First of all, we should ask ourselves another question: do we like maths? Answering is not as easy as it may seem. Let’s not give a quick answer based on years of mechanically using formulae. Let’s think and wonder if we want to understand, for instance, how to count the fingers of an extraterrestrial for whom 7+5 is 14 and not 12. Let’s consider if we are curious to know how to sum up an infinite amount of numbers, and that, under certain hypotheses, the result can change if we alter the order in which numbers were added up. Why not think whether we are fascinated by the possibility to learn to calculate the volume of a sphere within a space with 8 dimensions instead of 3.

Mathematics is a very varied and fascinating subject that combines abstract reasoning with powerful practical applications. This itself is already a good reason to study maths.

As regards life sciences and social sciences, maths is a powerful and elegant tool that allows to effectively and precisely describe concepts that are not accessible to ordinary language. This is how, for instance, we find "Pi" in fundamental distribution used in statistics, as the relation between the length of the circumference and the diameter.

In the field of theoretical physics, the classification and study of elementary particles is possible thanks to sophisticated algebraic and analytical techniques.

In economics, when analysing financial markets, an important role is played by complex methods for the calculation of probability.

There are many more examples to offer also in other fields like engineering, biology, medicine... Applied Mathematicians have a lot to say as regards these fields of study.

Basically, all main concepts and thoughts of modern science can be represented by a precise pre-existing mathematical language without which it would not be possible to discuss or even think. For instance, how could scientists who invented the standard model of elementary particles have a “ready to use” load of mathematical notions: let’s think of Lie’s group theory and the theory of their representations. An answer that explains most of the truth is that mathematicians who have accumulated such load of knowledge were not motivated by particularly applied reasons, but “just” wanted to understand how the world of mathematics works; so they moved in all possible directions creating a universe of ready-to-use concepts and techniques. This is what a pure mathematician does and his/her job is just as important as that of an applied mathematician.

If you study maths at university it is with passion and for passion. One must also consider that nowadays, a degree in mathematics can offer good working opportunities. Furthermore, one can interestingly combine a degree in mathematics with a different master degree, for instance in economics, in order to cover an even broader range of opportunities.

###### Can I manage even if I didn’t attend a scientific high school?

Some professors of the Department of Mathematics in Trento have technical or humanity backgrounds. Some of our best students studied art at high school or attended other schools that were not focused mainly of scientific subjects. Of course, a scientific high school is a very good start but basically all one needs will actually be taught during the course. Students are required to use a certain amount of logic reasoning (and since they love maths that shouldn’t be a problem) and most of all, must be willing to study day by day. Maths is in fact a typically cumulative subject. This means that every day in class students rise one step at the time and in the long run, will “stand on the shoulders of giants” as Newton wrote.

Students wishing to enrol in mathematics must pass an entry test since there are only 90 positions available. The test focuses on basic mathematics and logic. It is similar to the self-evaluation test prepared by Orientamat when the course still didn’t have limited access. One can try the Orientamat test that offers useful indications to study in preparation of the test. Other similar tests can be found at “Progetto Lauree Scientifiche” (refer to tests explicitly posted for mathematics).

###### Study programmes

The University of Trento offers a complete range of study programmes as regards maths:

- Bachelor degree in mathematics (three years);
- Master degree in mathematics (two years);
- Doctoral programme in mathematics (three years).

Qualifications have European validity. As a general comment, we can say that the three courses don’t have to be in the same subject (mathematics in this case) and can be attended even at different universities, including abroad. So, for instance, in general we can say that a student can be admitted to the master degree in mathematics in Trento even if he/she has a bachelor degree in mathematics, physics or engineering (or other subject, evaluated by a specific commission) issued by another Italian or European Community university. At the same time, for instance, a student with a master degree in mathematics in Trento can be admitted to a Doctoral programme in mathematics, physics or engineering in another Italian or European Community university.

At the University of Trento it is possible to attend a traineeship too

- il Tirocinio Formativo Attivo (active training, one year),

that prepares students interested in a teaching career and can be attended after the master degree.

###### Bachelor degree (three years)

The first two years of this bachelor degree are preparatory and include basic courses for each field of mathematics: analysis, geometry, algebra, numerical analysis, mathematical physics, probability and statistics. To these we must then add physics and IT and, optionally, biology and economics. One can choose among the following.

- Broad field of studies, in preparation of the master degree in mathematics and addressed mainly to research activity;
- Studies to prepare for a master degree in communication and teaching in high schools;
- Studies to prepare for a master degree in mathematics focusing on computational algebra, cryptography, error correction codes;
- Studies to prepare for a master degree in applied mathematics, particularly regarding mathematical models in biology or finance;
- Studies in economics and finance that prepare students who wish to continue with a master degree in finance, offered by the Department of economics and management

###### Master degree in mathematics

The Master degree course in mathematics in Trento is held in English. The main reason is that a good knowledge of English is vital to achieve a qualified job within the academic field or not. Furthermore, the growing number of foreign students creates a stimulating environment in which English has become the *lingua franca* allowing to create a network of friends all around the world.

The master degree in mathematics in Trento is divided in different curricula that we hereby describe

**Advanced Mathematics:**a vast study path in mathematics. This course prepares students for research in the main fields of advanced mathematics: algebra, analysis, numerical analysis, mathematical physics, geometry, mathematical logic, probability and statistics, dynamic systems and control theory. The natural continuation of such type of studies would be a Phd in mathematics and then hopefully, an academic career in research.**Teaching and Scientific Communication:**this course prepares students interested in teaching maths at high school and in the communication of maths and science. Once studies have been concluded the next natural step would be the active traineeship in mathematics. The Department has also activated a Lab for teaching and communicating maths that coordinates guidance for high school students, collaborates towards initial and permanent teacher training and organizes exhibitions and events to create awareness of this subject.**Coding Theory and Cryptography:**this course focuses on computational algebra, cryptography and error correction codes. In a period of crisis as the one we are experiencing, a field in which businesses do not try to save money is security. A bank, for instance, can save a huge amount of money by making its online banking systems safer. These studies bring students closer to the most sophisticated techniques with a deep content of algebra, geometry and probability used in modern cryptographic systems. Students are offered the chance to attend traineeships in important companies in this field where they can apply the mathematical tools learned during their studies to practical problems for companies.**Modelling, Statistics and Analysis of Biosystems:**this course focuses on models, statistics and bio-systems. It introduces students to the interesting field of bio-mathematics. For instance, the mathematical models for epidemics and the study of strategies for the prevention and limitation of infective diseases.**Modelling and Simulation for Biomedical Applications:**this course is addressed to modelling and simulation for bio-medical applications. It introduces interesting problems regarding mathematical modelling of blood flow in arteries and veins, in particular where a stent has been put into the blood flow.

The last two courses are included in a common path called **Mathematics for Life Sciences**. These courses foresee traineeships in hospitals, companies in the health sector, etc.

###### What if I want to know more?

You will find further information in the following pages about Degree course and Master degree course in Mathematics.

For any further information do not hesitate to write to the guidance managers of the Department of Mathematics: ana.alonso [at] unitn.it

e anneliese.defranceschi [at] unitn.it (anneliese.defranceschi [at] unitn.it)

.