devono conseguire 24 crediti scegliendo tra:
· insegnamenti in settori diversi da Mat/xx che compaiono nelle tabelle 1A,2A,1B,2B,1C,2C;
· ulteriori insegnamenti offerti dall'Ateneo, in settori diversi da Mat/xx fuori dalle citate tabelle;
· almeno 12 crediti tra gli insegnamenti appartenenti a settori scientifico-disciplinari MAT/01-09 compresi nelle tabelle 1A-2A-1B-2B-1C-2C in base all'orientamento scelto.
Tranne per la prima opzione, la scelta sarà soggetta all'approvazione del CDM.
a6 - ULTERIORI ATTIVITA' FORMATIVE: 3 CREDITI
Gli studenti devono conseguire 3 crediti preparando un seminario, su un argomento assegnato da un docente a scelta dello studente oppure seguendo altre attività quali quelle previste per il curriculum C o il corso di laboratorio di modellistica matematica o tramite l'attività "Tecnologie per la finanza" (rivolgersi al Prof.Maggis) o il "Laboratorio di Metodi e Modelli Matematici in Python" (rivolgersi al Prof. Paleari; gli studenti possono conseguire 3 crediti tramite i Laboratori di Didattica e di Divulgazione (rivolgersi al Prof.Penati).
Courses or activities Max ECTS Total hours Language Lesson period SSD
Financial Technologies 3 20 Italian Open sessions NN
Laboratory of Education and Public Engagement 3 0 Italian Open sessions NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian Open sessions NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian Open sessions NN
a7 - CREDITI A LIBERA SCELTA: gli studenti devono acquisire i crediti mancanti a raggiungere il numero di 93 seguendo insegnamenti a libera scelta, scegliendo tra tutti gli insegnamenti erogati dall'Ateneo, purché coerenti con il progetto formativo e previa approvazione del Collegio Didattico. La scelta verrà sottoposta ad approvazione della Commissione di valutazione del Piano di studi presentato dallo studente.
Gli insegnamenti della laurea triennale che non sono obbligatori per tutti possono essere inseriti nel piano studi solo tra i crediti liberi.
Gli insegnamenti della laurea triennale obbligatori per tutti possono essere solo assegnati dalla commissione di ammissione.
There are no prerequisites.
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
English Proficiency B2 (3 ECTS) 3 0 English NN
be activated by the A.Y. 2026/2027
Conclusive activities
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
Final Exam 27 0 Italian NN
First semester
Courses or activities Max ECTS Total hours Language SSD
Optional
Advanced Mathematical Statistics 9 78 Italian MAT/06
Advanced Partial Differential Equations 6 42 Italian MAT/05
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
Citologia e istologia 9 78 Italian BIO/06
Computability and Computational Complexity 6 42 Italian INF/01
Didactics of Infinitesimal Calculus 6 42 Italian MAT/04
Didactics of Mathematic 9 73 Italian MAT/04
Didactics of Mathematic 6 47 Italian MAT/04
Dynamical System 2 6 42 Italian MAT/07
Ecologia 9 80 Italian BIO/07
Fourier Analysis 6 42 Italian MAT/05
Functional Analysis 6 42 Italian MAT/05
Genetics 9 80 Italian BIO/18
Geometry 5 9 78 Italian MAT/03
Hamiltonian System 1 9 73 Italian MAT/07
Hamiltonian System 1 6 47 Italian MAT/07
Mathematical Analysis 5 6 60 Italian MAT/05
Mathematical Finance 1 9 73 Italian SECS-S/06
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
Optimal Transport and Applications. 6 42 Italian MAT/05
Real Analysis 9 73 Italian MAT/05
Scientific Computing 6 60 Italian MAT/08
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities Max ECTS Total hours Language SSD
Optional
Advanced Topics in Real Analysis 6 42 Italian MAT/05
Algebra 4 9 78 Italian MAT/02
Biologia molecolare e bioinformatica 12 96 Italian BIO/11
Calculus of Variations 6 42 Italian MAT/05
Complex Analysis 9 73 Italian MAT/05
Complex Analysis 6 47 Italian MAT/05
Didactics of Geometry 6 52 Italian MAT/04
Dynamical Systems 1 6 42 Italian MAT/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian MAT/04
Fisiologia generale e animale 9 80 Italian BIO/09
Foundations of Mathematics I 6 42 Italian MAT/04
History of Mathematics 1 6 42 Italian MAT/04
Lie Groups 6 42 Italian MAT/03
Mathematical Finance 2 6 42 Italian SECS-S/06
Mathematical Fluid-Mechanics 6 42 Italian MAT/07
Mathematical Modelling Laboratory 6 72 Italian MAT/06 MAT/07 MAT/08
Numerical Linear Algebra 6 60 English MAT/08
Numerical Methods for Partial Differential Equations 2 9 78 Italian MAT/08
Numerical Optimization 6 52 Italian MAT/08
