[16-263] Mathematics (d.m.270/04) | Università degli Studi di Modena e Reggio Emilia

Type

Master Degree Course

Access mode

Free

Length

2 years

Location

Modena

Language

Italian

Department

Department of Physics, Informatics and Mathematics

The Degree Course in brief

Mathematics is a very ancient, yet evolving discipline that develops its knowledge in an abstract context by means of inductive and deductive methods. Alongside problems that have been studied for centuries, the needs of an ever-changing society increasingly propose to Mathematics new problems derived from the Physical, Chemical, Natural, Economic, Social Sciences, Engineering, and Medicine. In addition, in all countries around the world, Mathematics contributes to the cultural education of students in schools of all levels.

The Master’s Degree Programme in Mathematics aims to complete the preparation of students in a focused way, focusing on the threefold vocation of a mathematician toward academic research, teaching in secondary schools or employment in public and private research institutions, industry, banking, insurance and finance, and, more generally, the high-tech service sector.

For this reason, the programme is organised in three separate curricula:

- General curriculum, for an in-depth preparation both on the theoretical aspects and on the applied aspects of mathematics, in order to introduce students to the scientific research sector.

- Teaching curriculum, history and foundations of mathematics, for a solid preparation on mathematics, its history and teaching methods, with the aim of training a highly professional figure in the field of teaching.

- Data Science Curriculum, for a particularly in-depth preparation on modelling and computational aspects of Mathematics and Computer Science, with the aim of training a highly professional figure in working sectors that require advanced skills in Machine Learning, Statistics, Big Data Analytics and Signal Analysis for applied research both in business and industry and in the academic environment.

The customised design of the curriculum is facilitated by offering a wide range of electives, allowing for different educational paths. Through practical exercises, workshops and drawing up the degree thesis, students have the opportunity to independently develop their abilities and interests.

Info

Department: Department of Physics, Informatics and Mathematics

Degree class:

CFU: 120

Didactic method: PRESENCE

Study plan

Teachings

Study plan

Year of study: 1

Required

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

ADVANCED ANALYSIS
12 CFU - 84 hours - Single Annual Cycle

INGLESE SCIENTIFICO AVANZATO
3 CFU - 21 hours - Second Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

GEN attività opzionali caratterizzanti I anno (12 CFU)

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

GEN opzionali affini I anno (between 6 and 18 CFU)

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

PARTIAL DIFFERENTIAL EQUATIONS
6 CFU - 42 hours - Second Half-Year Cycle

FONDAMENTI DI ALGEBRA E GEOMETRIA
6 CFU - 42 hours - Single Annual Cycle

FONDAMENTI DI LOGICA E ANALISI MATEMATICA
6 CFU - 42 hours - Single Annual Cycle

STORIA DEL CALCOLO INFINITESIMALE
6 CFU - 42 hours - Single Annual Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta del CdS 1 anno (between 1 and 99 CFU)

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

ANALISI DI FOURIER
6 CFU - 42 hours - Single Annual Cycle

ANALISI FUNZIONALE
6 CFU - 42 hours - Single Annual Cycle

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

SCIENTIFIC DATA PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

PARTIAL DIFFERENTIAL EQUATIONS
6 CFU - 42 hours - Second Half-Year Cycle

FONDAMENTI DI ALGEBRA E GEOMETRIA
6 CFU - 42 hours - Single Annual Cycle

FONDAMENTI DI LOGICA E ANALISI MATEMATICA
6 CFU - 42 hours - Single Annual Cycle

INTRODUCTION TO QUANTUM INFORMATION PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

PHYSICS EDUCATION: THEORETICAL AND EXPERIMENTAL METHODS
6 CFU - 36 hours - Second Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

STORIA DEL CALCOLO INFINITESIMALE
6 CFU - 42 hours - Single Annual Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta primo anno (between 1 and 99 CFU)

Year of study: 2

Required

ALTRE ATTIVITÀ
3 CFU - 0 hours -

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

FINAL EXAMINATION
24 CFU - 0 hours -

GEN opzionali affini II anno (between 6 and 18 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

