Equilibria and their Stability, introduction to KAM-Theory, Chaotic Behaviour: Shadowing Techniques

Equations are a topic omnipresent in Mathematics. It is therefore particularly suited for a course directed towards future mathematics teachers at the gymnasium. We treat historical and philosophical aspects, the two main themes being a) ill-posed inverse problems, b) degree theory (intermediate value theorem, winding numbers, Brouwer degree), with application.

The students give 2 examination lessons.

Educational objectives in geometry classes, didactical approaches to key concepts in plane geometry (congruence, parallelism, similarity, maps, length, area, volume), aspects of 3-d geometry, learning obstacles, didactical principles and historical aspects relevant to geometry learning, heuristics in problem solving, to design teaching units and to reflect on them, curriculum development questions

Students learn about and learn to use findings from empirical research into mathematical didactics and best practice, as well as theoretical approaches to teaching various topics in mathematics. Methodological suggestions are compared and draft tuition concepts discussed.

Mathematics I/II is an introduction to one- and multidimensional calculusand linear algebra emphasizing on applications.

Mathematics I/II is an introduction to one- and multidimensional calculusand linear algebra emphasizing on applications.

In the mentored work on their subject specialisation, students link high-school and university aspects of the subject, thus strengthening their teaching competence with regard to curriculum decisions and the future development of the tuition. They compile texts under supervision that are directly comprehensible to the targeted readers - generally specialist-subject teachers at high-school level.

In der mentorierten Arbeit in FV verknüpfen die Studierenden gymnasiale und universitäre Aspekte des Fachs mit dem Ziel, ihre Lehrkompetenz im Hinblick auf curriculare Entscheidungen und auf die zukünftige Entwicklung des Unterrichts zu stärken. Angeleitet erstellen sie Texte, welche die anvisierte Leserschaft, in der Regel gymnasiale Fachlehrpersonen, unmittelbar verstehen.

In their mentored work on subject didactics, students put into practice the contents of the subject-didactics lectures and go into these in greater depth. Under supervision, they compile tuition materials that are conducive to learning and/or analyse and reflect on certain topics from a subject-based and pedagogical angle.

In their mentored work on subject didactics, students put into practice the contents of the subject-didactics lectures and go into these in greater depth. Under supervision, they compile tuition materials that are conducive to learning and/or analyse and reflect on certain topics from a subject-based and pedagogical angle.

Students are offered topics beyond what is taught in a first year mathematics curriculum to provide supplementary insight. Topics covered: Modular Arithmetics, Lagrange Theorem, Fermat's Little Theorem, Euler's Extension, RSA Cryptography, Two-Square and Four-Square Theorem. Brouwer & Schauder Fixed Point Theorem, Perron-Frobenius Theorem, Google Page Ranking. Elementary Bifurcation Theory.

Students apply the insights, abilities and skills they have acquired within the context of an educational institution. They observe 10 lessons and teach 20 lessons independently. Two of them are as assessed as Examination Lessons.

The teaching practice takes in 50 lessons: 30 are taught by the students, and the students sit in on 20 lessons. The teaching practice lasts 4-6 weeks. It gives students the opportunity to implement the contents of their specialist-subject, educational science and subject-didactics training in the classroom. Students also conduct work assignments in parallel to their teaching practice.

In the final phase of their training, students have to apply and test the insights, abilities and skills they have acquired. They spend 3-5 weeks in an educational institution, during which time they observe 10 lessons and teach 30 lessons independently. The Teaching Internship is complemented by 10 further observed lessons, which are integrated into the Mentored Work in Subject Didactics.