The core module is also called A-module. This is a collection of general subjects required throughout the entire programme, hence the name. You need to complete 18 ECTS points in order to finish this module. Courses are split into lectures (4.5 ECTS each) and exercises (1.5 ECTS each). In order to finish the core module, you have to obtain a positive grade in 3 lectures and their corresponding exercises (so for example A.1 + A.2, A.7 + A.8 and A.20 + A.21).

If you want to graduate with a specialisation, you need to obtain a positive grade in pre-selected pairs of lectures and exercises. The courses required per specialisation are listed in Graduating with a specialisation.

Below are the courses offered in the core module:

The specialisation module, also called B-module, is where you choose in which topics you want to deepen your knowledge. You need to choose 2 of the 10 blocks and complete them by getting 18 ECTS per chosen block (so 36 ECTS in total). The available blocks are:

1. B.1 Algebra and number theory
2. B.2 Applied mathematics
3. B.3 Combinatorics and graph theory
4. B.4 Computational mathematics
5. B.5 Discrete optimisation and complexity
6. B.6 Acturial and financial mathematics
7. B.7 Geometry and analysis
8. B.8 Mathematics of data science
9. B.9 Modelling and applications in engineering
10. B.10 Statitstics

Like in the core module, you need to complete pairs of lectures and exercises. Per block, there are some recommended courses from the core module, which we list below. The blocks B.2, B.4, B.6, B.8 and B.9 have required courses, which we also list below.

The elective module is also called C-module. This module is split into C.1 (the elective module), and C.2 (the interanational module). You choose one of these and complete it, by obtaining 24 ECTS points. Note that if you choose C.2, at least 18 of the 24 ECTS need to be obtained at a university outside of Austria. A list of potential universities will follow. Please verify that the courses offered at your chosen university can be accepted in Graz. If you are unsere whether your courses are adequate, you can ask the office of the dean via E-Mail.

For C.1 (and the remaining ECTS from C.2), you can choose any courses from the core and specialisation module. Note that they cannot be courses, that you already completed. However, you don't have to complete lecture and exercise. You can only obtain 12 ECTS from B.9.

Not to be confused with the elective module. You need 6 ECTS for your electives. These can come from any lecture offered at TU or KF, so the do not have to be lectures focused on mathematics.

You need to attend both a master's seminar and write a master's thesis in order to graduate. Talk with lectureres in order to find topics. The topic of the seminar does not need to overlap with your master's thesis.

In order to graduate, you need to pass the master's examination. In order to be able to attend this examination, you need to have completed all courses and submitted your thesis. The examination is performed by a committee and is split into three parts (20 minutes per part):

1. presentation of your thesis
2. oral exam in the topic of your thesis, performed by your supervisor
3. oral exam in a topic of your choice, performed by a person of your choice (except your supervisor)

By choosing certain B-modules and courses from the core module, you can graduate with a specialisation. Said specialisation is then also written on your diploma. There are 5 specialisations:

• Applied mathematics
• Discrete mathematics
• Pure Mathematics
• Statistics, acturial and financial mathematics
• Technomathematics

Here you specialise in mathematical modelling in topics like natural sciences, medicine or e.g. economics. The required modules are:

• from the core module (three of the pairs):
  • A.3 and A.4 (Advanced functional analysis, lecture and exercise)
  • A.5 and A.6 (Advanced probability, lecture and ecercise)
  • A.13 and A.14 (Mathematical statistics, lecture and exercise)
  • A.15 and A.16 (Advanced theory of partial differential equations, lecture and exercise)
• from the specialisation module:
  • B.2 (Applied mathematics)
  • B.8 (Mathematics of data science)

Here you focus on discrete optimisation and graph theory. The required modules are:

• from the core module:
  • A.9 and A.10 (Graph theory, lecture and exercise)
• from the specialisation module:
  • B.3 (Combinatorics and graph theory)
  • B.5 (Discrete optimisation and complexity)

This is a new specialisation. Here you focus more on general theory, such as algebra, number theory or analysis. The required modules are:

• from the core module (three of the pairs):
  • A.1 and A.2 (Advanced analysis, lecture and exercise)
  • A.7 and A.8 (Graduate algebra, lecture and exercise)
  • A.11 and A.12 (Number theory, leccture and exercise)
  • A.20 and A.21 (Topology, lecture and exercise)
• from the specialisation module:
  • B.1 (Algebra and number theory)
  • B.7 (Geometry and analysis)

Here you enter the world of financial and insurance mathematics or start your journey on becoming an actuary. The required modules are:

• from the core module:
  • A.5 and A.6 (Advanced probability, lecture and exercise)
  • A.13 and A.14 (Mathematical statistics, lecture and exercise)
  • A.18 and A.19 (Stochastic analysis, lecture and exercise)
• from the specialisation module:
  • B.6 (Acturial and financial mathematics)
  • B.10 (Statistics)

Here you focus on mathematics in technology and engineering. The required modules are:

• from the core module:
  • A.3 and A.4 (Advanced functional analysis, lecture and exercise)
  • A.15 and A.16 (Advanced theory of partial differential equations, lecture and exercise)
  • A.17 (Scientific computing and FEM)
• from the specialsiation module:
  • B.4 (Computational mathematics)
  • B.9 (Modelling and applications in engineering)