Operating Systems and Computer Networks 6 47 Italian INF/01
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
Ricerca operativa 6 48 Italian MAT/09
Stochastic Calculus and Applications 9 73 Italian MAT/06
First four month period
Courses or activities Max ECTS Total hours Language SSD
Optional
Complementi di ricerca operativa 6 48 Italian MAT/09
Decision methods and models 6 48 Italian MAT/09
Second four month period
Courses or activities Max ECTS Total hours Language SSD
Optional
Logistica 6 48 Italian MAT/09
Ottimizzazione combinatoria 6 48 Italian MAT/09
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Optional
Financial Technologies 3 20 Italian NN
Laboratory of Education and Public Engagement 3 0 Italian NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian NN
Optional activities and study plan rules
b1 - ATTIVITA' CARATTERIZZANTI:45 CREDITI
Gli studenti devono conseguire almeno 9 crediti nei settori Mat/01-02-03-04-05 scegliendo corsi che compaiono nella seguente tabella 1B.
Courses or activities Max ECTS Total hours Language Lesson period SSD
Advanced Mathematical Statistics 9 78 Italian First semester MAT/06
Advanced Probability 9 78 Italian First semester MAT/06
Complex Analysis 9 73 Italian Second semester MAT/05
Complex Analysis 6 47 Italian Second semester MAT/05
Didactics of Geometry 6 52 Italian Second semester MAT/04
Didactics of Infinitesimal Calculus 6 42 Italian First semester MAT/04
Dynamical Systems 1 6 42 Italian Second semester MAT/07
Functional Analysis 6 42 Italian First semester MAT/05
Hamiltonian System 1 6 47 Italian First semester MAT/07
Hamiltonian System 1 9 73 Italian First semester MAT/07
Mathematical Finance 1 9 73 Italian First semester SECS-S/06
Numerical Methods for Partial Differential Equations 1 9 78 Italian First semester MAT/08
Numerical Methods for Partial Differential Equations 2 9 78 Italian Second semester MAT/08
Partial Differential Equations 6 42 Italian Second semester MAT/05
Real Analysis 9 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 - Gli studenti devono conseguire almeno 6 crediti nei settori Mat/01-02-03-04-05 scegliendo corsi che compaiono nella seguente tabella 2B, oppure nella precedente tabella 1B.
Courses or activities Max 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 Real Analysis 6 42 Italian Second semester MAT/05
Algebra 4 9 78 Italian Second semester MAT/02
Biologia molecolare e bioinformatica 12 96 Italian Second semester BIO/11
Biomathematics 1 6 42 Italian First semester MAT/07
Calculus of Variations 6 42 Italian Second semester MAT/05
Citologia e istologia 9 78 Italian First semester BIO/06
Complementi di ricerca operativa 6 48 Italian First four month period MAT/09
Computability and Computational Complexity 6 42 Italian First semester INF/01
Decision methods and models 6 48 Italian First four month period MAT/09
Didactics of Mathematic 9 73 Italian First semester MAT/04
Didactics of Mathematic 6 47 Italian First semester MAT/04
Dynamical System 2 6 42 Italian First semester MAT/07
Ecologia 9 80 Italian First semester BIO/07
Elementary Mathematics from an Advanced Standpoint 1 6 42 Italian Second semester MAT/04
Fisiologia generale e animale 9 80 Italian Second semester BIO/09
Foundations of Mathematics I 6 42 Italian Second semester MAT/04
Fourier Analysis 6 42 Italian First semester MAT/05
Genetics 9 80 Italian 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
Logistica 6 48 Italian Second four month period MAT/09
Mathematical Analysis 5 6 60 Italian First semester MAT/05
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
Non Linear Partial Differential Equations 6 42 Italian First semester MAT/05
Numerical Linear Algebra 6 60 English Second semester MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian First semester MAT/08
Numerical Optimization 6 52 Italian Second semester MAT/08
Operating Systems and Computer Networks 6 47 Italian Second semester INF/01
Optimal Transport and Applications. 6 42 Italian First semester MAT/05
Ottimizzazione combinatoria 6 48 Italian Second four month period MAT/09
Point Processes and Random Sets 6 47 Italian Second semester MAT/06
Ricerca operativa 6 48 Italian Second semester MAT/09
Scientific Computing 6 60 Italian First semester MAT/08
Stochastic Control Optimization 6 47 Italian First semester MAT/06
b3 - Gli studenti devono conseguire almeno 12 crediti nei settori Mat/06-07-08-09 inserendo nel proprio piano di studio corsi che compaiono nella tabella 1B.
