Mathematics

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.

(1) Applicants with a Bachelor's degree in Mathematics from the University of Copenhagen may be admitted to the MSc in Mathematics.(2) Applicants with a Bachelor's degree in Mathematics from other universities in Denmark or the Nordic Region may be admitted to the Master's programme in Mathematics.(3) Applicants with a Bachelor's degree in actuarial mathematics, statistics or mathematics-economics may be admitted if their programme included courses in:Linear algebra, corresponding to min. 7.5 ECTS creditsGeometry, corresponding to min. 7.5 ECTS credits.(4) Applicants with a Bachelor's degree in Natural Science may be admitted if their BSc incorporates min. 67.5 ECTS credits from courses in the following mathematical subject areas:Mathematical analysis, corresponding to min. 30 ECTS creditsLinear algebra and algebra, corresponding to min. 22.5 ECTS creditsGeometry and topology, corresponding to min. 15 ECTS credits.(5) In addition, the Faculty may admit applicants who, after a thorough assessment, are deemed to possess educational qualifications equivalent to those required in subsections (1)–(4).Prioritisation criteriaApplicants with Bachelor degrees in Mathematics from the University of Copenhagen are guaranteed admission on the first MSc intake after graduation.Second priority will be accorded to applicants with Bachelor degrees in mathematics from other universities in Denmark or the Nordic Region. After that, priority will be accorded to other applicants with a BSc in actuarial mathematics, statistics or mathematics-economics, as per (3) and then applicants with a Bachelor's degree in science as per (4).Language RequirementsTo gain admission to an MSc in the English language, non-Danish applicants must document qualifications on par with the Danish secondary school ‘English level B'. The Faculty of Science accepts the following 3 ways of documenting this:English is your native language. The Faculty of Science at the University of Copenhagen, accepts The University of Purdue view that citizens of the following countries are exempted from taking an English Language Proficiency exam: Anguilla, Antigua, Australia, Bahamas, Barbados, Barbuda, Belize, British Virgin Islands, Canada (except Quebec), Dominica, Grand Cayman Islands, Grenada, Guyana, Irish Republic, Jamaica, Montserrat, New Zealand, St. Kitts & Nevis, St. Lucia, St. Vincent & the Grenadines, Trinidad & Tobago, Turks & Caicos Islands, United Kingdom: England, Northern Ireland, Scotland, & Wales and United States of AmericaIf you are citizen of one of the above countries, you are not required to submit any proof of English proficiency. Your copy of your passport will suffice as sufficient proof.Prior studies completed in the English language/in an English speaking country. For example, if you have studied your Bachelor degree in England you are not required to complete an English language proficiency exam. We ask such students to provide a signed statement from the Educational institution (with the institution's stamp on it) stating that English is the main language of instruction. Furthermore, applicants from Nordic countries (Denmark, Sweden, Norway, Finland and Iceland) do not need to provide proof of English language proficiency.Applicants with English as their second language (except Scandinavians) must pass an IELTS, TOEFL or Cambridge Advanced English test before being admitted. The Faculty of Science, University of Copenhagen, accepts the following tests and scores:IELTS-test (British Council) with a minimum score of 6.5Computer-based TOEFL-test with a minimum score of 213 pointsPaper-based TOEFL-test with a minimum score of 560 pointsInternet-based TOEFL-test with a min score of 83 pointsLanguage tests older than 2 years are not accepted (from the application deadline) English Language Requirements IELTS band: 6.5 TOEFL paper-based test score : 560 TOEFL iBT® test: 83

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.