Master of Science (MSc) in Mathematics

Please note: The MSc in Mathematics with a minor subject is only for applicants with a Danish Bachelor’s degree in Mathematics including the required courses from the minor subject. The minor subject consists of courses taught in Danish, where the first part is compulsory in the Bachelor’s degree, and the remaining is part of the MSc.

Programme overview

You can study mathematics with a minor subject if you want to acquire the competences to teach or disseminate both subjects. This enables you to teach in Danish upper secondary schools and at university colleges. You will also be qualified to find work in the private and public sector e.g., in jobs that require your knowledge within two academic fields. Furthermore, you have the prerequisites for further studies e.g., a PhD programme.

The programme can be structured in different ways depending on whether your minor subject is within or outside the field of science, and whether you start in September or February. Below, you will find examples of course tables showing the study structure if you start in September or February with a minor subject within the field of science. 

See the full programme overview, description of the admission requirements, as well as the knowledge, competences, and skills you obtain in the curriculum for Mathematics with a Minor Subject.

Example 1: Study Start September, Minor Subject Within the Field of Science

Restricted elective courses: 45 ECTS
Minor subject: 45 ECTS
Master's thesis: 30 ECTS

One block each year equals nine weeks of study and 15 ECTS. The table is primarily for guidance and may be subject to revision.

Example 2: Study start February, Minor Subject Within the Field of Science

Study start in February is only for students with legal right of admission to the programme. Read about legal right of admission.

Restricted elective courses: 45 ECTS
Minor subject: 45 ECTS
Master's thesis: 30 ECTS

One block each year equals nine weeks of study and 15 ECTS. The table is primarily for guidance and may be subject to revision.

Restricted Elective Courses

Choose your restricted elective courses from the lists below. Click on each course for a detailed description.

You are obliged to choose courses worth 30 ECTS from this list:

• Advanced Didactics of Mathematics
• Advanced Vector Spaces
• Algebra 3
• Algebraic Topology
• Brownian Motion
• Commutative Algebra
• Differential Operators and Function Spaces
• Differentialligninger
• Functional Analysis
• Geometry 2
• History of Mathematics 2: Expeditions into Mathematics in the Making, Research, and Uses of History for Teaching
• Introduktion til talteori
• Kompleks funktionsteori

You are obliged to choose courses worth 15 ECTS from this list:

• Advanced Didactics of Mathematics
• Advanced Mathematical Physics
• Advanced Number Theory
• Advanced Vector Spaces
• Algebra 3
• Algebraic Geometry
• Algebraic Geometry 2
• Algebraic Number Theory
• Algebraic Topology
• Algebraic Topology 2
• Analysis in Quantum Information Theory
• Analytic Number Theory*
• Applied Algebra in Geometry
• Brownian Motion
• Categories and Topology
• Commutative Algebra
• Complex Analysis 2
• Computability, Turing Machines, and Gödel's Incompleteness Theorems
• Differential Operators and Function Spaces
• Differentialligninger
• Elliptic Curves
• Experimental Mathematics
• Functional Analysis
• Geometric Topology
• Geometry 2
• Graphs and Groups
• History of Mathematics 2: Expeditions into Mathematics in the Making, Research, and Uses of History for Teaching
• Homological Algebra
• Introduction to Mathematical Logic
• Introduction to Quantum Computing
• Introduction to Representation Theory
• Introduktion til talteori
• Invitation to Combinatorics*
• K-Theory
• Kompleks funktionsteori
• Operator Algebras
• Partial Differential Equations
• Partial Differential Equations 2
• Quantum Information Theory
• Riemannian Geometry
• Stochastic Processes in Continuous Time
• Topics in Geometry
• Topics in Operator Algebras
• Topics in Probability

* The course is not offered in the academic year 2025/2026.

Bo holds both a bachelor’s degree and a master’s degree in Mathematics. “The programme is called mathematics, just like in upper secondary school, but it’s very different. Our strength is that we are problem solvers: When presented with a problem, we quickly get to grips with it and find a way to solve it.”

Why did you choose to study mathematics?

After upper secondary school, I wanted to continue studying. I considered many other degree programmes, including Nanotechnology and Physics, but Mathematics seemed to be the most exciting. I like the theoretical element.

What does the programme involve?

Compared to mathematics in upper secondary school, university mathematics is far more abstract. It’s like being given a lot of imaginary tools and then being told: Solve this problem! And how do you do that? It takes time, a lot of thought and a creative approach. It’s an exercise in saying ‘if this is true and this is true, then this must also be true’.

Pure mathematics is basic research, so you can’t say exactly where you will be able to use the conclusions you reach. One of the interesting aspects is the theoretical conclusions that have turned out to be useful in areas like quantum mechanics. We test whether the theories work – afterwards there are other people who can make use of what we worked out.

Can you make it more concrete?

It’s difficult, because the discipline is very abstract. However, in my bachelor project I did operational analysis in cooperation with SAS, which is relatively tangible.

I looked at ways to optimise SAS’ earnings by analysing a lot of statistical data on the destinations served by the company, the staff required, and the collective agreements concluded with the trade unions.

This resulted in a huge system of variables and conditions that could be used for calculations. Computers are normally used for such calculations, but it can take weeks even for a computer to tackle such complexity.

There’s often not time to wait so long, as the assumptions underlying the calculations may change, e.g. in the event of illness or an aircraft accident. The factors included in the calculation therefore need evaluating, and you have to decide which are the least important ones and which can be relaxed, in order to get a near-optimal calculation in just a few hours.

What was your thesis about?

It was on the Lindelöf hypothesis. It looks at how a complex function behaves within a specific delimited area.