CALCULUS OF VARIATIONS
6 CFU - 42 hours - Second Half-Year Cycle

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

EQUAZIONI DI EVOLUZIONE
6 CFU - 42 hours - Second Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta del CdS 2 anno (between 1 and 99 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

ALGORITMI DISTRIBUITI
6 CFU - 42 hours - First Half-Year Cycle

BIG DATA ANALYTICS
6 CFU - 42 hours - Second Half-Year Cycle

CALCULUS OF VARIATIONS
6 CFU - 42 hours - Second Half-Year Cycle

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

EQUAZIONI DI EVOLUZIONE
6 CFU - 42 hours - Second Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta secondo anno (between 1 and 99 CFU)

Year of study: 1

Required

ADVANCED ANALYSIS
12 CFU - 84 hours - Single Annual Cycle

COMPUTATIONAL AND STATISTICAL LEARNING
9 CFU - 63 hours - Second Half-Year Cycle

INGLESE SCIENTIFICO AVANZATO
3 CFU - 21 hours - Second Half-Year Cycle

INTRODUCTION TO SCIENTIFIC PYTHON
3 CFU - 12 hours - First Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

DS opzionali modellistico-applicativi (12 CFU)

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

DS opzionali affini I anno (between 6 and 12 CFU)

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

SCIENTIFIC DATA PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

PARTIAL DIFFERENTIAL EQUATIONS
6 CFU - 42 hours - Second Half-Year Cycle

INTRODUCTION TO QUANTUM INFORMATION PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta del CdS 1 anno (between 1 and 99 CFU)

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

ANALISI DI FOURIER
6 CFU - 42 hours - Single Annual Cycle

ANALISI FUNZIONALE
6 CFU - 42 hours - Single Annual Cycle

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

SCIENTIFIC DATA PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

PARTIAL DIFFERENTIAL EQUATIONS
6 CFU - 42 hours - Second Half-Year Cycle

FONDAMENTI DI ALGEBRA E GEOMETRIA
6 CFU - 42 hours - Single Annual Cycle

FONDAMENTI DI LOGICA E ANALISI MATEMATICA
6 CFU - 42 hours - Single Annual Cycle

INTRODUCTION TO QUANTUM INFORMATION PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

PHYSICS EDUCATION: THEORETICAL AND EXPERIMENTAL METHODS
6 CFU - 36 hours - Second Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

STORIA DEL CALCOLO INFINITESIMALE
6 CFU - 42 hours - Single Annual Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta primo anno (between 1 and 99 CFU)

Year of study: 2

Required

ALTRE ATTIVITÀ
3 CFU - 0 hours -

FINAL EXAMINATION
24 CFU - 0 hours -

DS opzionali affini II anno (between 6 and 12 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

ALGORITMI DISTRIBUITI
6 CFU - 42 hours - First Half-Year Cycle

BIG DATA ANALYTICS
6 CFU - 42 hours - Second Half-Year Cycle

CALCULUS OF VARIATIONS
6 CFU - 42 hours - Second Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

EQUAZIONI DI EVOLUZIONE
6 CFU - 42 hours - Second Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

DS opzionali formazione teorica avanzata (6 CFU)

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

AD a libera scelta del CdS 2 anno (between 1 and 99 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

ALGORITMI DISTRIBUITI
6 CFU - 42 hours - First Half-Year Cycle

BIG DATA ANALYTICS
6 CFU - 42 hours - Second Half-Year Cycle

CALCULUS OF VARIATIONS
6 CFU - 42 hours - Second Half-Year Cycle

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

EQUAZIONI DI EVOLUZIONE
6 CFU - 42 hours - Second Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta secondo anno (between 1 and 99 CFU)

Year of study: 1

Required

TEACHING OF MATHEMATICS
6 CFU - 42 hours - Second Half-Year Cycle

FONDAMENTI DI MATEMATICA
12 CFU - 84 hours - Single Annual Cycle

INGLESE SCIENTIFICO AVANZATO
3 CFU - 21 hours - Second Half-Year Cycle

HISTORY OF MATHEMATICS
6 CFU - 42 hours - First Half-Year Cycle

DSF opzionali caratterizzanti I anno (24 CFU)

