Department of Mathematics

Preparatory Course for M.Sc. Mathematical Physics 2026/27

Liability Notice

The preparatory course starts on 28 September, before the official beginning of the semester on 1 October. Participation in the sessions taking place before 1 October is therefore voluntary, private, and at the participants’ own risk. University insurance coverage may not apply during this period. Participants are responsible for ensuring that they have adequate insurance coverage. The liability of the organizers is, to the extent permitted by law, limited to intent and gross negligence.

About the Course

In order to establish a common foundation for the MSc in Mathematical Physics, this course reviews core mathematical results and notation (especially oriented for students coming from physics and engineering) and provides an introduction to classical and quantum physics (especially oriented for students coming from maths).

It will take place from September 28 to October 9. The course will consist of 13 lectures and 7 exercise sessions (42 hours in total), as well as several social events.

Course Schedule 

Both the lectures and exercise sessions will take place in the C building of the Morgenstelle campus (Auf der Morgenstelle 10, 72076 Tübingen), in lecture hall C4H33 on the fourth floor (the glass-walled room).

The lectures will also be streamed online in the Discord group:

https://discord.gg/27E3wYaUV (invitation link "refreshed" 21/09/2026)

Upon request (send me an email), recordings of the lectures will be provided —at least of the theory lectures.

The course will cover:

1. Mathematical notation. [Notes+Exercises]

2. Notions of Algebra. Vector spaces of arbitrary dimension. [Notes+Exercises] (Updated: 30/09)

3. Topological, metric and normed spaces. [Notes+Exercises] (Updated: 13/10)

4. Continuity and compactness. [Notes+Exercies] (Updated: 13/10)

5. Measures and Lebesgue integration. [Notes+Exercises]

6. Differential calculus in arbitrary dimensions.

7. Ordinary differential equations + the implicit function theorem. 

8. Constructions that defy reason: a nowhere differentiable continuous function, a space filling curve and a non-measurable set.

9. Submanifolds of Rn.

10.  Notions of classical mechanics.

11. Hilbert spaces.

12. Notions of quantum mechanics.

13. Philosophy of quantum mechanics.

Participation in the lectures, exercises, and social events is optional but highly recommended.

Important: You don’t need to register for this course. For all other courses in the department, registration procedures are covered in the first lecture—so no pre-registration needed in any.

At the first meeting (September 28, 10:00), we will clarify any questions about the programme, schedule, and planning. You can also contact the lecturer via:

 xabier.oianguren-asua@math.uni-tuebingen.de


Interesting Links

  • To find the courses of the Physics Department for the current semester, in Alma (https://alma.uni-tuebingen.de/) go to "Stdies Offered">" Search for Courses". There, click "Show all possible search criteria" and under "Organiztional unit" type "Department of Physics". Then, click "Search".