FI MU Study Catalogue 2023/2024
Study catalogue in all-in-one version
The FI MU Study Catalogue is a document describing the conditions of study at the Faculty of Informatics in Bachelor's and Follow-up Master's Degree Programs, which are valid for students who have started their studies in one of those study programs in the given academic year. Faculty of Informatics is committed to preserve these conditions as much as possible during the whole period of studies.
Bachelor's Degree Programs
Follow-up Master's Degree Programs (Czech)
Follow-up Master's Degree Programs (English)
Bachelor's Degree Programs
bachelor's program without specializations supporting Major/Minor study
This study programme is recommended to students who intend to get fundamental knowledge in informatics and get acquainted with the general principals of making and using information technology. Besides, the basic orientation in the field students will get enough knowledge and practical training to be able to find employment in the field immediately after graduation. The programme offers some options to aim the profile of the education towards selected basic areas of computer science, such as computer graphics, data processing, information security, networking, artificial intelligence, and computer science.
Graduates may immediately start working on junior IT positions and will be ready to deepen their knowledge according to the needs of their employer. Graduates are also ready to continue their studies in any master degree programme related to informatics or to opt for some other discipline to get interesting interdisciplinary knowledge.
Requirements for successful graduation
- Obtain at least 180 credits overall and pass the final state exam.
- Obtain 10 credits for SBAPR subject and successfully defend Bachelor's Thesis. See more details.
- Fulfil requirements of a single-field study option or Major study option.
- Pass all the compulsory and elective courses of the program, selected study option, and selected focus with the highest possible graduation form.
- Obtain at least two credits from Physical training. See University Sport Centre.
Compulsory subjects of the program
IB000 |
Mathematical Foundations of Computer Science |
|---|---|
IB002 |
Algorithms and data structures I |
IB005 |
Formal Languages and Automata |
IB015 |
Non-Imperative Programming |
IB111 |
Foundations of Programming |
MB151 |
Linear models |
MB152 |
Differential and Integral Calculus |
MB153 |
Statistics I |
MB154 |
Discrete mathematics |
PB006 |
Principles of Programming Languages and OOP |
PB007 |
Software Engineering I |
PB071 |
Principles of low-level programming |
PB151 |
Computer Systems |
PB152 |
Operating Systems |
PB152zk |
Operating Systems - Exam |
PB154 |
Database Systems |
PB156 |
Computer Networks |
PV004 |
UNIX |
PV080 |
Information security and cryptography |
VB001 |
English Exam |
SBPrip |
Revisions for Bachelor State Exam |
SOBHA |
Defence of Thesis |
SZB |
State Exam (Bc degree) |
| Typesetting and academic writing Pass at least 1 course of the following list | |
VB000
|
Elements of Style |
VB000Eng
|
Introduction to Academic Writing |
PB029
|
Electronic Document Preparation |
| English Obtain at least 3 credits by passing subjects of the following list | |
VB035
|
English I |
VB036
|
English II |
VV064
|
Academic and Professional Skills in English for IT |
| Common university background Obtain at least 9 credits by passing subjects of the following list | |
CORE*
|
Courses with prefix CORE |
Study option: Single-field study of Informatics
Compulsory subjects and other obligations of the study option
| Pass all obligatory courses of the program. | |
IB107 |
Computability and Complexity |
|---|---|
IB031 |
Introduction to Machine Learning |
PB016 |
Introduction to Artificial Intelligence |
| Programming Pass at least 1 course of the following list | |
PB161
|
C++ Programming |
PB162
|
Java |
PV178
|
Introduction to Development in C#/.NET |
| Fulfil the conditions of at least one focus group. | |
Focus groups
Open Informatics
This focus is recommended for students who want to choose their own profile.
| Choice in open informatics Obtain at least 25 credits by passing subjects of the following list | |
MV008
|
Algebra I |
|---|---|
IA006
|
Selected topics on automata theory |
IV029
|
Introduction to Transparent Intensional Logic |
IV100
|
Parallel and distributed computations |
IV107
|
Bioinformatics I |
IV126
|
Fundamentals of Artificial Intelligence |
PB029
|
Electronic Document Preparation |
PB050
|
Modelling and Prediction in Systems Biology |
PB095
|
Introduction to Speech Processing |
PB173
|
Domain specific development |
PV005
|
Computer Network Services |
PV017
|
Information Technology Security |
PV061
|
Machine Translation |
PV065
|
UNIX -- Programming and System Management I |
PV090
|
UNIX -- Seminar of System Management |
PV110
|
Basics of Film Narratives |
PV112
|
Computer Graphics API |
PV119
|
Elements of Law |
PV123
|
Introduction to Visual Communication |
PV168
|
Seminar in Java programming |
PV169
|
Communication Systems Basics |
PV170
|
Design of Digital Systems |
PV171
|
Digital Systems Diagnostics |
PV175
|
MS Windows Systems Management I |
PV197
|
GPU Programming |
PV210
|
Cybersecurity in an Organization |
PV248
|
Python Seminar |
PV251
|
Visualization |
PV281
|
Programming in Rust |
PV288
|
Python |
IB016
|
Seminar on Functional Programming |
IB030
|
Introduction to Natural Language Processing |
IB047
|
Introduction to Corpus Linguistics and Computer Lexicography |
IB109
|
Design and Implementation of Parallel Systems |
IV109
|
Modeling and Simulation |
IV124
|
Complex Networks |
IV128
|
Online Communication from Social Science Perspective |
IV130
|
Pros and Cons of Intelligent Systems |
PB009
|
Principles of Computer Graphics |
PB051
|
Computational methods in Bioinformatics and Systems Biology |
PB138
|
Basics of web development and markup languages |
PB176
|
Basics of Quality and Managment of Source Code |
PV003
|
Relational Database System Architecture |
PV056
|
Machine Learning and Data Mining |
PV077
|
UNIX -- Programming and System Management II |
PV113
|
Production of Audiovisual Artefacts |
PV291
|
Introduction to Digital Signal Processing |
PV165
|
Process Management |
PV176
|
MS Windows Systems Management II |
PV182
|
Human-Computer Interaction |
PV211
|
Introduction to Information Retrieval |
PV249
|
Development in Ruby |
PV254
|
Recommender Systems |
PV285
|
IoT Security |
PV287
|
Artificial Intelligence and Machine Learning in Healthcare |
VV076
|
Ethics and Information Technology |
Computer Systems, Communication and Security
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Computer Systems, Communication and Security.
PV170 |
Design of Digital Systems |
|---|---|
PV065 |
UNIX -- Programming and System Management I |
PB138 |
Basics of web development and markup languages |
PV077 |
UNIX -- Programming and System Management II |
PV005 |
Computer Network Services |
IB109 |
Design and Implementation of Parallel Systems |
| Choice in computer systems Pass at least 1 course of the following list | |
PB176
|
Basics of Quality and Managment of Source Code |
PB173
|
Domain specific development |
Visual Informatics
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Visual Informatics.
PB130 |
Introduction to Digital Image Processing |
|---|---|
PB009 |
Principles of Computer Graphics |
PV112 |
Computer Graphics API |
PV291 |
Introduction to Digital Signal Processing |
| Choice in visual informatics Obtain at least 2 credits by passing subjects of the following list | |
PV160
|
Laboratory of Human-Computer Interaction |
PV162
|
Image Processing Project |
Graphic Design
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Visual Informatics specialized in Graphic Design.
PB130 |
Introduction to Digital Image Processing |
|---|---|
PV123 |
Introduction to Visual Communication |
PB009 |
Principles of Computer Graphics |
PV078 |
Graphic Design I |
PV272 |
3D Modelling |
PV066 |
Typography I |
PV291 |
Introduction to Digital Signal Processing |
PV084 |
Type Design I |
Bioinformatics and System Biology
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Artificial Intelligence and Data Processing specialized in Bioinformatics and System Biology.
IV107 |
Bioinformatics I |
|---|---|
VV071 |
Biochemistry for bioinformatics |
PA052 |
Introduction to Systems Biology |
VV072 |
Molecular biology for bioinformatics |
IV114 |
Bioinformatics and Systems Biology Project |
PB051 |
Computational methods in Bioinformatics and Systems Biology |
Math Informatics
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Theoretical Computer Science or follow-up Masters' degree program Artificial Intelligence and Data Processing.
MV008 |
Algebra I |
|---|---|
IV109 |
Modeling and Simulation |
IV119 |
Seminar on Discrete Mathematical Methods |
MA010 |
Graph Theory |
MA018 |
Numerical Methods |
Natural Language Processing
This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Artificial Intelligence and Data Processing specialized in Natural Language Processing.
MV008 |
Algebra I |
|---|---|
IB030 |
Introduction to Natural Language Processing |
IB047 |
Introduction to Corpus Linguistics and Computer Lexicography |
PB095 |
Introduction to Speech Processing |
PB106 |
Corpus Linguistic Project I |
PV173 |
Natural Language Processing Seminar |
Extended math education
When selecting this option, the obligation of courses with prefix MB is cancelled. This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Theoretical Computer Science or follow-up Masters' degree program Artificial Intelligence and Data Processing.
PřF:MIN101 |
Mathematics I |
|---|---|
PřF:M1VM01 |
Algorithmization and numerical computations |
PřF:MIN201 |
Mathematics II |
PřF:MIN202 |
Numerical calculations |
PřF:MIN301 |
Mathematics III |
PřF:MIN401 |
Mathematics IV |
PřF:M3121 |
Probability and Statistics I |
PřF:M4122 |
Probability and Statistics II |
Fundaments of mathematics
When selecting this option, the obligation of courses with prefixes MB151 and MB152 is cancelled. This focus is recommended to students who intend to continue their studies in follow-up Masters' degree program Theoretical Computer Science or follow-up Masters' degree program Artificial Intelligence and Data Processing.
PřF:M1110 |
Linear Algebra and Geometry I |
|---|---|
PřF:M2110 |
Linear Algebra and Geometry II |
PřF:M1100 |
Mathematical Analysis I |
PřF:M2100 |
Mathematical Analysis II |
PřF:M2150 |
Algebra I |
| Choice in advanced mathematics Pass at least 1 course of the following list | |
PřF:M3150
|
Algebra II |
PřF:M3100
|
Mathematical Analysis III |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
Fall 2025 (5. term)
Study option: Major
Compulsory subjects and other obligations of the study option
| Pass all obligatory courses of the program. | |
| Fulfill conditions of Minor of another study program. |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
Fall 2025 (5. term)
Study option: Minor
Compulsory subjects and other obligations of the study option
IB000 |
Mathematical Foundations of Computer Science |
|---|---|
IB110 |
Introduction to Informatics |
IB113 |
Introduction to Programming and Algorithms |
IB114 |
Introduction to Programming and Algorithms II |
PB001 |
Introduction to Information Technologies |
PB007 |
Software Engineering I |
PB153 |
Operating Systems and their Interfaces |
PB156 |
Computer Networks |
PB168 |
Introduction to DB and IS |
PV004 |
UNIX |
PV157 |
Authentication and Access Control |
IV130 |
Pros and Cons of Intelligent Systems |
IV109 |
Modeling and Simulation |
SZB |
State Exam (Bc degree) |
Recommended course of study
Fall 2024 (3. term)
Spring 2025 (4. term)
Fall 2025 (5. term)
bachelor's program without specializations
The focus of the Programming and development bachelor program is design, creation, implementation, and program maintenance technology and in lesser amount also technical equipment of modern computer systems and digitally controlled systems. Graduates of the program will have a fundamental understanding of the whole computer systems life cycle, starting with computer architectures, programming and software engineering, through computer networks and operating systems and ending with the development of embedded systems. This technological view is supported by the necessary mathematical foundations and by an introduction to design principles of secure computer systems. An important feature of the program is the focus on continuous practical verification of attained knowledge, including semestral project and voluntary semester-long internship. The goal of this program is to focus the graduates on the solving the technological (real world) problems.
Graduates are able to immediately work as junior programmers, designers or members of a test team with fundamentals broad enough for following professional and career growth.
