Prerequisites for the admission.

The 1st cycle degree programme in Mathematics has open access; admission to the 1st cycle degree programme in Mathematics is subject to the possession of a secondary school certificate or equivalent suitable and approved qualification obtained abroad. Students may enrol on a part-time basis.
The aptitude for undertaking a Degree Programme in Mathematics is assessed in an entrance exam or interview to assess the minimum requirements for students wishing to enrol in the degree programme. The assessment is based on mathematical topics relating to the secondary school curriculum, deemed to be prerequisites for studying Mathematics. The topics are defined in agreement with the secondary schools and the National Conference of Deans and Directors of University Sciences and Technologies Structures. Example tests are distributed to schools to allow students to evaluate their own skills level prior to enrolment.
The outcome of the test does not prejudice the possibility to enrol in the programme, as the programme organises preparatory courses to fill any learning gaps immediately prior to the start of lessons in Year I, as well as a tutoring services to help student fill any gaps.
Specific remedial activities are offered to overcome such gaps.
Enrolment to year II of the programme is subordinate to the passing of any additional learning requirements.

Skills associated with the function

(1st cycle) graduate Mathematician
Graduates have general knowledge of all mathematical sectors and basic training in physics.
They are able to use programming languages. They are able to autonomously perform technical or professional tasks required for working in industry, finance, services and the public administration, in mathematics learning and the dissemination of the scientific culture.

Function in a work context

(1st cycle) graduate Mathematician
Graduates in Mathematics have the ability to tackle logical problems using methodological rigour. Mathematical training allows them to successfully enter the labour market of computing, industry and services, as they are able to acquire any additional specific skills required in a short time.

Educational goals

The degrees in this class provide a solid base of theoretical, methodological and applied competences in the fundamental areas of mathematics. The first-cycle degree in Mathematics develops competencies in analysis and synthesis, individual learning and "problem solving". All graduates in Mathematics are required to have solid basic knowledge in the following areas, delivered in fundamental course units: algebra and basic mathematics, some algebraic structures, linear algebra, Euclidean geometry, basic geometry of curves and surfaces, differential and integral calculus, basic differential equations, basic statistics and calculation of probability, the applications of mathematics to other subjects, particularly Physics, the use of computational techniques for the numerical solution of specific problems.
These outcomes are pursued in a single curriculum covering mainly the fundamental course units to which a consistent number of credits are allocated; only in the third year, students are offered a choice of complementary elective course units.
The privileged teaching tools to develop this knowledge include lectures and practical exercises. These are considered a very effective method for students to learn part of the broad range of materials in the corpus of mathematics. In some cases, students receive lesson notes (some freely available on the web) or have one or more reference texts; in other cases, note-taking is deemed to be part of the learning process. The practical exercises are essential for Mathematics, where understanding is acquired through practice and not through simple memorisation. These exercises are often done autonomously by the students, who are encouraged to explore the limits of their own abilities. Assessment is based on written tests and/or oral exams.
Additional teaching tools to achieve specific learning outcomes include computer laboratories. These represent perhaps the most significant change in teaching Mathematics in the past few years, as they introduce an experimental aspect to the subject. These characterise not only the computer sciences correlated to computing courses, but also statistics, financial mathematics, dynamic systems, etc.
In particular, learning skills are assessed through the passing of exams in some third year course units, and the production of the final dissertation, in which students are usually required to consult scientific texts and references in a foreign language, personally studying subjects that were not covered in the general teaching activities.
A consistent portion of the learning activities envisaged is marked by particular logical rigour and a high level of abstraction. The programme also includes seminars and tutorials aiming in particular to develop problem solving skills, as well as computational and IT laboratories. Ample room is also given to the students' choice of elective learning activities, designed to develop specific competences characterising the class in the general scientific, technological, cultural, social and economic context.

Communication skills

Students:
- are able to communicate problems, ideas and solutions concerning Mathematics, produced by themselves and by other authors, to a specialised or general public, in their own language and in English, in both written and spoken form;
- the ability to work in groups, working with set levels of autonomy and ready to enter the labour market.
These learning outcomes are achieved through computer and computational mathematics laboratories involving group work, in the production of the dissertation, as well as optional study periods spent abroad; they are assessed during oral exams and in the final examination.

