Introduction and development of some basic algebraic structures - groups, rings, fields.

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Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.

Selected topics concerning fields, including Galois theory.

Galois theory and related topics.

Es werden ausführlich die Axiome der Mengenlehre besprochen und parallel dazu wird die Theorie der Ordinal- und Kardinalzahlen aufgebaut. Zudem werden Ultrafilter untersucht und es wird das Martinaxiom eingeführt.

The lecture course covers basic notions of mathematical logic, set theory, algebra, elementary number theory, graph theory, and combinatorics.

Mit Hilfe der Forcing-Technik werden verschiedene Unabhaengigkeitsbeweise gefuehrt. Insbesondere wird gezeigt, dass die Kontinuumshypothese von den Axiomen der Mengenlehre unabhaengig ist.

This course gives an introduction into various geometrical topics, such as euclidean and projective geometry, as well as geometrical properties of special curves like conics and cubics.

Introduction to the theory of vector spaces for students of mathematics or physics: Basics, vector spaces, linear transformations, solutions of systems of equations, matrices, determinants, endomorphisms, eigenvalues, eigenvectors.

This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.

This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.

Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.The main focus of Mathematics II is multivariable calculus.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.

Consolidation and extension of mathematics as the universal language for scientific facts:The lecture aims on one hand at learning and exercising the mathematical trade and in the other hand at applying the learnt concept to medical, biological, chemical and mechanical problems.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.

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.