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Mathematics is the science of structures in a broad sense. They may be numerical structures, spatial structures, colour structures, musical structures, logical structures or a thousand other things. Mathematicians study these structures: they form them, stretch them, bend them, play with them and form connections between them.

When you start looking, you find structures everywhere. And mathematics is the language that we use to express many of our deepest thoughts about the world. Mathematical applications can be used as a way to get inside the structures. Or you can become engrossed in the abstract game. You're allowed - in fact, you're encouraged! - to use both approaches as a graduate student in mathematics.

If you are interested in the way Mathematics is shared and learned in various institutions, you can also study Didactics of Mathematics at the University of Copenhagen.

#### Profile and Career

Mathematics is an exact science, and a mathematical theorem is not accepted until a stringent proof has been produced for it. Acquiring the requisite precision is demanding, and continual practice is necessary.

Before a mathematician can produce a stringent proof, he or she must undergo a creative process in order to achieve an understanding of what the theorem is about and how it can be proved. At this stage, the mathematician draws especially on imagination and experience.

In some cases, computers can also be used to develop ideas about what is right or wrong, but only in rare cases can they be used to prove a theorem.

Mathematics is also communication. Mathematicians talk about things outside the experience of daily life, and a strong talent for storytelling is needed to make it comprehensible. Presentation is a high priority among mathematicians, and a key aspect of the programme.

#### Competence Description

**A graduate in mathematics will be able to:**

- Conduct independent, stringent argumentation
- Structure a study of open mathematical issues
- Define mathematical disciplines in relation to each other, but also to take advantage of interdisciplinary skills.
- Independently take responsibility for his or her own professional development and specialisation.

**A graduate in mathematics will also have acquired the skills to:**

- Read and understand original mathematical literature
- Convey and communicate mathematical issues and problems on a scientific basis
- Explain, orally and in writing, mathematical studies of open issues.

#### Career Opportunities

MSc graduates in mathematics have many different job opportunities, and there is basically no unemployment. Many graduates find employment in the private sector, where they either work specifically with applying mathematics to specialised problems, for instance within economics or telecommunications, or act as "trouble shooters" in a broader sense.

When we ask employers why they hire our graduates, they often emphasise the mathematician's abilities to see patterns in problems that often arise and to solve them once and for all.

There is also a high demand for mathematics teachers in upper secondary education and other post compulsory education programmes. Moreover, there is the opportunity to continue conducting research in mathematics after earning a PhD.

You can choose from a wide variety of courses to design a course of study that adresses issues that arouse your curiosity. Mathematics has many disciplines: algebra, analysis, geometry, topology... It also includes application-oriented disciplines such as mathematical physics, probability theory and optimisation, as well as cultural disciplines like the history of mathematics and the didactics of mathematics.

Although these disciplines are studied independently, it is remarkable how closely related they are when you take a closer look. Mathematics as a whole can be approached in many ways.

In addition to the elective courses of study, a number of recommended courses of study have been designed for those with teaching or industrial ambitions.

#### Specialisations

If you are interested in the way Mathematics is shared and learned in various institutions, you can also study Didactics of Mathematics at the University of Copenhagen.

#### Master's thesis

Your studies will conclude with a thesis project in which you work in more detail within one of the themes that you focused on in your course of study. Often the thesis will be written in association with one of the Department's research teams, where you have access to both a supervisor and the entire team's knowledge and involvement. In other cases, you might instead be investigating something entirely new. In recent years, solutions have been found to profound problems that have existed for hundreds of years or more (Poincaré's conjecture and Fermat's last theorem), and the enthusiasm that accompanies these new breakthroughs has led to many thesis topics.

**Examples of thesis topics:**

- Algebra and the theory of numbers
- Geometric analysis and mathematical physics
- Noncommutative geometry
- Topology
- Didactics of mathematics

#### Study Abroad

It is also possible to study abroad during your degree. You can choose to study abroad for one or two semesters or for a shorter period of time; e.g. take a summer school course.

The Faculty of Science will not be awarding any scholarships for the academic year 2014/2015.

Please note that many scholarships are offered by companies or organisations, it can be worthwhile to research your particular options from your home country.