# 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.

**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

**Specialisation in Didactics of Mathematics**

If you are interested in the way Mathematics is shared and learned in various institutions, you can also study Didactics of Mathematics at the University of Copenhagen.

**The MSc programme in Mathematics is structured as follows:**

Block 1 | Block 2 | Block 3 | Block 4 | |

Year 1 |
Advanced Vector Spaces | |||

Year 2 |
Thesis | |||

Compulsory course | ||

Restricted elective course | ||

Elective course |

## 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 at least 22,5 ECTS from this list:

- Algebra 3
- Algebraic Topology
- Advanced Didactics of Mathematics
- Advanced Probability Theory 1
- Functional Analysis
- Geometry 2
- History of Mathematics 2
- Advanced Probability Theory 2
- Homological Algebra
- Differential Operators and Function Spaces

Choose your remaining courses from this list:

- Categories and Topology
- Partial Differential Equations
- Introduction to Modern Cryptography
- Analysis of Manifolds
- Approximation Properties for Operator Algebras and Groups
- Algebraic Geometry 2
- Solving Polynomical Equations
- Riemannian Geometry and General Relativity
- Analytic Number Theory (the course is not offered in the academic year 2019/20)
- Experimental Mathematics (the course is not offered in the academic year 2019/20)
- Topics in Mathematical Logic
- Quantum Information Theory
- Elliptic Curves
- Introduction to Representation Theory
- Introduction to Operator Algebras
- Commutative Algebra
- Algebraic Topology 1.5: Cohomology
- Complex Analysis 2
- Algebraic Number Theory
- Introduction to Mathematical Logic
- Algebraic Geometry
- Algebraic Topology II
- Introduction to K-Theory
- Advanced Mathematical Physics
- Dynamical Systems

## Curriculum

Curriculum for MSc in Mathematics.

Curriculum for MSc in Mathematics with a minor subject.

Shared section of the curriculum for all programmes at the Faculty of SCIENCE.

## Didactics of Mathematics

You have the chance to study a subject area in depth. Read more about the Didactics of Mathematics specialisation.