# Specialization "Algebra, number theory, and discrete mathematics"

This page collects the most important information from the specialization "Algebra, number theory, and discrete mathematics", sorted by study programme.

## Teacher training programme

Students of the teacher training programme encounter contents belonging to the area of algebra, number theory, and discrete mathematics in many modules of the programme. In the introductory and orientation phase (StEOP) the basics of number theory are covered and they are also related to algebra. In the geometry module concepts of linear algebra are developed, in the stochastics module a major part is devoted to combinatorics. Finally, in applied mathematics models from discrete mathematics and from algebra play an important role.

## Bachelor programme

In the bachelor programme of mathematics the students acquire a comprehensive basic education in the most important fields of mathematics, starting with the introductory and orientation phase (StEOP). In the further course of the programme the following compulsory modules belong to the area "Algebra, number theory, and discrete mathematics":

- Linear algebra and geometry
- Number theory
- Discrete mathematics
- Algebra

You can find information on the contents of the lecture courses of these modules in the curriculum for the bachelor programme in mathematics. The concluding bachelor seminar offers, based on the already completed modules, various topics from the field of algebra, number theory, and discrete mathematics for bachelor theses.

## Master programme

In the master programme "Algebra, number theory, and discrete mathematics" is one of 7 main areas of specialization. You have to choose one of these 7 areas and the chosen main area of specialization results from the completion of the compulsory module group "basic courses in the area of specialization ...". The further modules of the master programme can be divided into courses from the chosen area of specialization and courses from other areas of specialization. The basic courses in the area of specialization "Algebra, number theory, and discrete mathematics" consists of the compulsory modules

- group theory
- algebraic number theory
- combinatorics

and a module that contains seminars on these fields. Further lecture courses are offered in the compulsory module "elective courses". A more detailed description of these modules can be found in the curriculum for the master programme in mathematics.

It is advisable to think about a possible topic and a supervisor of a master's thesis at an early stage of the master programme. When looking for a supervisor and a topic, you should also take into account whether you intend to do the doctoral programme based on the master programme. In this case the choice of a topic is more delicate and the connection to research should be stronger. Otherwise a broader range of topics is possible.

## Doctoral programme

As usual at the faculty of mathematics, there is no real difference between advanced courses for the master programme and courses for the doctoral programme in the area of specialization "Algebra, number theory, and discrete mathematics" but their recognition will be specified individually in an agreement ("Dissertationsvereinbarung").

The research interests of the individual faculty members play a much larger role in the choice of a topic and supervisor for a doctoral thesis than for a master's thesis. The topics are usually related to the (more or less) immediate research area of the supervisor. You can find a description of the current research areas within the area "Algebra, number theory, and discrete mathematics" at the faculty and a presentation of the involved people at http://www.mat.univie.ac.at/~algebra_hp/.