Master in Mathematics

Master in Mathematics is one of 5 English-taught Mathematics programmes at Master's Degree level in the register, offered by 3 institutions. 5 of them list an annual fee for students from outside the EU, EEA and Switzerland, from EUR 4,545 to EUR 17,300; this programme lists EUR 16,300 a year. 5 are recorded as free for EU, EEA and Swiss students. The same programme title is offered at 3 institutions, so compare the content, campus and requirements before you choose.

The Master's in Mathematics at Aarhus University is a two-year full-time programme taught in English. It builds on your bachelor's degree and lets you shape the degree around your own mathematical interests, with courses taught by active researchers.

What you study

The programme covers the three classical areas of mathematics: Algebra, Analysis, and Geometry/Topology. Many courses examine the interplay between these disciplines. You can also add courses in Probability Theory, Statistics, Data Science, Optimisation, Cryptology or other relevant subjects.

Each study programme must include 40 ECTS of core courses. The core courses offered are 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), and Differential and Riemannian Geometry (10 ECTS). At least 60 ECTS of the 90 ECTS in courses must be in mathematics.

You finish with a 30 ECTS master's thesis, written under the supervision of an experienced researcher in your chosen field. The thesis takes you to the forefront of research in a particular area of mathematics.

How the programme is organised

The degree consists of 90 ECTS of course activities and projects plus a 30 ECTS master's thesis. With help from a teacher at the Department of Mathematics, you compose your individual study programme from the course catalogue. The plan must be approved by the department.

Teaching includes traditional lectures and exercise sessions where you take the more active role, individually or in teams. Classes have a very good student-teacher ratio. Part of the teaching is in small groups, which introduces new angles compared with textbooks. You get extensive guidance on working with examples and projects, and a personal supervisor for your thesis.

An example programme with core courses from Algebra and Geometry/Topology includes 30 ECTS in Cryptography offered by the Computer Science department. Courses in that example include Cryptology, Cryptologic Protocol Theory, and Cryptographic Computing.

Who it suits

This programme suits you if you want to go deeper into pure mathematics and have the freedom to choose advanced topics that match your interests. It also suits you if you want to combine mathematics with cryptography, data science or optimisation.

Teaching focuses on independence, critical thinking and collaboration. You are encouraged to ask questions at lectures and during exercises, and the door to the professor's office is always open. The department makes heavy demands on your academic skills and independence.

Students are mostly Danes, with some international students. As a master's student you can get your own desk in an office shared with other master's students. The department has its own canteen, library and study areas, and student organisations such as Eulers Venner and the Kalkulerbar.

Admission, language and next steps

To be admitted with an international or other qualification, you need a bachelor's degree comparable to a Danish bachelor's degree in level and duration (180 ECTS). You must also meet specific requirements: 60 ECTS in mathematics covering a broad range of algebra, analysis and geometry, plus a 10 ECTS programming course, for a total of 70 ECTS.

The mathematics requirement covers topics such as the integers, congruences, linear algebra, group and ring theory, field extensions, uniform continuity, series, multivariate differentiability, Lebesgue integration, differential equations, the residue theorem, metric and topological spaces, compactness, differential geometry of curves and surfaces, curvature and geodesics.

Certain Danish bachelor's degrees give direct admission, including Mathematics from Aarhus University, the University of Southern Denmark, the University of Copenhagen, and the single subject Mathematics degree from Aalborg University under the 2022 or 2023 academic regulations with the course Complex functions. A bachelor's degree in Mathematics from Aarhus University gives a legal right of admission if you apply within three years of completing it.

All master's programmes at Aarhus University have limited intake. Applicants are ranked by grades from the qualifying degree, grades in relevant subject fields (Abstract Algebra, Complex Analysis, Differential Equations, Elementary Differential Geometry/Topology, Integration), and the proportion of ECTS in those fields. You must meet the university's English language requirements. Applications go directly to the institution. Students from the EU/EEA and Switzerland study free of charge; other students pay a fee set by the institution.

Master’s applications go straight to Aarhus University, not through optagelse.dk, and the institution sets its own deadline. Entry requirements and language tests are set by the institution, so start from the official programme page. Our guides cover tuition fees, residence permits and housing.