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Master's Degree Programme

About the programme
Language: English  (See language requirements)  | Place of study: Aarhus  |  Commencement: August / September and January / February (only applicants with a Danish Bachelor's degree)


The master’s programme in Mathematics at Aarhus University develops and expands the basic mathematical skills you have acquired during your Bachelor’s degree programme. During the programme you will be introduced to advanced topics of contemporary mathematics, selected according to your own mathematical interests and preferences. At the end of the programme you will write a master’s thesis, that takes you to the forefront of research for a particular area of mathematics. The master’s thesis is written under the supervision of an experienced researcher in the chosen field.

The range of courses on the master’s programme covers main elements of the three classical areas of mathematics:

  • Algebra, Analysis, and Geometry, and Topology,

and many of the courses examine and utilise the deep and fascinating interplay between these main mathematical disciplines. You can also choose to “spice up” your education with courses in Probability Theory, Statistics, Data Science, Optimisation, Cryptology or other subjects relevant to your degree programme The courses are taught in English by active researchers and include traditional lectures as well as exercise sessions, in which the students undertake the more active role - individually or in teams. The student population is generally a mix of Danish and international students.

Career opportunities

Traditionally, graduates of the master’s degree programme in Mathematics found employment as teachers in the Danish upper secondary school or pursued research careers at the university. Although these job opportunities are still highly accessible, an increasing number of large private companies have recognised the need and benefits of hiring employees with the ability to solve extensive and complex problems with a strategic and logical approach. Evidently, such skills are highly developed during the master’s degree programme in Mathematics, and over the last 20 years or so, an increasing part of our graduates have thus found jobs in the private business sector, including

  • banking, insurance, telecommunications, software development, wind power production

just to name a few relevant branches. This development has in fact resulted in a shortage of qualified math. teachers in the upper secondary school, and the bottom line is a very high demand for math. graduates in Denmark. As a consequence of this, there is essentially no unemployment among graduates in Mathematics from Aarhus University.

My team comes into the picture when our customers have to comply with new European Union legal requirements, for example. A typical task could involve developing a new type of billing, i.e. a new invoice form. Here we look at what elements should be included – what is possible, and how do we ensure that the programmes work together? I use mathematics in my job when I use logical thinking, abstraction and in being structured. I hardly code at all, but I use my IT and domain knowledge. At the same time, this job demands both good collaboration skills and the ability to communicate with people in many different fields.

Mette Strudsholm
Graduate, MSc in Mathematics
IT developer, Danske Bank

Admission requirements

To enter the Master’s degree programme in Mathematics, you must have obtained a Bachelor’s degree in Mathematics from Aarhus University, University of Southern Denmark or University of Copenhagen. A Bachelor of Science degree in Mathematics (single.subject degree) according to academic regulations of 2022 or 2023 and with the course Complex functions can give admission.

It is a requirement that the qualifying degree has a 10 ECTS programming course and contains at least 60 ECTS math courses covering essentially all of the following topics:

  • Algebra: the integers, congruences, linear algebra, theory of groups, rings and fields, homomorphisms, isomorphism theorems, permutations, polynomial rings, quotient rings and field extensions
  • Analysis: supremum property, uniform continuity, series, multivariate differentiability, Lebesgue integration, ordinary differential equations and the residue theorem in complex analysis
  • Geometry: metric and topological spaces, homeomorphisms, completeness, compactness, connectivity and differential geometry: curves, surfaces, the inverse function theorem for differentiable functions of several variables, fundamental forms, curvature and geodesics

Upon admission, further requirements regarding composition of the degree programme may be stipulated.

Language Requirements

Since English is the language of instruction in all subjects, all applicants are required to provide evidence of their English language proficiency. Please see the general admission requirements. https://masters.au.dk/am-i-qualified-for-admission


Please see the general admission requirements. https://masters.au.dk/am-i-qualified-for-admission

Selection criteria

As the Master’s programme only admits a limited number of students each year, meeting the admission requirements does not in itself guarantee admission to the programme. Allocation of student places is based on an overall assessment. In evaluating qualified applicants, the admissions committee assess applicants on the basis of the following criteria: Academic background Overall grade level – Bachelor’s degree Grades achieved on relevant courses* Relevant courses* (measured in credit units) included in your Bachelor’s degree

* Relevant courses include core courses within Abstract Algebra, Complex Analysis, Differential Equations, Elementary Differential Geometry/Topology and Measure and Integration.

Please note that grades obtained after the time of application cannot be included in the assessment of grade level.

The admissions committee assess each applicant on the basis of the information provided in diplomas, transcripts, and course descriptions

Programme structure

The Master’s degree programme in Mathematics consists of 90 ECTS course activities and projects and a 30 ECTS Master’s thesis. With the help of a teacher from the Department for Mathematics, you will compose your individual study programme based on courses from the course catalogue. Your programme will depend on your academic qualifications and interests. The plan must be approved by the department.

At least 60 ECTS of the 90 ECTS courses must be in mathematics. Each study programme must consist of 40 ECTS core courses. The following “core” courses are offered:

  • Advanced Analysis (10 ECTS)
  • Advanced Topics in Complex Analysis (5 ECTS)
  • Partial Differential Equations (5 ECTS)
  • Advanced Algebra (10 ECTS)
  • Homological Algebra (5 ECTS)
  • Algebraic Curves (5 ECTS)
  • Algebraic Topology (10 ECTS)
  • Differential and Riemannian Geometry (10 ECTS)

1. semester

Advanced Algebra

Algebraic Topology


2. semester





Some other math course

Cryptologic Protocol Theory

3. semester

Some other math course

Differential and

Riemannian Geometry

Cryptographic Computing

4. semester

Master’s thesis

This is an example of a programme with core courses from Algebra and Geometry/Topology. The programme includes 30 ECTS in cryptography offered by the Computer Science department.

