The Mandatory Courses of the Second Year

Algebra I and II

In the lectures Algebra I and II fundamental structures like groups, rings and fields are being treated.

Algorithms and Complexity

This lecture offers an introduction to theoretical computer science.

Complex Analysis

This course treats the complex analytical functions and their integration theory, which is important in analysis, geometry, number theory and physics.

Measure and Integration

The lecture Measure and Integration introduces students to Lebesgue’s measure and integration theory and some of its applications that are needed in other mathematical fields (e.g. probability).

Methods of Mathematical Physics I

The lecture Methods of Mathematical Physics I treats the theory of Fourier series, Fourier transformations and distributions, as well as their application to partial differential equations from Physics.

Numerical Analysis II

In this course minimization algorithms, numerics of ordinary differential equations and Monte Carlo methods are treated.

Physics III

The course Physics III deals with quantum physics, atomic physics in particular, and the laws of smallest scales in general.

Topology

In many mathematical fields, especially geometry and analysis, topology is of fundamental importance. In this course elementary concepts from set theory and algebraic topology are discussed.

Probability and Statistics

This course offers an introduction to elementary concepts of probability theory as well as estimation theories and tests of mathematical statistics.