Requirements for successful graduation
- Obtain at least 180 credits overall and pass the final state exam.
- Obtain 10 credits for SBAPR subject and successfully defend Bachelor's Thesis. See more details.
- Pass all the compulsory and elective courses of the program with the highest possible graduation form.
- Obtain at least two credits from Physical training. See University Sport Centre.
Compulsory subjects of the program
IB000 |
Mathematical Foundations of Computer Science |
|---|---|
IB002 |
Algorithms and data structures I |
IB015 |
Non-Imperative Programming |
IB109 |
Design and Implementation of Parallel Systems |
IB110 |
Introduction to Informatics |
IB111 |
Foundations of Programming |
PB006 |
Principles of Programming Languages and OOP |
PB007 |
Software Engineering I |
PB071 |
Principles of low-level programming |
PB138 |
Basics of web development and markup languages |
PB151 |
Computer Systems |
PB152 |
Operating Systems |
PB152cv |
Operating Systems - practicals |
PB154 |
Database Systems |
PB156 |
Computer Networks |
PB156cv |
Computer Networks - practicals |
PB175 |
Project managment and project |
PB176 |
Basics of Quality and Managment of Source Code |
PV004 |
UNIX |
PV028 |
Applied Information Systems |
PV080 |
Information security and cryptography |
PV170 |
Design of Digital Systems |
MB141 |
Linear algebra and discrete mathematics |
MB142 |
Applied math analysis |
MB143 |
Design and analysis of statistical experiments |
VB000 |
Elements of Style |
VB001 |
English Exam |
SBPrip |
Revisions for Bachelor State Exam |
SB100 |
Bachelor Internship - Programming and Development |
SOBHA |
Defence of Thesis |
SZB |
State Exam (Bc degree) |
| Programming 1 Pass at least 1 course of the following list | |
PB161
|
C++ Programming |
PB162
|
Java |
| Programming 2 Pass at least 1 course of the following list | |
PB173
|
Domain specific development |
PV168
|
Seminar in Java programming |
PV178
|
Introduction to Development in C#/.NET |
| English Obtain at least 2 credits by passing subjects of the following list | |
VB035
|
English I |
VB036
|
English II |
VV064
|
Academic and Professional Skills in English for IT |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
Fall 2025 (5. term)
Spring 2026 (6. term)
bachelor's program without specializations supporting Major/Minor study
The aim of this bachelor's study program is to equip applicants with the necessary professional knowledge and the necessary minimum of psychological-pedagogical knowledge for successful work in education in the field of informatics. The program is also a program that in combination with a follow-up teaching program at MU, prepares graduates for the teaching profession. The degree is open only in the minor version in cooperation with the degrees of the Faculty of Science of Masaryk University.
The graduate is ready to continue studying in a follow-up teaching program at MU or can work in various training centers with a focus on IT training.
Requirements for successful graduation
- Obtain at least 180 credits overall and pass the final state exam.
- Obtain 10 credits for SBAPR subject and successfully defend Bachelor's Thesis. See more details.
- Pass all the compulsory and elective courses of the selected study option with the highest possible graduation form.
Study option: Minor
Compulsory subjects and other obligations of the study option
IB000 |
Mathematical Foundations of Computer Science |
|---|---|
IB110 |
Introduction to Informatics |
IB113 |
Introduction to Programming and Algorithms |
IB114 |
Introduction to Programming and Algorithms II |
PB150 |
Computer-Systems Architectures |
PB153 |
Operating Systems and their Interfaces |
PB156 |
Computer Networks |
PV157 |
Authentication and Access Control |
PB007 |
Software Engineering I |
PB168 |
Introduction to DB and IS |
UB001 |
Assesment of teaching in Informatics |
VB036 |
English II |
SBPrip |
Revisions for Bachelor State Exam |
| Programming Pass at least 1 course of the following list | |
PB161
|
C++ Programming |
PB162
|
Java |
PB071
|
Principles of low-level programming |
| Application development Pass at least 1 course of the following list | |
PB069
|
Desktop Application Development in C#/.NET |
PB138
|
Basics of web development and markup languages |
PV256
|
Introduction to Development for Android |
| Collect at least 70 credits from courses tought at FI with prefixes IB, IB, PB, or PV. | |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
-
IB110Introduction to Informatics - Choice: Any course from Programming section
Fall 2025 (5. term)
bachelor's program without specializations
The program will meet the growing interest of both high school graduates and already employed jobseekers without formal education in the field who carry out professions where knowledge and skills in cybersecurity.
Graduates will be ready for a professional of system administrators, operators in information security operations center, CSIRT team members, lower- or middle management in cybersecurity; software engineers of security-relevant IT applications and systems, as well as cybersecurity trainers or assistants to cybersecurity managers.
Requirements for successful graduation
- Obtain at least 180 credits overall and pass the final state exam.
- Obtain 10 credits for SBAPR subject and successfully defend Bachelor's Thesis. See more details.
- Pass all the compulsory and elective courses of the program with the highest possible graduation form.
- Obtain at least two credits from Physical training. See University Sport Centre.
Compulsory subjects of the program
MB141 |
Linear algebra and discrete mathematics |
|---|---|
IB000 |
Mathematical Foundations of Computer Science |
IB110 |
Introduction to Informatics |
IB113 |
Introduction to Programming and Algorithms |
IB114 |
Introduction to Programming and Algorithms II |
PB007 |
Software Engineering I |
PB071 |
Principles of low-level programming |
PB151 |
Computer Systems |
PB152 |
Operating Systems |
PB152cv |
Operating Systems - practicals |
PB156 |
Computer Networks |
PB156cv |
Computer Networks - practicals |
| Databases Pass at least 1 course of the following list | |
PB168
|
Introduction to DB and IS |
PB154
|
Database Systems |
PV004 |
UNIX |
PV028 |
Applied Information Systems |
PV080 |
Information security and cryptography |
IV130 |
Pros and Cons of Intelligent Systems |
PV157 |
Authentication and Access Control |
PV175 |
MS Windows Systems Management I |
PV276 |
Seminar on Simulation of Cyber Attacks |
VB000 |
Elements of Style |
VB001 |
English Exam |
SB200 |
Bachelor Internship - Cybersecurity |
PrF:BI301K |
ICT Law II |
PrF:BVV03K |
Cybercriminality |
FSS:BSSb1101 |
Introduction into Security and Strategic Studies |
FSS:BSSb1103 |
Security Policy of the Czech Republic |
FSS:BSSb1152 |
Cyber Warfare |
| Programming Pass at least 1 course of the following list | |
PB161
|
C++ Programming |
PB162
|
Java |
| Cybersecurity Pass at least 1 course of the following list | |
PV017
|
Information Technology Security |
PV210
|
Cybersecurity in an Organization |
| English Obtain at least 2 credits by passing subjects of the following list | |
VB035
|
English I |
VB036
|
English II |
VV064
|
Academic and Professional Skills in English for IT |
SBPrip |
Revisions for Bachelor State Exam |
SOBHA |
Defence of Thesis |
SZB |
State Exam (Bc degree) |
Recommended course of study
Fall 2023 (1. term)
-
IB000Mathematical Foundations of Computer Science -
IB113Introduction to Programming and Algorithms -
PB151Computer Systems - Choice: Any course from Databases section
-
FSS:BSSb1101Introduction into Security and Strategic Studies -
VB035English I - Physical training
Spring 2024 (2. term)
Fall 2024 (3. term)
-
PrF:BI301KICT Law II - Choice: Any course from Cybersecurity section
-
FSS:BSSb1152Cyber Warfare -
PV028Applied Information Systems -
PV175MS Windows Systems Management I -
PB152cvOperating Systems - practicals
Spring 2025 (4. term)
-
FSS:BSSb1103Security Policy of the Czech Republic -
IB110Introduction to Informatics -
PV080Information security and cryptography -
IV130Pros and Cons of Intelligent Systems -
PB156cvComputer Networks - practicals - Choice: Any course from Programming section
Fall 2025 (5. term)
Follow-up Master's Degree Programs (Czech)
follow-up master's program (Czech) with specializations
The study of theoretical computer science focuses on a deeper understanding of basic principles underpinning the development of contemporary information technologies, including non-classical computational devices such as neural networks or quantum computers. Together with the active mastering of advanced theoretical as well as practical concepts, a special emphasis is put on the development of abstract thinking. The students gain a deeper understanding of advanced algorithms, principles of modern programming languages, and methods for verification and analysis of computer programs. Further, they understand the basic advantages and limitations of non-classical computational devices. After successfully completing the programme, the students are qualified for a wide variety of positions requiring complex expert skills.
After successfully completing the study programme, the students are qualified for a variety of IT positions including a developer, system architect, or verification engineer. Solid mathematical skills together with deep knowledge of non-trivial algorithms enable the students to find jobs in the financial sector. The acquired knowledge and skills may be well used also in the follow-up Ph.D. programme.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
IA006 |
Selected topics on automata theory |
|---|---|
| Logic and reasoning Pass at least 1 course of the following list | |
IA008
|
Computational Logic |
IA085
|
Satisfiability and Automated Reasoning |
IA011 |
Programming Language Semantics |
IA012 |
Complexity |
IV003 |
Algorithms and Data Structures II |
IV111 |
Probability in Computer Science |
MA007 |
Mathematical Logic |
PV027 |
Optimization |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
Specialization: Discrete algorithms and models
Students specializing in Discrete Algorithms and Models will gain advanced knowledge in a wide range of areas of theoretical computer science and related areas of mathematics. Graduates of the specialization will be able to solve very demanding tasks from selected areas of theoretical computer science and will have basic experience with scientific work similar to doctoral studies.
Compulsory subjects of the specialization
IA168 |
Algorithmic game theory |
|---|---|
MA010 |
Graph Theory |
MA026 |
Advanced Combinatorics |
MA009 |
Algebra II |
| Advanced mathematics Pass at least 1 course of the following list | |
IA062
|
Randomized Algorithms and Computations |
PřF:M8190
|
Number Theoretic Algorithms |
MA017
|
Geometric Algorithms |
MA015
|
Graph Algorithms |
| Choice of Seminar Obtain at least 2 credits by passing subjects of the following list | |
IA072
|
Seminar on Verification |
IV115
|
Parallel and Distributed Laboratory Seminar |
IV131
|
Seminar of Discrete Methods and Algorithms Laboratory |
IV125
|
Formela lab seminar |
IA174 |
Fundaments of Cryptography |
IA101 |
Algorithmics for Hard Problems |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Quantum and other Nonclassical Computational Models
Specialization Quantum and other Nonclassical Computational Models will familiarize students with problem solving methods, which are computationally demanding on conventional computers. Graduates are also familiar with the principles, benefits and limitations of non-classical computing systems such as neural networks or quantum computers.
Compulsory subjects of the specialization
IV100 |
Parallel and distributed computations |
|---|---|
IA062 |
Randomized Algorithms and Computations |
IA066 |
Introduction to Quantum Computing |
IA082 |
Physical concepts of quantum information processing |
IA101 |
Algorithmics for Hard Problems |
IA174 |
Fundaments of Cryptography |
PV056 |
Machine Learning and Data Mining |
PV021 |
Neural Networks |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Formal Analysis of Computer Systems
The specialization Formal Analysis of Computer Systems focuses on formal methods for modeling, analysis, testing, and verification of computer programs as one of the basic building blocks of software systems development. Students get acquainted with the principles of modern verification tools and master practical skills required for working in teams responsible for ensuring the quality of the software products (quality assurance teams).