For more information about the individual courses, go to: http://kursuskatalog.au.dk/en/

In connection with topics for a Master’s thesis, you can get an overview of the mathematical research conducted at the department by visiting https://math.au.dk/en/research/mathematics/.

Forms of teaching

At the University of Aarhus, you are in close contact with researchers in a way that you rarely experience at other universities. The door to the professor’s office is always open if you need clarification of the study material, and you are encouraged to ask questions at lectures and during exercises. We make heavy demands on your academic skills and independence. In return, you gain considerable benefits in the form of academic challenges and scientific knowledge, in addition to broad competences.

The teaching at the university focuses on independence, critical thinking and collaboration. Part of the teaching is in the form of lectures in small groups, and this introduces new angles to the material compared with the textbooks. You also receive extensive guidance in how to work with examples and projects, and you are given a personal supervisor in connection with your thesis.

The varied forms of teaching, collaboration in groups and the opportunity for close scientific dialogue with the researchers provide you with general competences that are in great demand in the global job market. These competences include abstract, critical and independent thinking, analytical skills and strategic planning. You can use these skills in many contexts – even in jobs you didn’t know you were qualified for. 

The teaching is divided into two semesters per year.

PhD programme

If you have the necessary skills and interest, you have the option of applying for admission to the PhD programme. You can apply when you have completed your Bachelor’s degree and one year of your Master’s degree or when you have completed your Master’s degree. In the PhD programme, you start working on a research project and are gradually trained through courses and personal guidance to become a researcher. Find more information about the PhD-programme in Mathematics or read examples of current research projects at the Department of Mathematical Sciences

Academic regulations

Programme structure

Student life

As a student on the programme, you are based at the Department of Mathematics, which has its own canteen, library, and study areas shared by students. As a Master’s student, you can get your own desk in an office that you share with other Master’s students. The department also has a number of student organisations such as Eulers Venner (Euler’s Friends) and the Kalkulerbar (Friday bar), through which academic activities, study trips and social functions are organised.

Campus - a unique place

Aarhus University campus is unique, with buildings closely grouped together and surrounded by nature. The campus is conveniently situated close to the city centre, and student accommodation is readily available as long as you apply on time. There are a range of activities, ranging from running to regatta on the lake, as well as guest lectures, film screenings, and university events taking place throughout the year. To ensure student well-being, counselling services are available for students, to offer support and guidance during their time at Aarhus.

Aarhus as a city

As the second-largest city in Denmark, Aarhus is a young and dynamic place with plenty of opportunities. The 40,000 students at the university make up 17.5% of the city’s population, which leaves its mark on city life. An attractive feature of Aarhus is that there are beaches and woods a short bike-ride away, as well as cultural events taking place throughout the year, including the Aarhus Festival in September. The theatres in the city and the ARoS international art museum offer many events that enable you to experience the Danish culture.

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Thomas Lundgaard Schmidt, M.Sc. and Ph.D. in Mathematics, working as a Quantitative Risk Manager at Siemens Gamesa Renewable Energy

Contrary to what most people think, studying Mathematics is not all about calculation and working with large numbers. Instead, you work with proofs, abstract ideas, and causality. You will experience the proof behind those things you just took for granted during high school, and you will understand how the different branches of Mathematics are related. During my time at the university, I spent a lot of time looking out the window trying to come up with good ideas – most of all, Mathematics is about immersion, and I experienced plenty of room for that as a student. Actually, I did not know what I wanted to use my degree in Mathematics for; I just studied Mathematics, because I couldn’t not study Mathematics.

My experience was that being a student was highly independent, but the study environment was good, and most of my fellow students studied Mathematics out of interest rather than to score a great starting salary after their diploma. The physical space was great with room for group work and the opportunity to get an office with your study group. Moreover, the study environment was very good because the department became the natural 'base' for most students – we spent time there mainly out of interest, not because we had to. It was not considered a problem to stay a couple of hours after class, and when the reading was completed, most people would meet in the Friday bar to finish of the week. It was a relaxed atmosphere with room for everyone. Many students had some geeky hobby, but this was not regarded odd - on the contrary, actually. My Master's courses often included students from different year groups, so it was easy to connect with both older and younger students. In many of my Master’s courses we were only a handful of students, which provided the opportunity to work closely together with the lecturers and experience their academic passion.

My job is about modelling errors in wind turbines: Which mistakes can we expect in a given wind turbine park in a given period of time? Part of the work is pure math: What mathematical model does best describe a particular situation? Additionally, the job contains a lot of data analysis and programming - and it turns out that the abstract way of thinking, which you for example use for implementing a new algorithm, is rather similar to trying to solve a mathematical problem. Last, but not least, in my job I need to be able to explain mathematical models to engineers, for example, and for this, I benefit from my experience with explaining theoretical exercises in class and at oral exams.
The transition from being a university student to working in my first job was abrupt in many ways: From an environment where everybody spoke 'Mathematics', I started in a company working alongside engineers and business people with completely different backgrounds. In my job, there is not always time to immerse myself in a problem; we just have to find a solution that will work within the given deadline. The responsibility you have in a job is also very different, because suddenly your effort affects the company's bottom line and other people's work - not just your own exam results. So yes, it was a bit of a cultural shock to go from university to a job, but I feel that my degree in Mathematics has opened many doors for me.