# 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

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
- Category Theory
- Exersices in Category Theory
- Number theory seminar
- Geometric Algorithms
- English for Mathematicians III
- Number theory
- Computational geometry
- Numerical methods for solving ordinary differential equations
- Protection of Data and Information Privacy
- Introduction to programming in Python
- Interesting Physics
- Algebra II
- Differential Geometry
- Semigroups and formal languages
- Logic foundations of mathematics
- Partial Differential Equations
- Ordered algebraic structures
- Homological algebra
- Representations of Lie groups and algebras
- Popularization of Science
- Selected topics on automata theory
- Modal and Temporal Logics for Processes
- Introduction to Transparent Intensional Logic
- Mathematical Logic
- Enterprise Applications in Java
- Applied Cryptography
- Laboratory of security and applied cryptography

### 2nd semester

- Diploma Thesis 2, non-teaching
- Cryptography
- Algebraic Geometry
- Number Theoretic Algorithms
- Functional Analysis I
- Theory of Instruction
- Sociological Theories of Gender
- Advanced Examination in English for Specific Purposes - Science
- English for Mathematicians IV
- Geometry 1
- Set Theory
- Seminar on high-school mathematics 2
- Non-linear dynamics
- Calculus of Variations
- Continuous deterministic models II
- Game Theory
- Galois Theory
- History of Mathematics 1
- Algebraic Topology
- Coding
- Number theory seminar
- Topics in category theory
- Didactics of Mathematics 1
- Algorithms and data structures I
- Formal Languages and Automata
- Algorithms and data structures II

### 3rd semester

- Advanced Examination in English for Specific Purposes - Science
- Diploma Thesis 3, non-teaching
- Category Theory
- Graph Algorithms
- Foundations of Sociology
- Interesting Physics
- Combinatorics
- Rings and Modules
- Differential Geometry
- Spectral Analysis I
- Exersices in Category Theory
- Semigroups and formal languages
- Probability theory
- School pedagogy
- Special pedagogy
- School management
- Educational Psychology
- Pedagogical communication
- Non-Imperative Programming
- Game Design I
- Social psychology
- Introduction into psychology 1

### 4th semester

- Algebraic Topology
- Diploma Thesis 4, non-teaching
- Master state exam - Mathematics
- Comparative mythology
- Hebrew II
- English for Mathematicians II
- English for Mathematicians IV
- Galois Theory
- Algebraic Geometry
- Seminar from semigroup theory
- Mathematics for Cartography
- Algorithms and data structures II
- Intensive Language Course
- Editing a journal
- School Psychology
- Developmental Psychology

#### Additional information

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