Compulsory subjects of the specialization
IA023 |
Petri Nets |
|---|---|
IA085 |
Satisfiability and Automated Reasoning |
IA159 |
Formal Methods for Software Analysis |
IA168 |
Algorithmic game theory |
IA169 |
Model Checking |
IA175 |
Algorithms for Quantitative Verification |
IV120 |
Continuous and Hybrid Systems |
| Choice of Seminar Obtain at least 4 credits by passing subjects of the following list | |
IA072
|
Seminar on Verification |
IV115
|
Parallel and Distributed Laboratory Seminar |
IV131
|
Seminar of Discrete Methods and Algorithms Laboratory |
IV125
|
Formela lab seminar |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Principles of Programming Languages
Specialization Principles of programming languages provide a deeper insight into the paradigms of modern programming languages and the structure of their compilers. Graduates can choose the optimal programming tools for a given application type and can quickly acquire new programming languages.
Compulsory subjects of the specialization
IA010 |
Principles of Programming Languages |
|---|---|
IA014 |
Advanced Functional Programming |
| Advanced Types Pass at least 1 course of the following list | |
IA038
|
Types and Proofs |
IA081
|
Lambda calculus |
IA158 |
Real Time Systems |
IA174 |
Fundaments of Cryptography |
IV010 |
Communication and Parallelism |
PA008 |
Compiler Construction |
PA037 |
Compiler Project |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
follow-up master's program (Czech) with specializations
The Artificial Intelligence and Data Processing program prepares students to work in the areas of design and development of intelligent systems and analysis of big data. These areas are currently undergoing very fast development and are becoming increasingly important. The program leads students to a thorough understanding of basic theoretical concepts and methods. During the study students also solve specific case studies to familiarize themselves with the currently used tools and technologies. Students will thus gain experience that will allow them to immediately use the current state of knowledge in practice, as well as solid foundations, which will enable them to continue to independently follow the developments in the field. The program is divided into four specializations that provide deeper knowledge in a chosen direction. Specializations share a common core, where students learn the most important mathematical, algorithmic, and technological aspects of the field. Machine Learning and Artificial Intelligence specialization lead graduates to gain in-depth knowledge of machine learning and artificial intelligence techniques and to gain experience with their practical application. Natural Language Processing specialization prepares graduates to work with natural languages (eg. Czech, English) in written and spoken form from the perspective of computer science. Data Management and Analysis specialization focus on data science, which creates value from big data by collecting, exploring, interpreting, and presenting data from different viewpoints with the goal of so-called business intelligence. Bioinformatics and Systems Biology specialization focuses on computational methods for automated analysis of large biological data and on creating predictive models of biological processes with the goal to better understand complex biological systems.
Due to the dynamic development of the area, the graduates have a wide range of career opportunities, with specific employment positions being created continuously during the course of their studies. Examples of different types of possible positions: positions in applied and basic research, typically concerning extensive data processing, often also in collaboration with experts from other disciplines such as biology or linguistics; positions in companies with an immediate interest in artificial intelligence and data processing (e.g., Seznam, Google) such as Data Scientist and Machine Learning Engineer; positions in companies that have extensive, valuable data (such as banking, telecom operators) or companies focusing on cloud data analysis, e.g., Business Intelligence Analyst or Data Analyst; graduates can also start their own start-up specializing in the use of artificial intelligence methods in a particular area.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
MA012 |
Statistics II |
|---|---|
IV126 |
Fundamentals of Artificial Intelligence |
PA039 |
Supercomputer Architecture and Intensive Computations |
PA152 |
Efficient Use of Database Systems |
PV021 |
Neural Networks |
PV056 |
Machine Learning and Data Mining |
PV211 |
Introduction to Information Retrieval |
PV251 |
Visualization |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
Specialization: Machine Learning and Artificial Intelligence
Machine Learning and Artificial Intelligence specialization leads graduates to gain in-depth knowledge of machine learning and artificial intelligence techniques and to gain experience with their practical application.
Compulsory subjects of the specialization
IV111 |
Probability in Computer Science |
|---|---|
IA008 |
Computational Logic |
PA163 |
Constraint programming |
PA153 |
Natural Language Processing |
PA228 |
Machine Learning in Image Processing |
| Applications of Machine Learning Pass at least 1 course of the following list | |
PA167
|
Scheduling |
PA212
|
Advanced Search Techniques for Large Scale Data Analytics |
PA128
|
Similarity Searching in Multimedia Data |
PV254
|
Recommender Systems |
PA164
|
Machine learning and natural language processing |
IA168
|
Algorithmic game theory |
| Projects and Laboratory Obtain at least 4 credits by passing subjects of the following list | |
PA026
|
Artificial Intelligence Project |
PV115
|
Laboratory of Knowledge Discovery |
IV127
|
Adaptive Learning Seminar |
IV125
|
Formela lab seminar |
PV253
|
Seminar of DISA Laboratory |
| Optimizations and Numeric Computing Pass at least 1 course of the following list | |
PV027
|
Optimization |
MA018
|
Numerical Methods |
PřF:M7PNM1
|
Advanced numerical methods I |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Data Management and Analysis
Data Management and Analysis specialization focuses on data science, which creates value from big data by collecting, exploring, interpreting, and presenting data from different viewpoints with the goal of so called business intelligence.
Compulsory subjects of the specialization
PA017 |
Software Engineering II |
|---|---|
PA128 |
Similarity Searching in Multimedia Data |
PA195 |
NoSQL Databases |
PA200 |
Cloud Computing |
PA212 |
Advanced Search Techniques for Large Scale Data Analytics |
PA220 |
Database systems for data analytics |
| Data Algorithms Obtain at least 4 credits by passing subjects of the following list | |
PA228
|
Machine Learning in Image Processing |
PV079
|
Applied Cryptography |
PA167
|
Scheduling |
PV254
|
Recommender Systems |
MA015
|
Graph Algorithms |
| Projects and Laboratory Obtain at least 4 credits by passing subjects of the following list | |
PV253
|
Seminar of DISA Laboratory |
PV115
|
Laboratory of Knowledge Discovery |
PV229
|
Multimedia Similarity Searching in Practice |
PA036
|
Database System Project |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
-
PV056Machine Learning and Data Mining -
PA152Efficient Use of Database Systems -
PA039Supercomputer Architecture and Intensive Computations -
PV211Introduction to Information Retrieval -
PA195NoSQL Databases -
PA212Advanced Search Techniques for Large Scale Data Analytics -
PA128Similarity Searching in Multimedia Data
Fall 2024 (3. term)
Specialization: Natural Language Processing
Natural Language Processing specialization prepares graduates to work with natural languages (eg. Czech, English) in written and spoken form from the perspective of computer science.
Compulsory subjects of the specialization
IA161 |
Natural Language Processing in Practice |
|---|---|
IV111 |
Probability in Computer Science |
PA153 |
Natural Language Processing |
PA154 |
Language Modeling |
PA156 |
Dialogue Systems |
| Math Pass at least 2 courses of the following list | |
MA007
|
Mathematical Logic |
IA008
|
Computational Logic |
MA010
|
Graph Theory |
MA015
|
Graph Algorithms |
MV008
|
Algebra I |
MA018
|
Numerical Methods |
PřF:M7130
|
Computational geometry |
| Natural Language Processing Pass at least 1 course of the following list | |
PA164
|
Machine learning and natural language processing |
PV061
|
Machine Translation |
IV029
|
Introduction to Transparent Intensional Logic |
| Seminar or Project Obtain at least 2 credits by passing subjects of the following list | |
PV173
|
Natural Language Processing Seminar |
PV277
|
Programming Applications for Social Robots |
PB106
|
Corpus Linguistic Project I |
PA107
|
Corpus Tools Project |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Bioinformatics and System Biology
Specialization Bioinformatics and System Biology is intended for students who want to acquire, besides the general knowledge of informatics, the latest knowledge in dynamically developing fields at the border of informatics and biology. By selecting this specialization, the student acquires deep knowledge about the processing, storage, and analysis of biological data or the use of formal methods for analysis and prediction of the behavior of biological systems.
Compulsory subjects of the specialization
IV106 |
Bioinformatics seminar |
|---|---|
IV108 |
Bioinformatics II |
IV110 |
Bioinformatics project I |
IV120 |
Continuous and Hybrid Systems |
PA054 |
Formal Methods in Systems Biology |
PA183 |
Project in Systems Biology |
PB050 |
Modelling and Prediction in Systems Biology |
PB172 |
Systems Biology Seminar |
PV225 |
Laboratory of Systems Biology |
PV290 |
Chemoinformatics |
| Applications Pass at least 1 course of the following list | |
PV269
|
Advanced methods in bioinformatics |
PV270
|
Biocomputing |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (Czech) with specializations
The study program Visual Informatics prepares students to work with image information and spatial scene models that involve or touch areas such as computer graphics, image processing, visualization, computer vision, virtual and expanded reality, video processing, pattern recognition, human-computer communication, 3D modeling, animation, graphic design, and machine learning.
The graduate will find application in various fields, such as the development of graphics applications, simulators, computer games, applications for multimedia processing and analysis, visualization of data, virtual and enhanced reality or creation of the professional-level graphic design. For example, a graduate may be an analyst, graphic designer, application programmer, research or development team leader. The acquired theoretical knowledge and practical skills allow them to thoroughly understand the problems solved and will make it possible in practice to use a wide range of modern technologies - from common mobile devices to dedicated systems with high computing power.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
IV003 |
Algorithms and Data Structures II |
|---|---|
MA018 |
Numerical Methods |
MV013 |
Statistics for Computer Science |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA010 |
Intermediate Computer Graphics |
PV021 |
Neural Networks |
PV182 |
Human-Computer Interaction |
PV189 |
Mathematics for Computer Graphics |
VV035 |
3D Modeling |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
Specialization: Computer Graphics and Visualization
Computer Graphics and Visualization specialization offers a set of courses about basic principles, as well as the latest achievements in computer graphics and data visualization. These are accompanied by courses providing the students with the necessary basic background in informatics. We are particularly focusing on the applicability of the presented topics and their utilization in other disciplines and research areas. Students will learn about basic principles and algorithms, forming the building blocks of final visual outputs. These can be, for example, in a form of real-time rendering or large scenes or visualization design of complex multidimensional datasets. In seminars and projects, students will enrich this knowledge by implementational tasks on selected topics.
Compulsory subjects of the specialization
MA017 |
Geometric Algorithms |
|---|---|
PA213 |
Advanced Computer Graphics |
PA093 |
Computational Geometry Project |
PA157 |
Seminar on Computer Graphics Research |
PA166 |
Advanced Methods of Digital Image Processing |
PA214 |
Visualization II |
PV160 |
Laboratory of Human-Computer Interaction |
PV227 |
GPU Rendering |
PV251 |
Visualization |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Image Processing and Analysis
Image Processing and Analysis specialization provides a comprehensive view of getting and processing image information, starting with simple image editing using point transformations or linear filters, and ending with sophisticated tools such as mathematical morphology or deformable models. Graduates will find their place in the development and deployment of imaging systems in a variety of fields, for example in medicine, biology, meteorological and geographic data processing, biometric applications, etc.
Compulsory subjects of the specialization
MA017 |
Geometric Algorithms |
|---|---|
PA093 |
Computational Geometry Project |
PA166 |
Advanced Methods of Digital Image Processing |
PA170 |
Digital Geometry |
PA171 |
Integral and Discrete Transforms in Image Processing |
PA172 |
Image Acquisition |
PA173 |
Mathematical Morphology |
PV187 |
Seminar of digital image processing |
PV197 |
GPU Programming |
PA228 |
Machine Learning in Image Processing |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Computer Game Development
Computer Games Development specialization gives students insight into the multidisciplinary process of digital games development. Students will get acquainted with the principles of game design as well as with modern tools and techniques for the implementation of games and other applications based on game technologies, including the use of augmented and virtual reality. Emphasis is also placed on the visual aspects of game development – from the authoring of 3D models up to the programming of modern graphics cards. In addition to lectures covering theoretical principles, the study also includes several project-oriented seminars that will enable students to gain experience in the area of the game development and expand their professional portfolio. A mandatory part of the studies is also an internship in a game studio lasting 480 hours.
