Programme Structure

You can choose from a wide variety of restricted elective and elective courses to design a programme of your interests. Mathematics has many disciplines: Algebra, analysis, geometry, topology, etc. 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.

You can also study mathematics with a minor subject. Read more at the bottom of this page >>

Do a Project in Practice or Study Abroad

You may choose to use some of your elective courses to do a project in practice or to study abroad for one or two semesters or for a shorter period of time.

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

The programme can be structured in two ways, depending on, whether you start your studies in September or February:

Programme Overview, Study Start in September

Restricted elective courses: 60 ECTS
Elective courses: 30 ECTS
Thesis: 30 ECTS

One block each year equals nine weeks of study and 15 ECTS.

Programme Overview, Study Start in February

Study start in February is only for students with a reserved access to the programme. Read about reserved access here >>

Restricted elective courses: 60 ECTS
Elective courses: 30 ECTS
Thesis: 30 ECTS

One block each year equals nine weeks of study and 15 ECTS.

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:

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

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

• Partial Differential Equations
• Advanced Vector Spaces
• Computability, Turing Machines, and Gödel's Incompleteness Theorems
• Stochastic Processes in Continuous Time
• Categories and Topology
• Algebraic Geometry 2
• Algebra 3
• Algebraic Topology
• Advanced Probability Theory 1
• Topics in Operator Algebras
• Advanced Number Theory
• Introduction to Quantum Computing
• Topics in Geometry*
• Brownian Motion
• Complex Analysis 2*
• Analytic Number Theory 
• Experimental Mathematics*
• Analysis in Quantum Information Theory
• Homological Algebra
• Functional Analysis
• Geometry 2
• Applied Algebra in Geometry
• Invitation to Combinatorics
• Quantum Information Theory
• Advanced Didactics of Mathematics
• Partial Differential Equations 2
• Topics in Probability
• Elliptic Curves
• Introduction to Representation Theory
• Operator Algebras
• Commutative Algebra
• Geometric Topology
• Introduction to Mathematical Logic
• History of Mathematics 2: Expeditions into Mathematics in the Making, Research, and Uses of History for Teaching
• Differential Operators and Function Spaces
• Riemannian Geometry
• Algebraic Number Theory
• Algebraic Geometry
• Algebraic Topology II
• K-Theory
• Advanced Mathematical Physics
• Graphs and Groups

* The course is not offered in the academic year 2024/2025.