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

DSF opzionali affini I anno (between 6 and 12 CFU)

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

ANALISI DI FOURIER
6 CFU - 42 hours - Single Annual Cycle

ANALISI FUNZIONALE
6 CFU - 42 hours - Single Annual Cycle

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

PHYSICS EDUCATION: THEORETICAL AND EXPERIMENTAL METHODS
6 CFU - 36 hours - Second Half-Year Cycle

STORIA DEL CALCOLO INFINITESIMALE
6 CFU - 42 hours - Single Annual Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta del CdS 1 anno (between 1 and 99 CFU)

HIGHER ALGEBRA
6 CFU - 42 hours - First Half-Year Cycle

ANALISI DI FOURIER
6 CFU - 42 hours - Single Annual Cycle

ANALISI FUNZIONALE
6 CFU - 42 hours - Single Annual Cycle

CURVE ALGEBRICHE SU CAMPI FINITI
6 CFU - 42 hours - Second Half-Year Cycle

SCIENTIFIC DATA PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

NUMERICAL ALGORITHMS FOR SIGNALS AND IMAGES PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

PARTIAL DIFFERENTIAL EQUATIONS
6 CFU - 42 hours - Second Half-Year Cycle

FONDAMENTI DI ALGEBRA E GEOMETRIA
6 CFU - 42 hours - Single Annual Cycle

FONDAMENTI DI LOGICA E ANALISI MATEMATICA
6 CFU - 42 hours - Single Annual Cycle

INTRODUCTION TO QUANTUM INFORMATION PROCESSING
6 CFU - 42 hours - First Half-Year Cycle

MECCANICA STATISTICA
6 CFU - 42 hours - First Half-Year Cycle

METODI STOCASTICI PER SIMULAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

OTTIMIZZAZIONE NUMERICA PER L'INTELLIGENZA ARTIFICIALE
6 CFU - 42 hours - Second Half-Year Cycle

PHYSICS EDUCATION: THEORETICAL AND EXPERIMENTAL METHODS
6 CFU - 36 hours - Second Half-Year Cycle

PROBLEMI INVERSI E APPLICAZIONI
6 CFU - 42 hours - Second Half-Year Cycle

STOCHASTIC PROCESSES
6 CFU - 42 hours - Second Half-Year Cycle

SISTEMI DI PARTICELLE INTERAGENTI
6 CFU - 42 hours - First Half-Year Cycle

STORIA DEL CALCOLO INFINITESIMALE
6 CFU - 42 hours - Single Annual Cycle

TEORIA DEI GRAFI
6 CFU - 42 hours - First Half-Year Cycle

TOPOLOGIA GEOMETRICA DELLE VARIETÀ
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta primo anno (between 1 and 99 CFU)

Year of study: 2

Required

ALTRE ATTIVITÀ
3 CFU - 0 hours -

ELEMENTARY MATHEMATICS FROM A HIGHER POINT OF VIEW
6 CFU - 42 hours - First Half-Year Cycle

FINAL EXAMINATION
24 CFU - 0 hours -

DSF opzionali affini II anno (between 6 and 12 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta del CdS 2 anno (between 1 and 99 CFU)

ALGORITMI DI CRITTOGRAFIA
6 CFU - 42 hours - First Half-Year Cycle

ALGORITMI DISTRIBUITI
6 CFU - 42 hours - First Half-Year Cycle

BIG DATA ANALYTICS
6 CFU - 42 hours - Second Half-Year Cycle

CALCULUS OF VARIATIONS
6 CFU - 42 hours - Second Half-Year Cycle

COMPUTATIONAL TOPOLOGY
6 CFU - 42 hours - Second Half-Year Cycle

CONVEX ANALYSIS AND OPTIMIZATION
6 CFU - 42 hours - First Half-Year Cycle

ELEMENTI DI FISICA MODERNA
6 CFU - 42 hours - Second Half-Year Cycle

EQUAZIONI DI EVOLUZIONE
6 CFU - 42 hours - Second Half-Year Cycle

GEOMETRIA SUPERIORE
6 CFU - 42 hours - First Half-Year Cycle

MATEMATICA DISCRETA
6 CFU - 42 hours - Second Half-Year Cycle

COMPLEX SYSTEMS
6 CFU - 42 hours - Second Half-Year Cycle

ALGEBRAIC STRUCTURES
6 CFU - 42 hours - First Half-Year Cycle

AD a libera scelta secondo anno (between 1 and 99 CFU)