Compulsory subjects of the specialization
PA213 |
Advanced Computer Graphics |
|---|---|
PA215 |
Game Design I |
PA216 |
Game Design II |
PA217 |
Artificial Intelligence for Computer Games |
SA300 |
Internship - Computer Games |
PV227 |
GPU Rendering |
PV255 |
Game Development I |
PV266 |
Game Development II |
VV036 |
3D Character Modeling |
| Game Development Pass at least 1 course of the following list | |
PA199
|
Game Engine Development |
PV283
|
Games User Research Lab |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Graphic Design
Graphic Design Specialization offers the study of graphic design and related disciplines in cooperation with the Graphic Design and Multimedia Studio (AGD + M). The studio focuses primarily on digital media, which nowadays replaces most of the printed forms. In terms of mastering high-quality graphic design, this is an identical problem, but digital media opens up new opportunities in communicating with the consumer. For these media, concurrent informatic education of students is necessary and is developed in the course of this specialization. Students work on topics such as game making, interactive information graphics, creating interactive media applications, generative programming, animation, video, 3D digital modeling and 3D printing, e-publishing, web-design, font creation, and more.
Compulsory subjects of the specialization
PV067 |
Typography II |
|---|---|
PV083 |
Graphic Design II |
PV085 |
Type Design II |
PV257 |
Graphic Design and Multimedia Project |
PV259 |
Generative Design Programming |
PV268 |
Digital Design |
VV051 |
Animation |
| Gr.Design I Pass at least 1 course of the following list | |
PV112
|
Computer Graphics API |
PV239
|
Mobile Application Development |
VV036
|
3D Character Modeling |
| Gr.Design II Pass at least 3 courses of the following list | |
PV156
|
Digital Photography |
VV067
|
Concept and Intermedia |
VV034
|
Photography - artificial effects |
VV050
|
Motion Design |
PV110
|
Basics of Film Narratives |
PV101
|
Type Design III |
PV251
|
Visualization |
PV097
|
Visual Creativity Informatics |
PV113
|
Production of Audiovisual Artefacts |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (Czech) with specializations
The study program Computer Systems, Communications and Security aims to lead its graduate to an understanding of architectures, principles, design methods and operations of secure computer systems, respecting both hardware and software aspects, including network communications. The graduate will also gain deeper knowledge in of the chose specializations of the programme.
Program graduate will be prepared to design and maintain operations of secure computer systems with respect to both hardware and software aspects, including network communications. Graduate in the specialization Hardware Systems will be prepared to design solutions to practical problems with the use of computer hardware, to creatively adjust hardware systems and to deploy them. Graduate in the specialization Software Systems will be ready to take various roles in the IT departments taking part in the development and operations of information systems and in the use of IT for support of organizations. Graduates of the specialization Information Security will be able to work in organizations developing or providing systems respecting security requirements, but also in advanced management and operations of such systems. Graduate on the specialization Computer Networks and Communications will be able to work as an architect of large networks, manage network operations and related projects, or to work as an expert in applications or security of computer networks.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
IA174 |
Fundaments of Cryptography |
|---|---|
MV013 |
Statistics for Computer Science |
PA191 |
Advanced Computer Networking |
PV079 |
Applied Cryptography |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
| Math Pass at least 2 courses of the following list | |
IV111
|
Probability in Computer Science |
MA007
|
Mathematical Logic |
MA010
|
Graph Theory |
MA012
|
Statistics II |
MA015
|
Graph Algorithms |
MA018
|
Numerical Methods |
MA026
|
Advanced Combinatorics |
| Theory of Informatics Pass at least 1 course of the following list | |
IA008
|
Computational Logic |
IA101
|
Algorithmics for Hard Problems |
IV003
|
Algorithms and Data Structures II |
IA158
|
Real Time Systems |
IA159
|
Formal Methods for Software Analysis |
IA169
|
Model Checking |
IV054
|
Coding, Cryptography and Cryptographic Protocols |
| Hardware Systems Pass at least 2 courses of the following list | |
IA158
|
Real Time Systems |
PA174
|
Design of Digital Systems II |
PA175
|
Digital Systems Diagnostics II |
PA176
|
Architecture of Digital Systems II |
PA190
|
Digital Signal Processing |
PA192
|
Secure hardware-based system design |
PA221
|
Hardware description languages |
PV191
|
Seminar in Digital System Design |
PV193
|
Accelerating Algorithms at Circuit Level |
PV194
|
External Environments of Digital Systems |
PV198
|
Onechip Controllers |
PV200
|
Introduction to hardware description languages |
Specialization: Hardware Systems
Specialization Hardware Systems provides specific knowledge to work with programmable structures extending into parallel and distributed systems, computer networks and cryptography. Teaching emphasizes the balance of courses providing the necessary theoretical basis and courses focusing on practical skills that are involved in the design, implementation, analysis, testing and operation of embedded systems. An integral part of the study is also working on a project with a small team and oriented towards experimental and prototype solutions to interesting problems associated with the solution of practical problems arising from research and development activities of the faculty.
Compulsory subjects of the specialization
PB170 |
Seminar on Digital System Design |
|---|---|
PB171 |
Seminar on Digital System Architecture |
PA175 |
Digital Systems Diagnostics II |
PA176 |
Architecture of Digital Systems II |
PV191 |
Seminar in Digital System Design |
PV198 |
Onechip Controllers |
PV200 |
Introduction to hardware description languages |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Software Systems
Specialization Software Systems will lead the graduate to knowledge and skills necessary in all stages of development and changes in extensive software systems, especially information systems. Emphasis is set on knowledge necessary at the design and development of systems with on deployed modern software technologies.
Compulsory subjects of the specialization
PA017 |
Software Engineering II |
|---|---|
PA039 |
Supercomputer Architecture and Intensive Computations |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA152 |
Efficient Use of Database Systems |
PA160 |
Net-Centric Computing II |
PA165 |
Enterprise Applications in Java |
PV217 |
Service Oriented Architecture |
PV258 |
Software Requirements Engineering |
PV260 |
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Information Security
Specialization Information Security focuses on areas of security in computer systems and networks, cryptography and its applications. The aim is to prepare such a graduate who will be able to work in a variety of roles critical to ensure security of ICTs – specific profiling (e.g., toward cryptography, technological aspects or security management) beyond a common basis of field of study is left to the choice of the student.
Compulsory subjects of the specialization
PV181 |
Laboratory of security and applied cryptography |
|---|---|
PV204 |
Security Technologies |
PA197 |
Secure Network Design |
PA193 |
Seminar on secure coding principles and practices |
PV286 |
Secure coding principles and practices |
PA018 |
Advanced Topics in Information Technology Security |
PA168 |
Postgraduate seminar on IT security and cryptography |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Networks and Communication
Computer Networks and Communications specialization focuses on acquiring advanced knowledge of architectures, operation principles, and principles of operation of computer networks. The field is conceived to satisfy both those interested in practically oriented advanced information and knowledge in the field of computer networks and their applications, as well as those interested in deeper acquaintance with the theoretical fundaments of the field and the study of computer networks as a special case of distributed systems. In addition to knowledge of computer networks, the student acquires knowledge of security, principles of working with multimedia data, basic knowledge of parallel systems and necessary theoretical background.
Compulsory subjects of the specialization
PA039 |
Supercomputer Architecture and Intensive Computations |
|---|---|
PA053 |
Distributed Systems and Middleware |
PA151 |
Wireless Networks |
PA160 |
Net-Centric Computing II |
PV169 |
Communication Systems Basics |
PV188 |
Principles of Multimedia Processing and Transport |
PV233 |
Switching, Routing and Wireless Essentials |
PV234 |
Enterprise Networking, Security, and Automation |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (Czech) with specializations
Software systems are in an increasing way supporting most activities of human endeavour, which puts emphasis on the quality of their design, development, testing, deployment and operations. Software engineering integrates skills, techniques and tools for systematic support of these activities, with emphasis on guaranteed quality of the software product. The goal of the study programme is to build the competencies of the students related to software engineering, including their understanding of deeper relations necessary when developing large-scale software systems, where each individual design decision critically impacts the quality and vitality of the final system or service. An integral part of the education is the practical training in terms of software development, as well as working within a software team, including experience with team-leading. These skills are necessary for meeting the expectations of the relevant job positions in industry. The practical skills will be acquired mainly within internships in industry, but also when leading projects of bachelor students at the faculty. Given that the degree program is accredited in a professional profile and the content of the curriculum does not include the full scope of compulsory practice, it is assumed that the student enters the degree program in a situation where he completed part of compulsory practice at the bachelor's degree. If this is not the case, he/she is obliged to complete this part of the compulsory practice beyond the scope of the study plan.
The graduates of this study programme are equipped for the position of a senior software developer (in case of the Design and development of software systems) and a deployment (or DevOps) engineer (in case of the Deployment and operations of software systems), including leading roles within software development teams.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
- Fulfil the condition of 18 weeks (in total) of supervised professional internship (at least 12 weeks need to be realized within this master study, while up to 6 weeks of internships can be included from the previous bachelor study).
Compulsory subjects of the program
PA017 |
Software Engineering II |
|---|---|
PV157 |
Authentication and Access Control |
PV260 |
Software Quality |
PA179 |
Project Management |
PA053 |
Distributed Systems and Middleware |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
SA200 |
Internship - Software Engineering |
| Programing Obtain at least 12 credits by passing subjects of the following list | |
IA014
|
Advanced Functional Programming |
IB016
|
Seminar on Functional Programming |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV168
|
Seminar in Java programming |
PV178
|
Introduction to Development in C#/.NET |
PV264
|
Seminar on programming in C++ |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV255
|
Game Development I |
PV197
|
GPU Programming |
PV198
|
Onechip Controllers |
PV239
|
Mobile Application Development |
PV281
|
Programming in Rust |
PV288
|
Python |
PV292
|
Multiplatform Flutter App Development |
| Advanced Programing Pass at least 1 course of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
| Data Storage Pass at least 1 course of the following list | |
PV003
|
Relational Database System Architecture |
PA152
|
Efficient Use of Database Systems |
| Networking Pass at least 1 course of the following list | |
PA159
|
Net-Centric Computing I |
PA191
|
Advanced Computer Networking |
Specialization: Design and Development of Software Systems
Within the Design and development of software systems specialization, the emphasis is put on the design of high-quality software architecture and skills in programming and software development as such (including user-interface design, secure coding principles, data analytics).
Compulsory subjects of the specialization
PA103 |
Object-oriented Methods for Design of Information Systems |
|---|---|
PA187 |
Project managment and project |
PA036 |
Database System Project |
| Extended Programing Obtain at least 17 credits by passing subjects of the following list | |
IA014
|
Advanced Functional Programming |
IB016
|
Seminar on Functional Programming |
PA165
|
Enterprise Applications in Java |
PA200
|
Cloud Computing |
PV179
|
System Development in C#/.NET |
PV168
|
Seminar in Java programming |
PV178
|
Introduction to Development in C#/.NET |
PV264
|
Seminar on programming in C++ |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV255
|
Game Development I |
PV197
|
GPU Programming |
PV198
|
Onechip Controllers |
PV239
|
Mobile Application Development |
PV281
|
Programming in Rust |
PV288
|
Python |
PV292
|
Multiplatform Flutter App Development |
| Data Analysis Pass at least 1 course of the following list | |
PA220
|
Database systems for data analytics |
PV212
|
Seminar on Machine Learning, Information Retrieval, and Scientific Visualization |
| Design and Analysis Pass at least 1 course of the following list | |
PV167
|
Seminar on Design and Architecture Patterns |
PV258
|
Software Requirements Engineering |
PV293
|
Softwarové architectures |
| Information Security Pass at least 1 course of the following list | |
PV286
|
Secure coding principles and practices |
PV276
|
Seminar on Simulation of Cyber Attacks |
PV017
|
Information Technology Security |
| User Interfaces Pass at least 1 course of the following list | |
PV247
|
Modern Development of User Interfaces |
PV278
|
Development of Intuitive User Interfaces |
PV182
|
Human-Computer Interaction |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Deployment and Operations of Software Systems
Within the Deployment and operations of software systems specialization, the emphasis is put on the design of high-quality infrastructure for the operation of the software system and the ability to interlink the software development with its deployment and operation (including topics like secure infrastructure design, computer networks, cloud computing, UNIX administration).
