# Algebra and Discrete Mathematics

## General information

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.

### A successful 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

## Graduate employment

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.

Faculty | Faculty of Science |
---|---|

Type of study | follow-up master's |

Mode | full-time |

Standard length of studies | 2 years |

Language of instruction | czech |

## Field of study combinations

#### Field combinations with Algebra and Discrete Mathematics

This field of study is only offered in single-subject study mode

## Admission Requirements

The information displayed in this block refers to a previous admission procedure.

A written or oral examination on the level of Bachelor's degree examination of the corresponding Bachelor's field of study is required. (only in Czech)

##### Recommended literature

See the requirements for the Bachelor's degree examination.

##### Evaluation criteria

The examination results.

## Frequently enrolled courses

Recommended study plans and other information can be found in the faculty study catalouge.

### 1st semester

- Diploma Thesis 1, non-teaching
- Rings and Modules
- Computational geometry
- English for Mathematicians III
- Number theory
- Numerical methods for solving ordinary differential equations
- Basic Course in Education
- Foundations of Education
- Introduction to programming in Python
- Interesting Physics
- Algebra II
- Differential Geometry
- Category Theory
- Exersices in Category Theory
- Semigroups and formal languages
- Logic foundations of mathematics
- Partial Differential Equations
- Number theory seminar
- Modal and Temporal Logics for Processes
- Introduction to Transparent Intensional Logic
- Mathematical Logic
- Enterprise Applications in Java
- Protection of Data and Information Privacy

### 2nd semester

- Diploma Thesis 2, non-teaching
- Game Theory
- Algebraic Geometry
- Cryptography
- Algorithms and data structures II
- Theory of Instruction
- Sociological Theories of Gender
- Classical, relativistic, quantum and statistical physics
- Advanced Examination in English for Specific Purposes - Science
- Topology
- Calculus of Variations
- Galois Theory
- Dynamical Systems
- Algebraic Topology
- Coding
- Number Theoretic Algorithms
- Homological algebra

### 3rd semester

- Number theory seminar
- Diploma Thesis 3, non-teaching
- Advanced Examination in English for Specific Purposes - Science
- Differential Geometry
- Category Theory
- Exersices in Category Theory
- Foundations of Sociology
- Hebrew I
- Optimization Theory
- Rings and Modules
- Calculus of Variations
- Semigroups and formal languages
- Dynamical Systems
- Survival analysis
- Diploma Thesis 2, non-teaching
- Seminar from semigroup theory
- Natural hazards - online
- Automata and Grammars
- Graph Algorithms
- English Online
- Social psychology
- Introduction into psychology 1
- Psychohygiene
- History of Money

### 4th semester

- Algebraic Topology
- Diploma Thesis 4, non-teaching
- Master state exam - Mathematics
- Algebraic Geometry
- Algorithms and data structures II
- Hebrew II
- Cryptography
- Mathematics of Finance
- Linear programming
- Galois Theory
- Number Theoretic Algorithms
- Number theory seminar
- Diploma Thesis 3, non-teaching
- Seminar from semigroup theory
- Formela lab seminar

#### Additional information

http://www.math.muni.cz/pro-studenty/studium-magisterske-studium.html