b4 - Gli studenti devono conseguire almeno 12 crediti nei settori Mat/06-07-08-09 inserendo nel proprio piano di studio corsi che compaiono nella tabella 2B.
b5 - Gli studenti devono conseguire i crediti rimanenti per il raggiungimento dei 45 crediti scegliendo corsi in un qualunque settore Mat/xx tra quelli che compaiono nelle tabelle 1A,2A,1B,2B,1C,2C.
b6 - ATTIVITA'AFFINI O INTEGRATIVE: 24 crediti
Gli studenti devono conseguire 24 crediti scegliendo:
· insegnamenti in settori diversi da Mat/xx che compaiono nelle tabelle 1A,2A,1B,2B,1C,2C;
· ulteriori insegnamenti offerti dall'Ateneo, in settori diversi da Mat/xx fuori dalle citate tabelle;
· almeno 12 crediti tra gli insegnamenti appartenenti a settori scientifico-disciplinari MAT/01-09 compresi nelle tabelle 1A,2A,1B,2B,1C,2C in base all'orientamento scelto.
Tranne per la prima opzione, la scelta sarà soggetta all'approvazione del CDM.
b7 - ULTERIORI ATTIVITA' FORMATIVE: 3 CREDITI
Gli studenti devono conseguire 3 crediti preparando un seminario, su un argomento assegnato da un docente a scelta dello studente oppure seguendo altre attivita' quali quelle previste per il curriculum C o il corso di laboratorio di modellistica matematica o tramite l'attività "Tecnologie per la finanza" (rivolgersi al Prof.Maggis) o il "Laboratorio di Metodi e Modelli Matematici in Python" (rivolgersi al Prof. Paleari); gli studenti possono conseguire 3 crediti tramite i Laboratori di Didattica e di Divulgazione (rivolgersi al Prof.Penati).
Courses or activities Max ECTS Total hours Language Lesson period SSD
Financial Technologies 3 20 Italian Open sessions NN
Laboratory of Education and Public Engagement 3 0 Italian Open sessions NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian Open sessions NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian Open sessions NN
b8 - CREDITI A LIBERA SCELTA: gli studenti devono acquisire i crediti mancanti a raggiungere il numero di 93 seguendo insegnamenti a libera scelta, scegliendo tra tutti gli insegnamenti erogati dall'Ateneo,purché coerenti con il progetto formativo e previa approvazione del Collegio Didattico. La scelta verrà sottoposta ad approvazione della Commissione di valutazione del Piano di studi presentato dallo studente.
Gli insegnamenti della laurea triennale che non sono obbligatori per tutti possono essere inseriti nel piano studi solo tra i crediti liberi.
Gli insegnamenti della laurea triennale obbligatori per tutti possono essere solo assegnati dalla commissione di ammissione.
There are no prerequisites.
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
English Proficiency B2 (3 ECTS) 3 0 English NN
be activated by the A.Y. 2026/2027
Conclusive activities
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Compulsory
Final Exam 27 0 Italian NN
First semester
Courses or activities Max ECTS Total hours Language SSD
Optional
Advanced Mathematical Statistics 9 78 Italian MAT/06
Advanced Partial Differential Equations 6 42 Italian MAT/05
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
Dynamical System 2 6 42 Italian MAT/07
Fourier Analysis 6 42 Italian MAT/05
Functional Analysis 6 42 Italian MAT/05
Geometry 5 9 78 Italian MAT/03
Hamiltonian System 1 9 73 Italian MAT/07
Hamiltonian System 1 6 47 Italian MAT/07
Mathematical Analysis 5 6 60 Italian MAT/05
Mathematical Finance 1 9 73 Italian SECS-S/06
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
Scientific Computing 6 60 Italian MAT/08
Stochastic Control Optimization 6 47 Italian MAT/06
Second semester
Courses or activities Max 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
Complex Analysis 6 47 Italian MAT/05
Dynamical Systems 1 6 42 Italian MAT/07
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
Numerical Optimization 6 52 Italian MAT/08
Operating Systems and Computer Networks 6 47 Italian INF/01
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
Ricerca operativa 6 48 Italian MAT/09
Stochastic Calculus and Applications 9 73 Italian MAT/06
First four month period
Courses or activities Max ECTS Total hours Language SSD
Optional
Complementi di ricerca operativa 6 48 Italian MAT/09
Decision methods and models 6 48 Italian MAT/09
Second four month period
Courses or activities Max ECTS Total hours Language SSD
Optional
Logistica 6 48 Italian MAT/09
Ottimizzazione combinatoria 6 48 Italian MAT/09
Open sessions
There are no specific sessions for these activities.
