# Analysis, Algebra and Geometry

**The "Analysis, Algebra and Geometry" doctoral programme introduces itself**

The doctoral programme, which is supported by the Faculty of Mathematics, Physics and Computer Science, prepares particularly well-suited students for independent research in the field of theoretical mathematics, especially analysis, algebra, number theory, and geometry.

**Mathematics as science**

Analysis, algebra and number theory as well as geometry are central areas of theoretical mathematics. Although mathematics is one of the oldest sciences, there has been spectacular progress in all these areas over the last 20 years. In addition to traditional applications, such as differential equations in the natural sciences, this has also opened up completely new and surprising application possibilities, for example in cryptology.

**Context, relationship, application**

The areas mentioned above are not just randomly grouped together; on the contrary, there are manifold relationships between them. For example, many methods devised in analysis and algebra are used in geometry. Indeed, many of the most important developments of recent years have been made possible by mathematically interdisciplinary methods.

**Mathematical interdisciplinary research**

This ought also be reflected in the doctoral programme: students should not only conduct research in their own field, but also acquire an overview of the latest results and methods in neighbouring fields, not least to be able to apply them in their thesis project if necessary.