More information

Admission requirements and admission procedures

Students willing to enrol in the Master’s Degree Programme in Mathematics must possess a suitable background knowledge in the fields of algebra, geometry, mathematical analysis, probability, mathematical physics, and numerical analysis, as well as good knowledge of basic physics and ITC. They must also be able to prepare and recognise precise demonstrations, use a mathematical language to formalise problems formulated in the natural language, build and develop mathematics topics clearly identifying assumptions and conclusions, read and understand even advanced texts of Mathematics.

The background knowledge of students with a three-year degree in one of classes L-08, L-30, L-31, L-35, or a university degree obtained under former M.D. 509/99 in classes recognised as equivalent to those listed under former M.D. 270/04, will be assessed by evaluating their qualifications and through an oral interview.

Students with a three-year degree of a different class or a degree obtained under the former regulation, or other qualification obtained abroad and deemed suitable pursuant to the applicable legislation shall previously possess the following curriculum requirements:
1) 30 CFUs in the SDS MAT/01-08;
2) 18 CFUs in the SDS FIS/01-04, INF/01, ING-INF/05.
They shall also pass an oral interview aimed at proving a good background of theoretical, methodological, and applicative skills in the essential areas of mathematics. In addition, students must have acquired at least 3 university credits (CFUs) in sector L-LIN12 or have an international certification deemed equivalent at least to a level B1.

In case the verification of the initial background does not give positive results, the evaluation board indicates the specific curriculum integrations, the procedures and the terms to meet by the enrolment deadline.

Students willing to enrol in the DP must have a three-year university degree or diploma, or another qualification obtained abroad and recognised as valid pursuant to the applicable legislation, along with the curriculum requirements and a proper academic background.

In accordance with the provisions of the degree programme, students wishing to enrol must first meet the following curricular requirements:
1) 30 CFUs in the SDS MAT/01-08;
2) 18 CFUs in the SDS FIS/01-04, INF/01, ING-INF/05.

For students holding a Bachelor's degree in one of the classes L-08, L-30, L-31, L-35, the fulfilment of the curricular requirements is verified through the evaluation of the curriculum by a Commission appointed by the Department.

For students holding a three-year degree in a different class or a degree awarded under the previous system, or another degree awarded abroad that is recognised as suitable under current legislation, possession of the curricular requirements is verified through an assessment of the curriculum and qualifications by a Commission appointed by the Department. Should the assessment not be positive, specific curriculum integrations will be assigned to the student to comply with within the set deadlines and anyway by the date specified in the call for applications each year. Integration is verified by passing examinations specified by the Commission.

The means of assessment are published in detail, well in advance, on the relevant call for applications or notification.

Students willing to enrol must possess a suitable academic background in the fields of algebra, geometry, mathematical analysis, probability, mathematical physics, and numerical analysis, as well as good knowledge of basic physics and ITC. They must also be able to prepare and recognise precise demonstrations, use a mathematical language to formalise problems formulated in the natural language, build and develop mathematics topics clearly identifying assumptions and conclusions, read and understand even advanced texts of Mathematics.

This preparation is verified through an interview, to be held before the deadline for enrolling in the degree programme.

Profile and career opportunities

Graduate mathematician (master’s degree)
Graduates have a background knowledge in almost all sectors of mathematics. They are able to use programming languages. They are skilled on the teaching aspects of mathematics. Based on the training programme chosen, they have broadened some specific subjects, in which almost often they are able to independently solve issues, even of a complex nature.