Courses or activities Max ECTS Total hours Language SSD
Optional
Algant Summer School 3 0 Italian NN
Ecmi Modelling Week 3 0 Italian NN
Financial Technologies 3 20 Italian NN
Internship in Industry 6 0 Italian NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian NN
Optional activities and study plan rules
c1 - ATTIVITA' CARATTERIZZANTI: 45 CREDITI
Gli studenti devono conseguire ALMENO 15 crediti nel settore Mat/05, 9 crediti nel settore Mat/06, 9 nel settore Mat/08, inserendo nel proprio piano di studi corsi che compaiono nella seguente tabella 1C. Nel caso ciò non fosse possibile per qualche SSD (per es. quando l'esame di alcuni di questi insegnamenti fosse già stato sostenuto nel corso di un CdL triennale) lo studente deve inserire nel proprio piano degli studi gli eventuali insegnamenti di quel SSD rimasti nella tabella e, se necessario, aggiungere insegnamenti di quel SSD fino al raggiungimento dei crediti prescritti scegliendoli tra quelli attivati e presenti nella tabella 2C.
Courses or activities Max ECTS Total hours Language Lesson period SSD
Advanced Mathematical Statistics 9 78 Italian First semester MAT/06
Dynamical Systems 1 6 42 Italian Second semester MAT/07
Functional Analysis 6 42 Italian First semester MAT/05
Hamiltonian System 1 9 73 Italian First semester MAT/07
Hamiltonian System 1 6 47 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 - Gli studenti devono conseguire almeno 6 crediti nei settori mat/06-07-08-09 inserendo nel proprio piano di studi corsi che compaiono nella seguente tabella 2C.
Courses or activities Max 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 Real Analysis 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
Complementi di ricerca operativa 6 48 Italian First four month period MAT/09
Complex Analysis 9 73 Italian Second semester MAT/05
Complex Analysis 6 47 Italian Second semester MAT/05
Decision methods and models 6 48 Italian First four month period 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
Logistica 6 48 Italian Second four month period MAT/09
Mathematical Analysis 5 6 60 Italian First semester MAT/05
Mathematical Finance 1 9 73 Italian 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
Non Linear Partial Differential Equations 6 42 Italian First semester MAT/05
Numerical Linear Algebra 6 60 English Second semester MAT/08
Numerical Methods for Partial Differential Equations 3 9 78 Italian First semester MAT/08
Numerical Optimization 6 52 Italian Second semester MAT/08
Operating Systems and Computer Networks 6 47 Italian Second semester INF/01
Ottimizzazione combinatoria 6 48 Italian Second four month period MAT/09
Point Processes and Random Sets 6 47 Italian Second semester MAT/06
Relativity 1 9 78 Italian Second semester MAT/07
Ricerca operativa 6 48 Italian Second semester MAT/09
Scientific Computing 6 60 Italian First semester MAT/08
Stochastic Control Optimization 6 47 Italian First semester MAT/06
c3 - Gli studenti devono conseguire i crediti al raggiungimento dei 45 scegliendo insegnamenti in un qualunque settore mat/xx tra quelli che compaiono nelle tabelle 1C,2C.
c4 - ATTIVITA' AFFINI O INTEGRATIVE: 18 CREDITI
Gli studenti devono conseguire
- almeno 12 crediti scegliendo tra:
· insegnamenti in settori diversi da Mat/xx che compaiono nelle tabelle 1A,2A,1B,2B,1C,2C;
· ulteriori insegnamenti in settori diversi da Mat/xx fuori dalle citate tabelle;
- fino a 6 crediti scegliendo tra:
· insegnamenti nei settori Mat/xx.
