# State Exam "Lehramt an Gymnasien", Subject Mathematics

Teachers for the teaching profession at grammar schools are entitled to teach their chosen subjects in all year groups at grammar schools. Prospective students should be communicative and open for dialogue. They should be patient, enjoy explaining and discussing, and be enthusiastic about imparting knowledge and values.

TU Dresden offers modularized teacher training courses with a state degree. The standard period of study up to the first state exam is 10 semesters. This is followed by a preparatory school service of 12 months and the second state examination.

By choosing mathematics as a subject, you are setting an important focus, as mathematics is taught in all year groups. Mathematics can be combined with all other subjects on offer. The aim of the teacher training course in mathematics is to acquire a broad knowledge of higher mathematics and subject didactics. The course covers the basics and main areas of mathematics and its didactics, including subject-specific scientific methods.

### Structure of the courses

**Introductory courses**provide students with knowledge of the fundamentals of mathematics in the following areas:- linear algebra
- analytical geometry
- analysis
- geometry

**Advanced courses**, each supplemented by a proseminar, a seminar and a specialization on selected topics in mathematics, offer knowledge in the following areas:- computer-oriented arithmetic
- stochastics
- algebra and number theory
- numerical mathematics
- ordinary differential equations

**Mathematics didactics**helps students to deepen their understanding of- processes of teaching and learning mathematics and become familiar with didactic research approaches
- development of concepts to promote students' mathematical interests and skills.
- knowledge of applications of mathematics through to current developments and the reflection of mathematical conceptualization

**Practical school studies**guarantee experience in the planning, methodical design and evaluation of mathematics lessons.**Supplementary studies**also offer the opportunity to expand and deepen mathematical and mathematical didactic knowledge in selected courses according to your own interests, especially with regard to the requirements of academic work.

### Summary of the course content

- Algebra, including set theory, logic and number range extensions, basic structures of algebra, linear algebra, elements of algebraic number theory
- Analysis, including functions and basic properties, differential and integral calculus for one and more variables, differential equations,
- Applied mathematics, including numerical mathematics, modeling, elements of computer science and mathematical software,
- Geometry, including analytic geometry, Euclidean and non-Euclidean geometry, geometric mappings, elements of differential geometry,
- Stochastics, including probability theory, introduction to mathematical statistics,
- Didactics of mathematics, including teaching-learning research, central concepts and methods of school mathematics, planning, design and analysis of mathematics lessons.

### Further information

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