Graduate mathematician (master’s degree)
Master graduates in Mathematics stand out for their skill to face logical problems with precision, both individually and in a team. For this reason, they are able to carry out scientific research tasks fully independently within theoretical or applicative contexts.
Their specific skills to communicate issues and methods of mathematics, as well as their knowledge of the relevant teaching methodologies make them perfect for school and university teaching, and for research activities.
They are able to carry out high responsibility functions, even at management level.

Graduate mathematician (master’s degree)
Graduates with the requirements set up by the regulations may access teacher training programmes. They may also enrol in 2nd level Master programmes and start a university career after obtaining a PhD qualification. They are skilled to disseminate the scientific culture with expertise.
Ultimately, they may aspire to take on high responsibility roles, regarding the construction, the theoretical study, and the computational development of mathematical models of various kinds, in different application fields (scientific, environmental, healthcare, industrial, financial, service, and public administration).

Objectives and educational background

The Master’s Degree in Mathematics is addressed to students interested in deepening both the theoretical and applicative aspects of mathematics. The Programme aims to lay firm foundations so that students may continue their studies through a PhD or a second level Master Programme, become teachers in public or private schools, or enter the job market in the industrial and tertiary sector. Therefore, students shall be able to: start research in a specialisation field; analyse and solve complex problems, even in applicative contexts; use mathematical models to translate situations occurring in the real world and transfer mathematical knowledge to non-mathematical contexts; be ready to pay attention to issues arising in new areas, including the difficulties to extract their essential elements; formulate complex optimisation and decision-making problems and interpret the solutions in the original contexts of such problems. Also, students must be able to present topics and their conclusions in mathematical terms, clearly and accurately and with suitable means to the audience, both orally and in writing.

The best educational tool for the development of such knowledge includes traditional lectures and practical exercises. Practical exercises are essential in Mathematics, where understanding is strengthened through practice. Practical exercises are offered to be carried out independently, through which students are encouraged to explore the limits of their knowledge. The educational material includes text books, scientific articles and lesson handouts. The assessment is made in a traditional form by evaluating a written paper and/or an oral interview. Students are also offered training activities that are useful to place the specific skills that are characteristic of the class in the general scientific-technological, cultural, social, and economic context.
A further, essential educational tool characterising the Master’s Degree Programme are the IT laboratories. In addition to practical exercises of ITC and computational mathematics teachings, in laboratories numerical experiments are carried out on themes as they emerge from theoretical insights presented during the lessons or from real applications.
Seminar and tutoring activities are also provided and mainly aimed to develop the abilities to face and solve issues. The training programme may include an internship period, to be taken under the supervision of an external tutor and a university tutor. The training programme ends by preparing the final dissertation, which generally requires students to read scientific texts and bibliography in a foreign language, and to personally explore issues that are not dealt with in the common teaching activities.
Most training activities provided feature a strong logic precision and a high level of abstraction.

The Master’s Degree Programme in Mathematics also provides for some teachings be given fully in English.

The Course according to the Dublin Descriptors

Students are required to:

- be able to propose and analyse mathematical models associated to real situations resulting from other subjects even of a complex nature, and to use such models to make the study of the original situation easier;

- be able to work independently, even taking scientific and organisational responsibilities;

- be able to understand and assess the difficulties of the teaching/learning process based on the topic dealt with and the condition of learners.

The educational tools useful to reach such objectives are the individual study, the preparation and the discussion of the Degree Thesis. Such skills are specific of teachings provided in the study programme. More specifically, teachings in the application field are aimed at reaching the first objective, whereas teachings in the theoretical and educational field are addressed to the fulfilment of the third objective. The internship is not compulsory but may be used to develop these skills. These objectives are assessed in the examination tests and during the discussion of the final thesis.

Students are required to:

- have the specific skills to communicate the issues and methods of mathematics;

- know and be able to apply the different teaching methods;

- be able to use fluently, both in writing and orally, at least one of the EU languages, other than Italian.