It’s a good example of a case where ‘if one thing is true, the other must also be true’. If one of the major mathematical conjectures – the Reimann hypothesis – is one day proven, several results in my thesis will directly follow. (Un)fortunately this did not happen before I submitted it.

Why do you find abstract mathematics so interesting?

At times during my studies I felt that the course was perhaps too theoretical, and that I should have done Mathematics-Economics instead. But what you learn is how to use a mathematical language that is absolutely correct. When we think of mathematics, we generally think that there is always a single correct answer, and this is still true when you move to higher levels of abstraction. Everything is clinically structured, so you can always express yourself 100% clearly.

A mathematician’s key strength is being a problem solver. When presented with a problem, we quickly get to grips with it and find a way to solve it.

The degree programme is so theoretical that it would seem that we are not directly employable anywhere – but we learn a mindset that makes us employable everywhere! Additional training will always be needed when you join a private company, for example, in order to get an insight into the kind of problems you have to solve.

What does your current job involve?

I work at Edlund A/S, which develops pension software. It is a program in which case processors enter information. It can then keep track of policies, prepare quotations, do forecasts, calculate bonuses etc. There are mathematicians involved in all of this – both the underlying calculations and the actual development of the software.

Mathematicians find it relatively easy to understand the pension rules and programming, so most of my colleagues are mathematicians. Programming is probably the closest you get to using pure mathematics.

Where else can you get a job?

Mathematicians generally tend to work in three main areas: as upper-secondary school teachers, as theoretical researchers – i.e. doing PhDs – and in the private sector. 

Typical private-sector employers are pension companies, banks and consultancy companies like Deloitte and SimCorp, which make stock trading systems, or Oticon, where mathematicians help calculate how to optimise the hearing aids. We can make calculations about everything that engineers work with.

What are your former fellow students doing?

There were 70 students in my year when we started, and 20 had graduated by the time I finished my studies. Almost half of us work at Edlund, which is extraordinary compared to other years. Some are with Danske Bank, and a handful have done PhDs. Several of them have since landed PostDoc positions around the world. 

Would you recommend the degree programme to prospective students?

Yes, I would. I didn’t realise Mathematics was so theoretical. But it’s a really good programme and you shouldn’t be intimidated by all the theory, because it gives you the general meta knowledge that makes it easy to feel at home in a wide range of workplaces.

The way you learn to think is more important than the specific things you learn. If you start the degree programme with these expectations, you will not be disappointed. You also need not fear ending up unemployed when you graduate!

The social life on the degree programme is just fantastic. It exceeded my expectations. During my studies, I worked as a first-year student tutor, I worked for our journal and took part in the student revue – to make sure I had something other than just theoretical mathematics to focus on.

Do you have any tips for new students?

You don’t have to know what area you want to work in afterwards. Simply take in the experiences and tasks and think about which ones you find interesting. This makes it much easier to tailor your degree programme to your interests, so you are in a good position when you finish – and you can always work out exactly what workplace to look for then.

Interview with Mauricio, MSc Student, from Columbia.

I applied to Copenhagen because the University has some of the best teachers in the world in Operator Algebras, which is my field, perhaps the very best. I can only say that my dreams were fulfilled a hundred per cent.

Originally I got a taste for Scandinavia as an exchange student in Norway. I was able to take in and appreciate the natural beauty of the countryside and the Scandinavian lifestyle. But I must admit that before I got to Copenhagen I was worried that Scandinavia was academically isolated, despite the really good teachers in my on field. Now I know better.

The teaching is also different from the teaching in Columbia where I did my bachelor at a public university in Bogota. There is more interaction between students and teachers in Denmark.

Back home there is more emphasis on exams and good grades. In Denmark there is more joy of learning than pressure of passing, although of course you have to meet the deadlines of your exams and assignments. But there is more of a collective feeling than an individual race to get the best grades among the students at Copenhagen.

And the contact between the professor and students is very close. He can give me good advice, but I can also give him good advice in connection with solving mathematical problems.

With regards to the social side of life in Denmark, I've made Danish friends. Friends I can trust through and through. In South America you can make friends with somebody in just one day. In Denmark it's more step by step, although you shouldn't go thinking that the Danes lack spontaneity. It just takes a bit longer, that's all.

Another good thing about Denmark is that 98 per cent of the population have a sense of civic responsibility. This rubs off on the way people get along together.

It means that Copenhagen is a clean city and crime is at a low compared to many other places in the world. The city is also beautiful architecturally, with many lovely buildings from the end of the 19th century. It's a city with plenty of opportunities to cycle around in green spaces. Living in Copenhagen is like living in a small town with the advantages of a big city.

And one more thing I really notice: sexism or machismo as we call it in Latin America is pretty well non-existent in Denmark. I like that. There is more equality of the sexes than in many other places.

Mathematics does not lead to endless career paths, but the possibilities are far greater and more varied than most people realise. From teaching in upper-secondary schools to research positions or jobs in the public or private sector. I’ve been employed as an IT developer at Danske Bank since I graduated from the University of Copenhagen last year.

Kamilla Drimer Berg – mathematics graduate employed at Danske Bank in Lyngby.

I can draw on my mathematics degree in my work because mathematics makes you think logically and in a structured way, which is necessary when developing computer systems. The bank also has a programme for new graduates like me. This means I get plenty of support from my colleagues and also get to know the workplace really well.

The job? I visited an education fair, where the Danske Bank stand attracted my attention. It’s great to get out into the real world after university. I’ve been given a very warm welcome.

It’s like starting over again in a new and exciting way. You have to get to grips with many new things, and it’s challenging. I still have a lot of contact with my former fellow students and other university friends. To prospective students I would say that you have to be driven by genuine interest. Not just the prospect of landing a good job afterwards.