Compulsory subjects of the specialization
PA195 |
NoSQL Databases |
|---|---|
PA160 |
Net-Centric Computing II |
PV175 |
MS Windows Systems Management I |
PV065 |
UNIX -- Programming and System Management I |
PV077 |
UNIX -- Programming and System Management II |
PA200 |
Cloud Computing |
| Information Security Pass at least 2 courses of the following list | |
PA018
|
Advanced Topics in Information Technology Security |
PA211
|
Advanced Topics of Cyber Security |
PV276
|
Seminar on Simulation of Cyber Attacks |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (Czech) with specializations
The study program develops unique competence profile of the student based on the intersection of multiple areas of knowledge that are relevant for managing the development of software systems and services, as well as cybersecurity management. A specific feature is a focus on strategic and operational management related to the targeting, design, implementation, and operation of software systems and services within the context of organizations and different types with a possible focus on their safe operation or IT services. In addition to developing basic theoretical and technological knowledge and practical developmental skills acquired in the bachelor's study, the content of the follow-up study is extended by other dimensions such as theories and practices of team, project and process management, communication, soft skills and knowledge essential to functioning in economic relations - the basics of marketing, law and others, which especially (but not only) concerns the specialization of service development. The cybersecurity study takes into account aspects of overlapping computer data processing outside of tightly defined system perimeters (e.g. impacting on critical infrastructure), thus enabling a specific multidisciplinary overlap of technical, social and legal aspects in this area.
The graduates find employment in companies and organizations of different sizes and orientation, but they also get the motivation and the possibility of basic preparation for their own innovative business. The strong competitive advantage of the program graduates is the ability to solve complex management-related problems of the development of systems and services for which they can use the acquired skills by the study. Their potential is predestined to hold managerial positions, such as the Chief Information Officer (CIO), project manager, and risk manager. Graduates of the cybersecurity management specialization will find application primarily in companies and institutions that need specialists able to work with relevant coordinating institutions and ensure the management of cybersecurity processes. These are positions as a cybersecurity manager and Chief Information Security Officer (CISO).
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
PA017 |
Software Engineering II |
|---|---|
PV206 |
Communication and Soft Skills |
PV079 |
Applied Cryptography |
MV013 |
Statistics for Computer Science |
PA152 |
Efficient Use of Database Systems |
PA179 |
Project Management |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
SA100 |
Internship - Management |
| Management Pass at least 1 course of the following list | |
PA182
|
Managing in Reality |
PV214
|
IT Service Management based on ITIL |
PV215
|
Management by Competencies |
PV237
|
Strategy and Leadership |
PV271
|
Risk Management in IT |
PV203
|
IT Services Management |
Specialization: Software Systems Development and Management
Software Systems Development and Managment specialization focuses on software engineering, i.e., to acquire the knowledge and skills needed at all stages of development, management and maintenance of information, and other types of large software systems. The specialization emphasizes the ability to analyse and specify system requirements, system design, and implementation and deployment.
Compulsory subjects of the specialization
IA159 |
Formal Methods for Software Analysis |
|---|---|
PA053 |
Distributed Systems and Middleware |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA165 |
Enterprise Applications in Java |
PA197 |
Secure Network Design |
PV028 |
Applied Information Systems |
PV247 |
Modern Development of User Interfaces |
| Programming Pass at least 1 course of the following list | |
PA036
|
Database System Project |
PV179
|
System Development in C#/.NET |
PV229
|
Multimedia Similarity Searching in Practice |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV288
|
Python |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Service Development Management
Services Development Management specialization follows the current large shift from the traditional paradigm of IT design to IT as a service and from product-oriented economy to service-oriented one. Problems and tasks in IT are becoming more complex and the knowledge of IT technology is not sufficient for solving them. A multidisciplinary view is the core of this specialization. Students will gain not only sound IT knowledge (programming, databases, computer security, networks, etc.), but also the skills necessary to understand problems in their complexity (marketing, management, finance or law) as well as necessary communication competencies.
Compulsory subjects of the specialization
PA116 |
Domain Understanding and Modeling |
|---|---|
PA194 |
Introduction to Service Science |
PA181 |
Services - Systems, Modeling and Execution |
PV207 |
Business Process Management |
| Computer networks Pass at least 1 course of the following list | |
PA151
|
Wireless Networks |
PA159
|
Net-Centric Computing I |
PA191
|
Advanced Computer Networking |
PA211
|
Advanced Topics of Cyber Security |
PV210
|
Cybersecurity in an Organization |
PV177
|
Laboratory of Advanced Network Technologies |
| Economy Pass at least 1 course of the following list | |
PV028
|
Applied Information Systems |
PV241
|
Enterprise and Financial Management |
| Programming Pass at least 1 course of the following list | |
PA036
|
Database System Project |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV229
|
Multimedia Similarity Searching in Practice |
PV247
|
Modern Development of User Interfaces |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV288
|
Python |
| Soft skills Pass at least 1 course of the following list | |
ESF:MPV_RKMD
|
Communication and Managerial Skills training |
ESF:MPV_COMA
|
Communication and Managerial Skills Training |
ESF:MPP_CEIT
|
Czech and European Law of Information Technologies |
PV236
|
Time Management and Effectiveness |
PV209
|
Person Centered Communication |
IV057
|
Seminar on Information Society |
IV064
|
Information Society |
PA212
|
Advanced Search Techniques for Large Scale Data Analytics |
PV263
|
Intercultural Management |
| Marketing Pass at least 1 course of the following list | |
PV216
|
Marketing Strategy in Service Business |
PV240
|
Introduction to service marketing |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Specialization: Cybersecurity Managment
Cybersecurity Management specialization takes into account the aspects of computer data processing beyond the well-defined system perimeters (e.g., critical infrastructure impact), reflected in the area of cybersecurity and allowing a specific multi-disciplinary overlap of both technical and social and legal aspects of cybersecurity.
Compulsory subjects of the specialization
PrF:BVV14K |
Theory and Method of ICT Law |
|---|---|
IA174 |
Fundaments of Cryptography |
PrF:BI301K |
ICT Law II |
PA197 |
Secure Network Design |
PV204 |
Security Technologies |
PA018 |
Advanced Topics in Information Technology Security |
PrF:BVV03K |
Cybercriminality |
IV128 |
Online Communication from Social Science Perspective |
| Computer networks Pass at least 1 course of the following list | |
PA151
|
Wireless Networks |
PA159
|
Net-Centric Computing I |
PA191
|
Advanced Computer Networking |
PA211
|
Advanced Topics of Cyber Security |
PV210
|
Cybersecurity in an Organization |
PV177
|
Laboratory of Advanced Network Technologies |
Recommended course of study
Fall 2023 (1. term)
-
PA017Software Engineering II -
PV206Communication and Soft Skills -
PV079Applied Cryptography -
PrF:BVV14KTheory and Method of ICT Law -
IA174Fundaments of Cryptography - Choice: Any course from Computer networks section
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
- Choice: Any course from Management section
-
PrF:BVV03KCybercrime and Cybersecurity -
IV128Online Communication from Social Science Perspective -
SDIPRDiploma Thesis -
SOBHADefence of Thesis -
SZMGRState Exam (MSc degree)
follow-up master's program (Czech) without specializations supporting Major/Minor study
The Joint Master Programme in Digital Linguistics will train highly qualified interdisciplinar profile combining knowledge and competencies from the field of computer science, information technology (IT), linguistics and humanities. Holders of the master’s degree in Digital Linguistics will have a broad set of applied IT skills and will be trained for programming, using and compiling language resources, using and adapting language technologies and autonomously conducting language data analyses. In addition, they will have a high level of competence in communication in at least two languages, will be able to recognise and adjust themselves to all types of written, spoken and digital texts as well as understand the principles of interlingual communication in all forms.
Holder of the master's degree in Digital Linguistics will be employable in various professional environments where technology-assisted language services are developed, offered or used.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
Compulsory subjects of the program
FF:CJBB105 |
Introduction in Corpus Linguistics – Lecture |
|---|---|
MV013 |
Statistics for Computer Science |
PA153 |
Natural Language Processing |
FF:PLIN063 |
Alghoritmic Descript. of Morphology |
SA400 |
Foreign Studies - Digital Linguistics |
| Foundations Pass at least 2 courses of the following list | |
FF:CJJ15
|
Czech Comparative Grammar |
FF:PLIN041
|
History of Computational Linguistics |
IB000
|
Mathematical Foundations of Computer Science |
IV029
|
Introduction to Transparent Intensional Logic |
| Introduction to programming Pass at least 1 course of the following list | |
IB111
|
Foundations of Programming |
IB113
|
Introduction to Programming and Algorithms |
| Application Oriented Electives I Pass at least 1 course of the following list | |
FF:PLIN045
|
Introduction to development of multiplatform applications |
FF:PLIN055
|
Project from corpus and computational linguistics |
PV061
|
Machine Translation |
PV251
|
Visualization |
| Application Oriented Electives II Pass at least 1 course of the following list | |
FF:PLIN078
|
Quantitative analysis |
PA107
|
Corpus Tools Project |
PB138
|
Basics of web development and markup languages |
PV211
|
Introduction to Information Retrieval |
| Methods and Tools I Pass at least 1 course of the following list | |
FF:PLIN032
|
Grammar and Corpus |
FF:PLIN033
|
Algorithmic Description of Word Formation |
PV027
|
Optimization |
IA161
|
Natural Language Processing in Practice |
| Methods and Tools II Pass at least 2 courses of the following list | |
FF:PLIN037
|
Semantic Computing |
FF:PLIN077
|
Stylometry |
IB047
|
Introduction to Corpus Linguistics and Computer Lexicography |
PV004
|
UNIX |
PV056
|
Machine Learning and Data Mining |
PV080
|
Information security and cryptography |
PA152
|
Efficient Use of Database Systems |
| Advanced Topics Pass at least 2 courses of the following list | |
FF:CJJ45
|
Topics in semantics |
FF:PLIN065
|
Tools for theories |
FF:PLIN068
|
Applied Machine Learning |
FF:PLIN069
|
Applied Machine Learning Project |
IV003
|
Algorithms and Data Structures II |
PA128
|
Similarity Searching in Multimedia Data |
PA154
|
Language Modeling |
PA156
|
Dialogue Systems |
SDIPR |
Diploma Thesis |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
Study option: Study plan for local students
Compulsory subjects and other obligations of the study option
| Internshipe abroad equal to 30 credits is expected in the third term. |
Recommended course of study
Fall 2023 (1. term)
-
PA153Natural Language Processing - Choice: Any course from Foundations section
- Choice: Any course from Introduction to programming section
- Choice: Any course from Methods and Tools I section
- Choice: Any course from Application Oriented Electives I section
Spring 2024 (2. term)
-
MV013Statistics for Computer Science -
FF:CJBB105Introduction in Corpus Linguistics - Lecture -
FF:PLIN063Alghoritmic Descript. of Morphology - Choice: Any course from Methods and Tools II section
- Choice: Any course from Application Oriented Electives II section
Fall 2024 (3. term)
- Internship abroad
Study option: Study plan for students from abroad
Students are expected to collect 30 credits within the term.