The educational tools used to reach such objectives are the examinations, the preparation and the discussion of the Degree Thesis. The additional language activities and the optional teachings provided in English are educational tools offered to reach the third objective. The internship is not compulsory but may be used to develop these skills. These objectives are assessed in the examination tests, also taken by means of multimedia tools and during the discussion of the final thesis.

Students are required to:

- be able to do searches also using the material available in English, as well as other sources of information that is relevant for the development of the research;

- be able to keep up-to-date and informed on the new developments and methods, and deal with new fields through an independent study.

The educational tools useful to reach such objectives are the individual study, the preparation and the discussion of the Degree Thesis. These objectives are assessed in the examination tests and during the discussion of the final thesis.

General area
Students are required to:
- be able to read and explore a topic of Mathematics literature, as well as present it in a clear and accurate manner;
- master abstraction skills, including the logical development of formal theories and their relations;
- be able to link the various mathematical concepts between them, taking into account the logical and hierarchical structure of mathematics;
- have an in-depth knowledge of the scientific and deductive logical method.
The favoured teaching tools for achieving such objectives are the practical lessons and sessions; they are assessed in a traditional form through the assessment of a written paper and/or an oral interview.

Advanced theoretical area
Students are expected to have high-level knowledge in the following areas:
- algebra, differential and combinatorial geometry, topology;
- functional analysis, convex analysis, differential equations and calculus of variations;
- probability, statistics and mathematical physics;
- numerical analysis and signal processing.

Teacher training area
Students are expected to have advanced knowledge in the following areas:
- history of mathematics and related educational experiences;
- teaching methodologies and related teaching experiences.

Application training area
Students are required to have advanced knowledge, with a focus on modelling and computational aspects, in the following areas:
- computational geometry, functional analysis, probability and statistics;
- extraction of information from large amounts of data, easily using computer and computational tools to support mathematical processes.

General area
Students are required to:
- have specialist mathematical knowledge, also to support other sciences;
- be able to build examples or exercises suitably calibrated in terms of difficulty and linked as much as possible to reality and other disciplines;
- be able to deal with issues the modelling and resolution of which may lead to the discovery of a concept or development of a theory;
- be skilled to realise, imagine, suppose, deduct, and verify, with the purpose of interpreting, order, quantify, forecast, and measure real phenomena;
- be able to mathematically formalise highly difficult issues formulated in a non-mathematical language and independently identify and use the most suitable mathematical techniques for their study.
These skills are acquired and verified in all compulsory teachings, in most optional teachings of the Degree Programme, and in the preparation of the thesis. The internship is not compulsory but may be used to develop these skills.

Advanced theoretical area
Students are required to have the ability to:
- support mathematical reasoning and produce rigorous demonstrations of even advanced mathematical results in different areas of mathematics;
- solve complex problems in different fields of mathematics.
These skills are acquired and verified in the compulsory teachings of the General Curriculum, in the optional teachings of the Degree Programme, and in the preparation of the Thesis. The internship, which is not compulsory, can be used to develop these skills through internal placements with lecturers from the degree programme or seminar activities.

Teacher training area
Students are required to have the ability to:
- ideate lessons and teaching projects that are suitable to different school levels and able to encourage, stimulate, facilitate and drive the interest for the mathematical thinking aimed at the teaching profession;
- use multimedia tools and educational software for the teaching and dissemination of mathematics;
- frame the acquired knowledge in the historical development of mathematics.
These skills to apply knowledge and understanding are acquired and verified in the compulsory teachings of the Teaching Curriculum and in other teachings of the Degree Programme and in the thesis work. The internship in schools is not compulsory but may be used to develop these skills.

Application training area
Students are required to have the ability to:
- propose and analyse mathematical models for even complex problems or problems from other disciplines;
- use computer and computational tools to support mathematical processes, and to acquire further information;
- extract qualitative information from quantitative data even in complex situations.
These skills to apply knowledge and understanding are acquired and verified in the compulsory teachings of the Data Science Curriculum and in other teachings of the Degree Programme and in the thesis work. The internship in a company is not compulsory but may be used to develop these skills.