Contents of the university education

• Mathematics
• Educational and social studies
• Didactics of Mathematics

1. Mathematics

Basics
The first 4-5 semesters are organized as study of the basics:

• analysis (advanced calculus)
• linear algebra
• numerical mathematics

An intermediate examination opens up the main course of studies.

Main course
During the following 4-5 semesters the students deal with lectures and exercises on

• complex analysis,
• algebra and number theory,
• logic,
• geometry and topology,
• probability, and
• introduction to computer-oriented mathematics.

Areas of specialization and in-depth study could be

• advanced complex analysis,
• differential equations,
• functional analysis,
• differential geometry and advanced topology, and
• statistics and probability.

Pure mathematics predominates over applied mathematics.
Students are expected to join seminars (for gradual participation in research) in addition to lectures and exercises.

At almost all universities it is obligatory that the written examination is a take-home essay on a mathematical theme and on mathematical exercises, in most cases with no connection to school mathematics at all.

2. Studies in educational and social sciences

This field of studies is described only generally and quite differently concretized at each university.

The same courses, seminars, and lectures are usually offered to teachers in all subjects by the departments of education:

• education
• general didactics, and
• teaching methodology,
  without reference to the specific content of the school subject studied.

They follow some main headings like:

• didactical theories,
• concepts and methods of educational sciences;
• philosophical and anthropological foundations of education;
• cognitive psychology and learning theories;
• migration and cultural change;
• history of the educational system and educational policy;
• socialization and school as a social institution;
• general and subject matter didactics (Fachdidaktik);
• curriculum development and instruction; and
• diagnosis, assessment, and special aids for teaching.

Some programs of study require practical studies, that is, several periods observing and teaching in schools under the supervision of either the educationalist (orienting practical phase) or the didactician (teaching practical phase).

3. Studies in didactics of mathematics

Didactics of mathematics is separately organized around the following (typical) scheme:

• After an introductory or survey lecture, or a seminar/coursework on problems,
• there follows a basic course in specific topics (either subject matter oriented like "algebra in schools" or more general like "how to use textbooks," "mathematical applications in schools," etc.).
• A seminar on analyzing and planning mathematics lessons prepares the students for a practical period of teaching in schools,
• and a main seminar, which perhaps offers participation in research in fields of mathematics education, may require a written report on individual research tasks undertaken by the students.

The most common topics in the programs are:

• history of mathematics education,
• mathematics as a school subject,
• relationship between mathematics didactics and mathematics,
• development of mathematical concepts,
• theories and aspects of teaching and learning mathematics,
• assessment in mathematics education, and
• didactics of selected topics in mathematics (didactics of algebra, didactics of geometry, didactics of probability and statistics, etc.).