# Algebra and Discrete Mathematics – Field of study catalogue MU

## Algebra and Discrete Mathematics“Via abstraction to understanding” |

The objective of this Master's degree programme is to educate experts in mathematics with the highly developed abstract thinking.

It is designed especially for students who do not like to accept

knowledge without a deep understanding of its background and context.

The programme focuses on modern branches of algebra and discrete

mathematics including applications in theoretical computer science.

During the instruction a precise formulation of ideas is crucial.

The studies are designed so that the students, in addition to the broader base of the branch, acquire also a thorough knowledge in a particular discipline of their own choice.

In the course of their studies, it is typical for students to be in a close contact with a scientific team specializing in the given branch.

The graduates will have a clear idea of whether they should focus on research in the future, or apply the obtained knowledge in practice.

After successfully completing his/her studies the graduate is able to:

- explain fundamental results in algebra and discrete mathematics
- identify general algebraic concepts in other mathematical disciplines
- use formal mathematical language to represent ideas
- write a formal mathematical text
- compose correct mathematical proofs

The graduates have mastered advanced methods of algebra and discreet mathematics. They can find employment in basic research and as teachers at universities. They can also specialize in informatics and be ready for practice - for example creating mathematical models, using combinatorial algorithms, and designing software.

The standard duration of studies is four semesters. To be admitted to the final state examination students must earn a total of 120 ECTS credits for required, selective, and elective courses. Required courses constitute the basis of the discipline and make up 68 credits (including credits for courses focusing on writing a Master’s thesis).

Out of the selective courses, which make up 18 credits in total, students choose according to their interests and intended professional specialization. The remaining 34 credits can be earned in optional courses offered in the study plan of the given study programme, or from courses offered by any other study programme.

During the course of their studies students should follow the Course Catalogue for their year of matriculation. They can access the Course Catalogues through the faculty website.

The final state examination consists of the defence of the Master's thesis and an oral examination. During the defence of the Master's thesis, the understanding of the topic of the thesis and the quality of presentation are evaluated. During the oral examination, students should demonstrate their understanding of basic concepts and results from various branches and relationships between them. Students have to answer three questions, one from each of the following areas: 1) Basics of Abstract Mathematics; 2) Algebraic Structures and Applications; and 3) Discrete Mathematics.

More information about graduation requirements can be found on the department's website: "http://www.math.muni.cz/pro-studenty/studium-magisterske-studium/310-mgr-szz-algebra-a-diskr-matematika.html".

After completion of the Master's degree programme it is possible to progress to further studies in any doctoral degree programme (after satisfying the admission requirements). At Masaryk University students can apply for admission to various programmes within the doctoral degree programmes of Mathematics and Informatics.