Tranne per la prima opzione, la scelta sarà soggetta all'approvazione del CDM.
c5 - ULTERIORI ATTIVITA' FORMATIVE: 12 CREDITI
Gli studenti possono conseguire i 12 cfu mediante uno stage/tirocinio industriale (6 cfu) o l'insegnamento di Laboratorio di modellistica matematica(6 cfu) o tramite la partecipazione alle attività della ECMI Modelling Week che si svolgerà a Lund (Svezia) nell'estate del 2026. Per ulteriori informazioni sulla Modelling Week rivolgersi alla prof.ssa Paola Causin.
In alternativa si possono conseguire tramite:
attività "Tecnologie per la finanza" (3 cfu), rivolgersi al Prof. Maggis o il "Laboratorio di Metodi e Modelli Matematici in Python"(rivolgersi al Prof. Paleari).
Gli studenti Algant possono acquisire 3 cfu in seguito a partecipazione attiva alla Algant Summer School e/o mediante TER (=Travaux d'étude et de recherche) certificato da una sede francese partner in Algant.
Al più 3 cfu si possono acquisire anche preparando un seminario, su un argomento assegnato da un docente o tramite l'attività "Tecnologie per la finanza" o il "Laboratorio di Metodi e Modelli Matematici in Python"
Courses or activities Max ECTS Total hours Language Lesson period SSD
Algant Summer School 3 0 Italian Open sessions NN
Ecmi Modelling Week 3 0 Italian Open sessions NN
Financial Technologies 3 20 Italian Open sessions NN
Internship in Industry 6 0 Italian Open sessions NN
Laboratory of Mathematical Methods and Models in Python 3 30 Italian Open sessions NN
Supplementary Seminar in an Advanced Mathematics Area 3 0 Italian Open sessions NN
c6 - CREDITI A LIBERA SCELTA: gli studenti devono acquisire i crediti mancanti a raggiungere il numero di 93 seguendo insegnamenti a libera scelta, scegliendo tra tutti gli insegnamenti erogati dall'Ateneo, purché coerenti con il progetto formativo e previa approvazione del Collegio Didattico. La scelta verrà sottoposta ad approvazione della Commissione di valutazione del Piano di studi presentato dallo studente.
Gli insegnamenti della laurea triennale che non sono obbligatori per tutti possono essere inseriti nel piano studi solo tra i crediti liberi.
Gli insegnamenti della laurea triennale obbligatori per tutti possono essere solo assegnati dalla commissione di ammissione.
There are no prerequisites.
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Location
Milan
Head of study programme
Contacts
  • Master's Degree Organization Board
    VIGNATI Marco (Presidente), ALZATI Alberto, SCACCHI Simone, MAZZA Carlo
  • Orientation and Internship Board
    TORTORA Alfonso (Presidente), NALDI Giovanni, MICHELETTI Alessandra, MAGGIS Marco, COZZI Matteo, BRANCHETTI Laura
  • Secondary school teacher training activities
    BRANCHETTI Laura (Presidente), ASENOVA Miglena, RIZZO Ottavio
  • Master's Degree Study Plan Board
    PAYNE Kevin (Presidente), COLOMBO Elisabetta, PIZZOCCHERO Livio, UGOLINI Stefania
  • Timetables Board
    LOVADINA Carlo (Presidente), ZAMPIERI Elena, ZANOTTI Pietro
  • Student registrar
    CONTATTI, SEDI E ORARI
    https://www.unimi.it/it/node/360
    https://www.unimi.it/it/node/359
  • Piano Lauree Scientifiche" academic tutor
    CAUSIN Paola
  • Other Activities and Credit Award Board
    SCACCHI Simone (Presidente), MOLTENI Giuseppe, TORTORA Alfonso
  • Degree programme administration
    Milano-via Celoria20
    https://informastudenti.unimi.it/saw/ess?AUTH=SAML
    +390250316107 - 0250316122
    9.30-11.30 su appuntamento il LUNEDì
  • ALGANT academic tutor
    MAZZA Carlo
  • Disability academic tutor
    SCACCHI Simone
  • Web pages and website academic tutors
    PALEARI Simone
  • ECMI academic tutor
    CAUSIN Paola
  • academic tutor
    PENATI Tiziano
  • 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, REGGIO Luca

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