Compulsory subjects and other obligations of the study option
IA161 |
Natural Language Processing in Practice |
|---|---|
FF:PLIN055 |
Project from corpus and computational linguistics |
| Selected Topics in Digital Linguistics Pass at least 3 courses of the following list | |
FF:CJBB184
|
Language Typology |
FF:PLIN035
|
Computational Lexicography |
FF:PLIN064
|
Introduction to Digital Humanities |
FF:PLIN075
|
Linguistic Webinar |
PA164
|
Machine learning and natural language processing |
PA220
|
Database systems for data analytics |
PV021
|
Neural Networks |
PV061
|
Machine Translation |
PV251
|
Visualization |
IV111
|
Probability in Computer Science |
| Projects Obtain at least 4 credits by passing subjects of the following list | |
FF:PLIN034
|
Algorithmic Description of Syntax |
FF:PLIN053
|
Mobile application programming project |
PB106
|
Corpus Linguistic Project I |
PV277
|
Programming Applications for Social Robots |
Recommended course of study
Fall 2023 (1. term)
-
IA161Natural Language Processing in Practice -
FF:PLIN055Project from corpus and computational linguistics - Choice: Any course from Selected Topics in Digital Linguistics section
- Choice: Any course from Selected Topics in Digital Linguistics section
- Choice: Any course from Selected Topics in Digital Linguistics section
- Choice: Any course from Projects section
Spring 2024 (2. term)
follow-up master's program (Czech) without specializations supporting Major/Minor study
The aim of this program is to prepare graduates with a range of competencies necessary for the teaching profession. They have both knowledge and skills regarding pupil education, classroom management, and addressing specific learning situations and pupils. The knowledge of individual subjects and the didactic competence ensure a high level of knowledge of the given discipline, which is in accordance to the expected requirements of the secondary schools and the ability of the graduates to mediate the knowledge of the given discipline using a wide range of didactic methods. Graduates are also equipped with the skills and abilities to lead pedagogical communication with students, their parents, colleagues and other subjects (social and communication competencies), educate and motivate pupils, manage classes, participate in school activities and solve specific situations associated with teaching pedagogical-psychological competencies). In addition, graduates are equipped with diagnostic and special pedagogical competencies that enable them to recognize the individual educational and other needs of students, to prepare individual plans for students, to work with counseling specialists, and to apply a wide range of support measures within an inclusive approach. In addition to pedagogical abilities, this program intends to prepare graduates also for the position of school information system manager and administrator.
Graduates of this master degree study program will primarily act as teachers of relevant subjects at secondary schools (grammar schools and secondary technical schools) with accordance of the accredited fields and their focus. In the case the IT administration study plan, graduates will be able to operate in positions of IT administrators at secondary schools.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Fulfil requirements of IT Teacher and Administrator study option or Major study option.
- Pass all the compulsory and elective courses of the program, selected study option with the highest possible graduation form.
Compulsory subjects of the program
PA159 |
Net-Centric Computing I |
|---|---|
PV094 |
PC Hardware |
PV175 |
MS Windows Systems Management I |
PV004 |
UNIX |
UA104 |
Didactics for Informatics I |
UA105 |
Didactics for Informatics II |
UA442 |
Exercises in Practical Education I |
UA542 |
Exercises in Practical Education II |
UA642 |
Exercises in Practical Education III |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
PřF:XS080 |
Special pedagogy |
PřF:XS092 |
School management |
PřF:XS093 |
Educational activity with gifted learners |
PřF:XS100 |
Teacher and school administration |
PřF:XS130 |
Personality psychology |
PřF:XS150 |
Educational Psychology |
PřF:XS170 |
Technology for didactics |
PřF:XS350 |
Group dynamic workshop |
Study option: Teacher of Informatics and IT administrator
Study option The Informatics Teacher and Network Administrator prepares students for professional positioning as a Network Administrator at a secondary school in parallel with the pedagogical training necessary to obtain secondary school approbation in Informatics.
Compulsory subjects and other obligations of the study option
UB001 |
Assesment of teaching in Informatics |
|---|---|
UA742 |
Exercises in Practical Education IV |
UA842 |
Exercises in Practical Education V |
PB071 |
Principles of low-level programming |
PB138 |
Basics of web development and markup languages |
PřF:XS020 |
Inspiratorium for teachers |
PřF:XS050 |
School pedagogy |
PřF:XS060 |
General didactics |
PřF:XS140 |
Foundations of Psychology |
PřF:XS090 |
Initial teacher training |
PřF:XS220 |
Reflective seminar |
| Collect at least 36 credits from courses taught at FI with prefixes I or P. | |
Recommended course of study
Fall 2023 (1. term)
-
PA159Net-Centric Computing I -
PV094PC Hardware -
PřF:XS080Special pedagogy -
PřF:XS150Educational Psychology -
UB001Assesment of teaching in Informatics -
PřF:XS020Inspiratorium for teachers -
PřF:XS050School pedagogy -
PřF:XS093Educational activity with gifted learners -
PřF:XS170Technology for didactics -
PřF:XS092School management
Spring 2024 (2. term)
-
UA104Didactics for Informatics I -
UA442Exercises in Practical Education I -
PřF:XS130Personality psychology -
PřF:XS060General didactics -
PřF:XS140Foundations of Psychology -
PřF:XS090Initial teacher training -
PřF:XS220Reflective seminar -
VV064Academic and Professional Skills in English for IT -
PV004UNIX
Fall 2024 (3. term)
Study option: Minor
This study option leads students in cooperation with the Faculty of Science of Masaryk University to obtain two secondary school approbations.
Compulsory subjects and other obligations of the study option
PA159 |
Net-Centric Computing I |
|---|---|
PV175 |
MS Windows Systems Management I |
PV094 |
PC Hardware |
UA104 |
Didactics for Informatics I |
UA105 |
Didactics for Informatics II |
UA442 |
Exercises in Practical Education I |
UA542 |
Exercises in Practical Education II |
UA642 |
Exercises in Practical Education III |
SZMGR |
State Exam (MSc degree) |
| Collect at least 22 credits from courses taught at FI with prefixes I or P. | |
Recommended course of study
Fall 2023 (1. term)
Fall 2024 (3. term)
Follow-up Master's Degree Programs (English)
follow-up master's program (English) with specializations
- English
- doc. RNDr. Petr Matula, Ph.D.
The study program Visual Informatics prepares students to work with image information and spatial scene models that involve or touch areas such as computer graphics, image processing, visualization, computer vision, virtual and expanded reality, video processing, pattern recognition, human-computer communication, 3D modeling, animation, graphic design, and machine learning.
The graduate will find application in various fields, such as the development of graphics applications, simulators, computer games, applications for multimedia processing and analysis, visualization of data, virtual and enhanced reality or creation of the professional-level graphic design. For example, a graduate may be an analyst, graphic designer, application programmer, research or development team leader. The acquired theoretical knowledge and practical skills allow them to thoroughly understand the problems solved and will make it possible in practice to use a wide range of modern technologies - from common mobile devices to dedicated systems with high computing power.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
IV003 |
Algorithms and Data Structures II |
|---|---|
MA018 |
Numerical Methods |
MV013 |
Statistics for Computer Science |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA010 |
Intermediate Computer Graphics |
PV021 |
Neural Networks |
PV182 |
Human-Computer Interaction |
PV189 |
Mathematics for Computer Graphics |
VV035 |
3D Modeling |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
Specialization: Computer Graphics and Visualization
Computer Graphics and Visualization specialization offers a set of courses about basic principles, as well as the latest achievements in computer graphics and data visualization. These are accompanied by courses providing the students with the necessary basic background in informatics. We are particularly focusing on the applicability of the presented topics and their utilization in other disciplines and research areas. Students will learn about basic principles and algorithms, forming the building blocks of final visual outputs. These can be, for example, in a form of real-time rendering or large scenes or visualization design of complex multidimensional datasets. In seminars and projects, students will enrich this knowledge by implementational tasks on selected topics.
Compulsory subjects of the specialization
MA017 |
Geometric Algorithms |
|---|---|
PA213 |
Advanced Computer Graphics |
PA093 |
Computational Geometry Project |
PA157 |
Seminar on Computer Graphics Research |
PA166 |
Advanced Methods of Digital Image Processing |
PA214 |
Visualization II |
PV160 |
Laboratory of Human-Computer Interaction |
PV227 |
GPU Rendering |
PV251 |
Visualization |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Image Processing and Analysis
Image Processing and Analysis specialization provides a comprehensive view of getting and processing image information, starting with simple image editing using point transformations or linear filters, and ending with sophisticated tools such as mathematical morphology or deformable models. Graduates will find their place in the development and deployment of imaging systems in a variety of fields, for example in medicine, biology, meteorological and geographic data processing, biometric applications, etc.
Compulsory subjects of the specialization
MA017 |
Geometric Algorithms |
|---|---|
PA093 |
Computational Geometry Project |
PA166 |
Advanced Methods of Digital Image Processing |
PA170 |
Digital Geometry |
PA171 |
Integral and Discrete Transforms in Image Processing |
PA172 |
Image Acquisition |
PA173 |
Mathematical Morphology |
PV187 |
Seminar of digital image processing |
PV197 |
GPU Programming |
PA228 |
Machine Learning in Image Processing |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Computer Game Development
Computer Games Development specialization gives students insight into the multidisciplinary process of digital games development. Students will get acquainted with the principles of game design as well as with modern tools and techniques for the implementation of games and other applications based on game technologies, including the use of augmented and virtual reality. Emphasis is also placed on the visual aspects of game development – from the authoring of 3D models up to the programming of modern graphics cards. In addition to lectures covering theoretical principles, the study also includes several project-oriented seminars that will enable students to gain experience in the area of the game development and expand their professional portfolio. A mandatory part of the studies is also an internship in a game studio lasting 480 hours.
Compulsory subjects of the specialization
PA213 |
Advanced Computer Graphics |
|---|---|
PA215 |
Game Design I |
PA216 |
Game Design II |
PA217 |
Artificial Intelligence for Computer Games |
SA300 |
Internship - Computer Games |
PV227 |
GPU Rendering |
PV255 |
Game Development I |
PV266 |
Game Development II |
VV036 |
3D Character Modeling |
| Game Development Pass at least 1 course of the following list | |
PA199
|
Game Engine Development |
PV283
|
Games User Research Lab |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (English) with specializations
The study program Computer Systems, Communications and Security aims to lead its graduate to an understanding of architectures, principles, design methods and operations of secure computer systems, respecting both hardware and software aspects, including network communications. The graduate will also gain deeper knowledge in of the chose specializations of the programme.
Program graduate will be prepared to design and maintain operations of secure computer systems with respect to both hardware and software aspects, including network communications. Graduate in the specialization Hardware Systems will be prepared to design solutions to practical problems with the use of computer hardware, to creatively adjust hardware systems and to deploy them. Graduate in the specialization Software Systems will be ready to take various roles in the IT departments taking part in the development and operations of information systems and in the use of IT for support of organizations. Graduates of the specialization Information Security will be able to work in organizations developing or providing systems respecting security requirements, but also in advanced management and operations of such systems. Graduate on the specialization Computer Networks and Communications will be able to work as an architect of large networks, manage network operations and related projects, or to work as an expert in applications or security of computer networks.
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
IA174 |
Fundaments of Cryptography |
|---|---|
MV013 |
Statistics for Computer Science |
PA191 |
Advanced Computer Networking |
PV079 |
Applied Cryptography |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
| Math Pass at least 2 courses of the following list | |
IV111
|
Probability in Computer Science |
MA007
|
Mathematical Logic |
MA010
|
Graph Theory |
MA012
|
Statistics II |
MA015
|
Graph Algorithms |
MA018
|
Numerical Methods |
MA026
|
Advanced Combinatorics |
| Theory of Informatics Pass at least 1 course of the following list | |
IA008
|
Computational Logic |
IA101
|
Algorithmics for Hard Problems |
IV003
|
Algorithms and Data Structures II |
IA158
|
Real Time Systems |
IA159
|
Formal Methods for Software Analysis |
IA169
|
Model Checking |
IV054
|
Coding, Cryptography and Cryptographic Protocols |
| Hardware Systems Pass at least 2 courses of the following list | |
IA158
|
Real Time Systems |
PA174
|
Design of Digital Systems II |
PA175
|
Digital Systems Diagnostics II |
PA176
|
Architecture of Digital Systems II |
PA190
|
Digital Signal Processing |
PA192
|
Secure hardware-based system design |
PA221
|
Hardware description languages |
PV191
|
Seminar in Digital System Design |
PV193
|
Accelerating Algorithms at Circuit Level |
PV194
|
External Environments of Digital Systems |
PV198
|
Onechip Controllers |
PV200
|
Introduction to hardware description languages |
Specialization: Hardware Systems
Specialization Hardware Systems provides specific knowledge to work with programmable structures extending into parallel and distributed systems, computer networks and cryptography. Teaching emphasizes the balance of courses providing the necessary theoretical basis and courses focusing on practical skills that are involved in the design, implementation, analysis, testing and operation of embedded systems. An integral part of the study is also working on a project with a small team and oriented towards experimental and prototype solutions to interesting problems associated with the solution of practical problems arising from research and development activities of the faculty.
