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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 pure 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 the Master’s programme covers main elements of the three classical areas of mathematics:

  • Algebra, Analysis, and Geometry/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. Classes will have a very good student-teacher ratio. Students will be mostly Danes but you will also find some international.

Find more information about the research and the lecturers at the Department of Mathematics here: math.au.dk/en/research/mathematics

Why Aarhus University?

”Studying at Aarhus University gave me the perfect chance to really dive into and expand my understanding of mathematics. The teaching is top-notch, the learning environment is exceptionally supportive and the community at the university is unparalleled with cool international clubs and programs such as iMentor and Student Ambassadors. Additionally, I find the quality of life in Aarhus is very high. In this youthful and student-oriented city you can experience Danish hygge and feel a strong connection to nature.”

- Joschua Linke, MSc in Mathematics, from Germany

Career opportunities

The Master’s in Mathematics opens up many different career paths. There 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.

This is mainly due to the fact that 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 in Mathematics. Therefore, an increasing part of our graduates of the master’s degree programme in mathematics have found jobs in the private business sector, these include

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

just to name a few relevant branches. If you have the necessary skills and interest, you have the option of applying for admission to the PhD programme. In the PhD programme, you start working on a research project and are gradually trained through courses and personal guidance to become a researcher.

Admission requirements

A Bachelor of Science degree in Mathematics from Aarhus University, University of Southern Denmark or University of Copenhagen qualifies a student for admission to the Master’s degree programme in Mathematics.

A Bachelor of Science degree in Mathematics (single subject degree) from Aalborg University according to academic regulations of 2022 or 2023 and with the course Complex functions qualifies a student for admission.

Other degrees with subject components in Mathematics of at least 60 ECTS can provide admission to the Master’s degree programme, provided the university assesses that their level, extent and content correspond to the degrees mentioned above.

When assessing whether a Bachelor’s degree qualifies the student for admission to the Master’s Programme in Mathematics, emphasis is placed on whether it includes at least 60 ECTS broadly distributed among 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

Furthermore, the qualifying degree should include a 10 ECTS programming course.

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. Advanced Algebra Differential and Riemannian Geometry Cryptology
2. Some other math course Cryptologic Protocol Theory Algebraic Curves Homological Algebra
3. Some other math course Algebraic Topology Crytographic Computing
4. Master's thesis

This is an example of a programme with core courses from Algebra and Geometry/Typology. 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. The teaching and examination periods can be found here.

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 in 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, film screenings, as well as guest lectures and other 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 36,500 students at the university make up big part 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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"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 when working in a structured manner. 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