Mathematics: Topology
Topology investigates the structure of spaces appearing in Mathematics. It provides powerful abstract tools to analyse and solve problems in many areas of mathematics and its applications.
Start
Spring 2027
Level
Master's
Language
English
Place of study
Lund
Course code
MATM36
This course introduces key concepts and techniques in topology—an area of mathematics that explores the properties of topological spaces and their transformations. You will learn how topological concepts helps solve complex problems and reveal deep connections between different mathematical areas.
Topics covered include
- topological and metric spaces with examples, product topologies, continuity of functions
- connectedness, completeness, and compactness, including the Arzelà–Ascoli Theorem
- examples of applications and topological structures
- examples of metric and topological spaces relevant in other areas of mathematics, such as normed spaces and Hilbert spaces.
The course is alternative-compulsory within the Master’s Programme in Mathematics at Lund University. It is also available as a standalone course, and can be taken as an elective course by Bachelor’s students in mathematics.
You will learn through a mix of lectures, seminars, and assignments. The course encourages active participation and problem-solving, with opportunities to apply theory to practical examples.
Assessment includes a written exam and an oral exam at the end of the course. Bonus points from completed assignments may count toward your final score on the written exam. The oral exam is only available to students who pass the written exam. Re-examinations are offered shortly after the regular ones.
Topology is a powerful tool in many areas of mathematics and its applications. After completing the course, you will be able to recognize topological structures in various mathematical problems and apply topological concepts to solve them. This course strengthens your foundation for roles in academia, research, or industries where mathematical modelling and abstract reasoning are essential.
Entry requirements
For admission to the course, English 6/B is required as well as at least 90 credits in mathematics including knowledge corresponding to MATB33 Introduction to Higher Analysis, 7.5 credits or MATB34 Linear Analysis, 7.5 credits.
Selection criteria
Seats are allocated according to: ECTS (HPAV): 100 %.
Tuition fees for non-EU/EEA citizens
Citizens of countries outside:
- The European Union (EU)
- The European Economic Area (EEA) and
- Switzerland
are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.
Tuition fees, payments and exemptions
Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125
Note that you may also need to pay an application fee, or provide proof of exemption.
No tuition fees for citizens of the EU, EEA and Switzerland
There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.
A shared second home for mathematics
Matematikcentrum gathers students and researchers in mathematics, mathematical statistics, and numerical analysis and computational science. Along Sölvegatan, close to green spaces and the wider university area, you find a shared environment for everyone who uses mathematics as a common language. Research here has led to innovations and companies in areas such as optimisation, image analysis and software, with applications ranging from logistics to video analysis and mobile technology.