Compulsory subjects of the specialization
PB170 |
Seminar on Digital System Design |
|---|---|
PB171 |
Seminar on Digital System Architecture |
PA175 |
Digital Systems Diagnostics II |
PA176 |
Architecture of Digital Systems II |
PV191 |
Seminar in Digital System Design |
PV198 |
Onechip Controllers |
PV200 |
Introduction to hardware description languages |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Software Systems
Specialization Software Systems will lead the graduate to knowledge and skills necessary in all stages of development and changes in extensive software systems, especially information systems. Emphasis is set on knowledge necessary at the design and development of systems with on deployed modern software technologies.
Compulsory subjects of the specialization
PA017 |
Software Engineering II |
|---|---|
PA039 |
Supercomputer Architecture and Intensive Computations |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA152 |
Efficient Use of Database Systems |
PA160 |
Net-Centric Computing II |
PA165 |
Enterprise Applications in Java |
PV217 |
Service Oriented Architecture |
PV258 |
Software Requirements Engineering |
PV260 |
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Information Security
Specialization Information Security focuses on areas of security in computer systems and networks, cryptography and its applications. The aim is to prepare such a graduate who will be able to work in a variety of roles critical to ensure security of ICTs – specific profiling (e.g., toward cryptography, technological aspects or security management) beyond a common basis of field of study is left to the choice of the student.
Compulsory subjects of the specialization
PV181 |
Laboratory of security and applied cryptography |
|---|---|
PV204 |
Security Technologies |
PA197 |
Secure Network Design |
PA193 |
Seminar on secure coding principles and practices |
PV286 |
Secure coding principles and practices |
PA018 |
Advanced Topics in Information Technology Security |
PA168 |
Postgraduate seminar on IT security and cryptography |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Networks and Communication
Computer Networks and Communications specialization focuses on acquiring advanced knowledge of architectures, operation principles, and principles of operation of computer networks. The field is conceived to satisfy both those interested in practically oriented advanced information and knowledge in the field of computer networks and their applications, as well as those interested in deeper acquaintance with the theoretical fundaments of the field and the study of computer networks as a special case of distributed systems. In addition to knowledge of computer networks, the student acquires knowledge of security, principles of working with multimedia data, basic knowledge of parallel systems and necessary theoretical background.
Compulsory subjects of the specialization
PA039 |
Supercomputer Architecture and Intensive Computations |
|---|---|
PA053 |
Distributed Systems and Middleware |
PA151 |
Wireless Networks |
PA160 |
Net-Centric Computing II |
PV169 |
Communication Systems Basics |
PV188 |
Principles of Multimedia Processing and Transport |
PV233 |
Switching, Routing and Wireless Essentials |
PV234 |
Enterprise Networking, Security, and Automation |
| Programming Obtain at least 4 credits by passing subjects of the following list | |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV197
|
GPU Programming |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV284
|
Introduction to IoT |
PV288
|
Python |
PV260
|
Software Quality |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
follow-up master's program (English) with specializations
- English
- doc. RNDr. Tomáš Pitner, Ph.D.
The study program develops unique competence profile of the student based on the intersection of multiple areas of knowledge that are relevant for managing the development of software systems and services, as well as cybersecurity management. A specific feature is a focus on strategic and operational management related to the targeting, design, implementation, and operation of software systems and services within the context of organizations and different types with a possible focus on their safe operation or IT services. In addition to developing basic theoretical and technological knowledge and practical developmental skills acquired in the bachelor's study, the content of the follow-up study is extended by other dimensions such as theories and practices of team, project and process management, communication, soft skills and knowledge essential to functioning in economic relations - the basics of marketing, law and others, which especially (but not only) concerns the specialization of service development. The cybersecurity study takes into account aspects of overlapping computer data processing outside of tightly defined system perimeters (e.g. impacting on critical infrastructure), thus enabling a specific multidisciplinary overlap of technical, social and legal aspects in this area.
The graduates find employment in companies and organizations of different sizes and orientation, but they also get the motivation and the possibility of basic preparation for their own innovative business. The strong competitive advantage of the program graduates is the ability to solve complex management-related problems of the development of systems and services for which they can use the acquired skills by the study. Their potential is predestined to hold managerial positions, such as the Chief Information Officer (CIO), project manager, and risk manager. Graduates of the cybersecurity management specialization will find application primarily in companies and institutions that need specialists able to work with relevant coordinating institutions and ensure the management of cybersecurity processes. These are positions as a cybersecurity manager and Chief Information Security Officer (CISO).
Requirements for successful graduation
- Obtain at least 120 credits overall and pass the final state exam.
- Obtain 20 credits from SDIPR subject and successfully defend Master's Thesis. See more details.
- Pass all the compulsory and elective courses of the program and selected specialization with the highest possible graduation form.
- Fulfil requirements of at least one specialization.
Compulsory subjects of the program
PA017 |
Software Engineering II |
|---|---|
PV206 |
Communication and Soft Skills |
PV079 |
Applied Cryptography |
MV013 |
Statistics for Computer Science |
PA152 |
Efficient Use of Database Systems |
PA179 |
Project Management |
SOBHA |
Defence of Thesis |
SZMGR |
State Exam (MSc degree) |
SA100 |
Internship - Management |
| Management Pass at least 1 course of the following list | |
PA182
|
Managing in Reality |
PV214
|
IT Service Management based on ITIL |
PV215
|
Management by Competencies |
PV237
|
Strategy and Leadership |
PV271
|
Risk Management in IT |
PV203
|
IT Services Management |
Specialization: Software Systems Development and Management
Software Systems Development and Managment specialization focuses on software engineering, i.e., to acquire the knowledge and skills needed at all stages of development, management and maintenance of information, and other types of large software systems. The specialization emphasizes the ability to analyse and specify system requirements, system design, and implementation and deployment.
Compulsory subjects of the specialization
IA159 |
Formal Methods for Software Analysis |
|---|---|
PA053 |
Distributed Systems and Middleware |
PA103 |
Object-oriented Methods for Design of Information Systems |
PA165 |
Enterprise Applications in Java |
PA197 |
Secure Network Design |
PV028 |
Applied Information Systems |
PV247 |
Modern Development of User Interfaces |
| Programming Pass at least 1 course of the following list | |
PA036
|
Database System Project |
PV179
|
System Development in C#/.NET |
PV229
|
Multimedia Similarity Searching in Practice |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV288
|
Python |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Specialization: Service Development Management
Services Development Management specialization follows the current large shift from the traditional paradigm of IT design to IT as a service and from product-oriented economy to service-oriented one. Problems and tasks in IT are becoming more complex and the knowledge of IT technology is not sufficient for solving them. A multidisciplinary view is the core of this specialization. Students will gain not only sound IT knowledge (programming, databases, computer security, networks, etc.), but also the skills necessary to understand problems in their complexity (marketing, management, finance or law) as well as necessary communication competencies.
Compulsory subjects of the specialization
PA116 |
Domain Understanding and Modeling |
|---|---|
PA194 |
Introduction to Service Science |
PA181 |
Services - Systems, Modeling and Execution |
PV207 |
Business Process Management |
| Computer networks Pass at least 1 course of the following list | |
PA151
|
Wireless Networks |
PA159
|
Net-Centric Computing I |
PA191
|
Advanced Computer Networking |
PA211
|
Advanced Topics of Cyber Security |
PV210
|
Cybersecurity in an Organization |
PV177
|
Laboratory of Advanced Network Technologies |
| Economy Pass at least 1 course of the following list | |
PV028
|
Applied Information Systems |
PV241
|
Enterprise and Financial Management |
| Programming Pass at least 1 course of the following list | |
PA036
|
Database System Project |
PA165
|
Enterprise Applications in Java |
PV179
|
System Development in C#/.NET |
PV229
|
Multimedia Similarity Searching in Practice |
PV247
|
Modern Development of User Interfaces |
PV248
|
Python Seminar |
PV249
|
Development in Ruby |
PV288
|
Python |
| Soft skills Pass at least 1 course of the following list | |
ESF:MPV_RKMD
|
Communication and Managerial Skills training |
ESF:MPV_COMA
|
Communication and Managerial Skills Training |
ESF:MPP_CEIT
|
Czech and European Law of Information Technologies |
PV236
|
Time Management and Effectiveness |
PV209
|
Person Centered Communication |
IV057
|
Seminar on Information Society |
IV064
|
Information Society |
PA212
|
Advanced Search Techniques for Large Scale Data Analytics |
PV263
|
Intercultural Management |
| Marketing Pass at least 1 course of the following list | |
PV216
|
Marketing Strategy in Service Business |
PV240
|
Introduction to service marketing |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Specialization: Cybersecurity Managment
Cybersecurity Management specialization takes into account the aspects of computer data processing beyond the well-defined system perimeters (e.g., critical infrastructure impact), reflected in the area of cybersecurity and allowing a specific multi-disciplinary overlap of both technical and social and legal aspects of cybersecurity.
Compulsory subjects of the specialization
BVV14Keng |
Theory of Cyber-Law |
|---|---|
IA174 |
Fundaments of Cryptography |
PrF:MVV60K |
Cybersecurity Law |
PA197 |
Secure Network Design |
PV204 |
Security Technologies |
PA018 |
Advanced Topics in Information Technology Security |
PrF:SOC022 |
European Cyberlaw |
IV128 |
Online Communication from Social Science Perspective |
| Computer networks Pass at least 1 course of the following list | |
PA151
|
Wireless Networks |
PA159
|
Net-Centric Computing I |
PA191
|
Advanced Computer Networking |
PA211
|
Advanced Topics of Cyber Security |
PV210
|
Cybersecurity in an Organization |
PV177
|
Laboratory of Advanced Network Technologies |
Recommended course of study
Fall 2023 (1. term)
Spring 2024 (2. term)
Fall 2024 (3. term)
Spring 2025 (4. term)
- Choice: Any course from Management section
-
PrF:MVV60KCybersecurity Law -
IV128Online Communication from Social Science Perspective -
SDIPRDiploma Thesis -
SOBHADefence of Thesis -
SZMGRState Exam (MSc degree)
List of courses open at FI (2023/2024)
This list has been built on 25. 5. 2023. Some minor changes may appear during the year, for the current and most up-to-date details see IS MU.
MB141 Linear algebra and discrete mathematics
zk 2/2 3 kr., jaro
- Mgr. David Kruml, Ph.D.
- Prerequisities:
! NOW ( MB151 ) && ( ! MB151 || ! MB154 ) && ( ! MB101 || ! MB104 )
- Goals: Introduction to linear algebra, analytical geometry and elementary number theory.
- Learning outcomes: At the end of this course, students should be able to: understand basic concepts of linear algebra; apply these concepts to iterated linear processes; solve basic problems in analytical geometry; apply elemntary number theory on kryptography.
- Syllabus:
Obsah kurzu Lineární:
1. Geometry in plane. Complex numbers. 2. Systems of linear equations. Gauss elimination. 3. Operation with matrices. Inverse matrix, determinent. 4. Vector spaces, báses, dimension, coordinates. 5. Linear mappings, eigenvalues and eigenvectors. 6. Linear processes. 7. Afinne geometry. 8. Scalar product. 9. Eukleidian geometry. 10. Elementry number theory. 11. Congruences. 12. Application in kryptography.
MB142 Applied math analysis
zk 2/2 3 kr., podzim
- doc. RNDr. Michal Veselý, Ph.D.