Making Judgements

Students:
- are able to autonomously spend time at other Italian and European universities appropriately using the mathematical and computational skills acquired;
- are able to establish and develop logical arguments, clearly identifying the assumptions and conclusions;
- are able to recognise correct demonstrations and identify false reasoning;
- are able to propose and analyse mathematical models associated to concrete situations deriving from other disciplines, and use these model to facilitate the study of the original situation;
- have group working experience, but can also work well autonomously.
These learning outcomes are achieved through individual study, in computer and computational mathematics laboratories, in the production of the dissertation, as well as optional study periods spent abroad; they are assessed during oral exams and in the final examination.

Learning skills

Students:
- are able to work in a range of situations adapting to new problems and easily acquiring the relative specific knowledge;
- are able to autonomously continue studies to 2nd cycle level or 1st level Masters in both Mathematics and other subjects.
These learning outcomes are achieved through computer and computational mathematics laboratories involving group work, in the production of the dissertation; they are assessed during oral exams and in the final examination.

Knowledge and understanding

Mathematics
Students:
- possess appropriate basic knowledge of basic Mathematics. More specifically, all graduates in Mathematics must know: algebra and basic mathematics, some algebraic structures, linear algebra, Euclidean geometry, basic geometry of curves and surfaces, differential and integral calculus, basic differential equations, basic statistics and calculation of probability, the applications of mathematics to other subjects, the use of computational techniques for the numerical solution of specific problems.
- they have appropriate computational and computer skills;
- they are able to produce and recognise rigorous demonstrations and are able to mathematically formalise problems formulated in the natural language;
- they are able to establish and develop mathematical arguments, clearly identifying the assumptions and conclusions;
- they are able to read and understand even advanced Mathematics texts.
These learning outcomes are achieved through lectures and are assessed in oral exams.

Physics
Students:
- have appropriate knowledge of Physics and know the mathematical applications to Physics,
- are able to mathematically formalise problems formulated in the natural language;
- are able to read and understand even advanced Physics texts.
These learning outcomes are achieved through lectures and are assessed in oral exams.


Computing and Computational Mathematics area
Students:
- possess appropriate basic knowledge of Computational Mathematics and Computing. Specifically, all Mathematics graduates must be able to use computational techniques for the numerical resolution of specific problems;
- have appropriate computational and computing skills.
These learning outcomes are achieved through lectures and computer laboratory exercises, and are assessed in oral exams.

Applying knowledge and understanding

Mathematics
Students:
- are familiar with scientific method and are able to understand and use descriptions and mathematical models of concrete situations of scientific or economic interest;
- are able to perform the defined technical or professional tasks, for example providing modelling, mathematical and computational support to activities in industry, finance, services and the public administration, in mathematics learning and the dissemination of the scientific culture;
- are able to extract qualitative information from quantitative data;
- are able to mathematically formalise problems formulated in the natural language, exploiting these formulations for clarifying and solving them;
- are able to use computer tools to support mathematical processes and acquire further information;
- are able to work in a range of situations adapting to new problems and easily acquiring the relative specific knowledge.
These learning outcomes are achieved through practical exercises and are assessed in oral exams.

Physics
Students:
- are familiar with scientific method and are able to understand and use descriptions and mathematical models of concrete situations of scientific interest;
- are able to perform the defined technical or professional tasks, for example providing modelling, mathematical and computational support to activities in industry, finance, services and the public administration, in mathematics learning and the dissemination of the scientific culture;
- are able to mathematically formalise problems formulated in the natural language, exploiting these formulations for clarifying and solving them.
These learning outcomes are achieved through practical exercises and are assessed in oral exams.


Computing and Computational Mathematics area
Students:
- are familiar with scientific method and are able to understand and use descriptions and mathematical models of concrete situations of scientific or economic interest;
- are able to use computer tools to support mathematical processes and acquire further information;
- have knowledge of specific programming and software languages;
- communication skills, the ability to work in groups, working with set levels of autonomy and ready to enter the labour market.
These learning outcomes are achieved through practical exercises in the class and in the computer laboratory, and are assessed in oral exams.