- Prerequisities:
! MB152 && ! NOW ( MB152 ) && ! MB102 && ! MB202
High school mathematics - Goals: This is a basic course of mathematical analysis. The content is differential and integral calculus and infinite series. Students will understand practical methods and will be able to apply these methods to concrete problems. The course places more emphasis on examples.
- Learning outcomes:
At the end of the course students will be able to:
work practically with the derivative and (indefinite and definite) integral;
analyse the behaviour of functions;
understand the use of infinite number series and power series;
understand selected applications of the calculus;
apply the methods of the calculus to concrete problems. - Syllabus:
Continuous functions and limits
Derivatives of functions with applications
Indefinite integrals
Riemann integral and its applications
Series
MB143 Design and analysis of statistical experiments
zk 2/2 3 kr., jaro
- doc. Mgr. David Kraus, Ph.D.
- Prerequisities:
MB141 || MB142 || MB101 || MB201 || MB102 || MB202 || MB151 || MB152
- Goals: The course presents principles and methods of statistical analysis, and explains what types of data are suitable for answering questions of interest.
- Learning outcomes:
After the course the students:
- are able to formulate questions of interest in terms of statistical inference (parameter estimation or hypothesis test within a suitable model);
- are able to choose a suitable model for basic types of data, choose a suitable method of inference to answer most common questions, implement the method in the statistical software R, and correctly interpret the results;
- are able to judge which questions and with what accuracy/certainty can be answered based on available data, or suggest what data should be collected in order to answer given questions with a desired level of accuracy/certainty. - Syllabus:
Basic principles of Probability.
Random variables, their characteristics and mutual relationships.
Properties of functions of random variables.
Data as realisations of random variables.
Descriptive statistics and the choice of a suitable model.
Point and interval estimation: the framework and most common methods.
Hypotheses testing: the framework and most common methods.
Linear regression, Analysis of variance, Analysis of covariance.
Methods of data collection, their purpose, scope and limitations.
Design of experiment.
MB151 Linear models
zk 2/2 3 kr., jaro
- doc. Mgr. Ondřej Klíma, Ph.D.
- Prerequisities:
! MB101 && ! MB201
- Goals: Introduction to linear algebra and analytical geometry.
- Learning outcomes: At the end of this course, students should be able to: understand basic concepts of linear algebra; apply these concepts to iterated linear processes; solve basic problems in analytical geometry.
- Syllabus:
The course is the first part of the four semester block of Mathematics. In the entire course, the fundamentals
of general algebra and number theory, linear algebra, mathematical analysis, numerical methods, combinatorics, as well as probability and statistics are presented. Content of the course Linear models:
1. Introduction (3 weeks) -- motivating examples, real and complex numbers, roots of real polynomials, matrix multiplication, recurrence relations (incl. recurrence in combinatorics), geometry in two dimensions.
2. Vector spaces (4 weeks) -- systems of linear equalities, matrix calculus (determinant and inverse matrix), vector spaces (formal definition and examples), linear independence, basis, coordinates, scalar product, length of vector, orthogonality, explicit formulas for recurrence relations.
3. Linear mappings (2 weeks) -- representation of linear mappings, eigenvalues and eigenvectors; linear transformations in three dimensions, iterated linear processes (population models and discrete Markov chains).
4. Analytical geometry (4 weeks) -- affine and Euclidean spaces (line, plane descriptions, angle, length, volume); systems of linear (in)equalities - linear programming problem; elementary classification of quadrics.
MB152 Differential and Integral Calculus
zk 2/2 3 kr., podzim
- doc. Mgr. Petr Hasil, Ph.D.
- Prerequisities:
( ! MB202 && ! MB102 )
High school mathematics - Goals: This is a basic course of the mathematical analysis. The content is the differential and integral calculus and the theory of infinite series. Students will understand theoretical and practical methods and will be able to apply these methods to concrete problems. The emphasis on theory and examples is balanced in the course.
- Learning outcomes:
At the end of the course students will be able to:
work both practically and theoretically with the derivative and (indefinite and definite) integral;
analyse the behaviour of functions of one real variable.
understand the theory and use of infinite number series and power series;
understand the selected applications of the calculus;
apply the methods of the calculus to concrete problems. - Syllabus:
Continuous functions and limits
Derivative and its applications
Elementary functions
Indefinite integral
Riemann integral and its applications (including an introduction to basic differential equations)
Introduction to differential (and integral) calculus of functions of several variables
Infinite series
MB153 Statistics I
zk 2/2 3 kr., jaro
- doc. Mgr. Jan Koláček, Ph.D.
- Prerequisities:
( MB151 || MB101 || MB201 || MB152 || MB102 || MB202 || PřF:M1110 || PřF:M1100 ) && ( ! MB103 && ! MB203 && ! MV011 )
Prerequisites: calculus in one and several variables, basics of linear algebra. - Goals: Introductory course to educate students in descriptive statistics, theory of probability, random values and probabilistic distributions, including the theory of hypothesis testing.
- Learning outcomes: Upon completing this course, students will be able to perform basic computer aided statistical data set analysis in R language, resulting in tables, graphs and numerical characteristics; will understand basic probability concepts; will be able to solve probability tasks related to explained theory (in some cases using statistical software); will be able to generate realizations of selected types random variables using statistical software; has basic knowledge of statistical hypothesis testing, will be able carry out tests in statistical software and interpret the results.
- Syllabus:
Introduction to the probability theory.
Random variables and vectors. Probability distribution and distribution function.
Discrete and continuous random variables and vectors. Typical distribution laws. Simultaneous and marginal distributions.
Stochastic independence of random variables and vectors. The sequence of independent trials.
Quantiles, expectation, variance, covariance, correlation coeficient and their properties.
Weak law of large number and central limit theorem.
Data files, empirical characteristics and graphs, numerical characteristics. Descriptive statistics in R language.
Random sample, point and interval estimators.
Basics of testing hypothesis. Testing hypothesis in R language.
Regression analysis in R language.
MB154 Discrete mathematics
zk 2/2 3 kr., podzim
- prof. RNDr. Jan Slovák, DrSc. - doc. Lukáš Vokřínek, PhD.
- Prerequisities:
! MB104 && ! MB204 && ( MB101 || MB201 || MB151 || MB102 || MB202 || MB152 || PřF:M1110 || PřF:M1100 )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks. - Goals: Tho goal of this course is to introduce the basics of theory of numbers with its applications to cryptography, and also the basics of coding and more advanced combinatorial methods.
- Learning outcomes: At the end of this course, students should be able to: understand and use methods of number theory to solve simple tasks; understand approximately how results of number theory are applied in cryptography: understand basic computational context; model and solve simple combinatorial problems.
- Syllabus:
Number theory:
divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
Number theory applications:
short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
Combinatorics:
reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).
MA007 Mathematical Logic
zk 2/1 4 kr., podzim
- prof. RNDr. Antonín Kučera, Ph.D.
- Prerequisities:
IB000 || PřF:M1120 || PřF:M1125
Students should have passed the course IB000 Mathematical Foundations of Computer Science or a course covering the foundations of mathematics at the Faculty of Science. - Goals: The course covers basic results about propositional and first order logic, including Gödel's completeness and incompleteness theorems.
- Learning outcomes:
At the end of this course, students should be able to:
understand the difference between formal notions and notions defined at a meta-level;
understand the difference between validity and provability;
understand the syntax and semantics of first-order logic;
understand and appreciate the fundamental ideas in the proofs of Gödel's completeness and incompleteness theorems. - Syllabus:
Propositional calculus: propositional formulas, truth, provability,
completeness.
First-order logic: syntax, semantics.
A deductive system for first-order logic. Provability, correctness.
Completeness theorem: theories, models, Gödel's completeness theorem
Basic model theory, Löwenheim-Skolem theorem
Gödel's incompleteness theorem.
MA009 Algebra II
zk 2/2 3 kr., jaro
- doc. Mgr. Michal Kunc, Ph.D.
- Prerequisities:
( MB008 || MV008 || program ( N - IN )|| program ( N - AP )|| program ( N - SS ))
- Goals: The aim of the course is to become acquainted with basic notions of universal algebra employed in computer science, namely lattice-ordered sets and equational logic.
- Learning outcomes: After passing the course, students will be able to: use the basic notions of the theory of lattices and universal algebra; define and understand basic properties of lattices and complete lattices; verify simple algebraic statements; apply theoretical results to algorithmic calculations with operations and terms.
- Syllabus:
Lattice theory: semilattices, lattices, lattice homomorphisms, modular and distributive lattices, Boolean algebras, complete lattices, fixed point theorems, closure operators, completion of partially ordered sets, Galois connections, algebraic lattices.
Universal algebra: algebras, subalgebras, homomorphisms, term algebras, congruences, quotient algebras, direct products, subdirect products, identities, varieties, free algebras, presentations, Birkhoff's theorem, completeness theorem for equational logic, algebraic specifications, rewriting systems.
MA010 Graph Theory
zk 2/1 3 kr., podzim
- prof. RNDr. Daniel Kráľ, Ph.D., DSc.
- Prerequisities:
! PřF:M5140 &&! NOW ( PřF:M5140 )
Discrete mathematics. IB000 (or equivalent from other schools) is recommended. - Goals: This is a standard introductory course in graph theory, assuming no prior knowledge of graphs. The course aims to present basic graph theory concepts and statements with a particular focus on those relevant in algorithms and computer science in general. Selected advanced graph theory topics will also be covered. Although the content of this course is primarily targeted at computer science students, it should be accessible to all students.
- Learning outcomes: At the end of the course, students shall understand basic concenpts in graph theory; be able to reproduce the proofs of some fundamental statements in graph theory; be able to solve unseen simple graph theory problems; and be ready to apply their knowledge particularly in computer science.
- Syllabus:
Basic graph theory notions: graphs, subgraph, graph isomorphism, vertex degree, paths, cycles, connected components, directed graphs.
Trees, Hamilton cycles, Dirac’s and Ore’s conditions.
Planar graphs, duality of planar graphs, Euler's formula and its applications.
Graph coloring, Five Color Theorem, Brooks’ Theorem, Vizing’s Theorem.
Interval graphs, chordal graphs, and their chromatic properties.
Vertex and edge connectivity.
Matchings in graphs, Hall’s Theorem.
Ramsey's Theorem.
Selected advanced topics (to be chosen from): Graph minors, graph embeddings on surfaces, planarity testing, list coloring, Tutte’s Theorem, Cayley’s formula.
MA012 Statistics II
zk 2/2 3 kr., podzim
- Mgr. Ondřej Pokora, Ph.D.
- Prerequisities:
Basic knowledge of calculus: function, derivative, definite integral.
Basic knowledge of linear algebra: matrix, determinant, eigenavlues, eigenvectors.
Knowledge of probability a and statistics and practice with statistical language R within the scope of course MB153 Statistics I or MB143 Design and analysis of statistical experiments. Students without these knowledges and without practice with R are adviced to complete the course MB153 first. - Goals: The course introduces students to advanced methods of mathematical statistics – explains the algorithms, computational procedures, conditions, interpretation of results and practical use of these methods for the analysis of datasets in statistical software R. After completing the course, the student will understand advanced statistical methods and inferential principles (estimations, hypothesis testing). The student will be able to use this methods in analyzing datasets and will be able to statistically interpret the achieved results.
- Learning outcomes:
After completing the course the student will be able to:
- explain the principles and algorithms of advanced methods of mathematical statistics;
- perform a statistical analysis of a real dataset using tidyverse packages in software R;
- interpret the results obtained by the statistical analysis. - Syllabus:
Analysis of variance (ANOVA).
Nonparametric tests – rank tests.
Goodness-of-fit tests.
Correlation analysis, correlation coefficients.
Multiple regression.
Regression diagnostics.
Autocorrelation and multicollinearity.
Principal component Analysis (PCA).
Logistic regression and other generalized linear models (GLM).
Contingency tables and independence testing.
Bootstrapping.
MA015 Graph Algorithms
zk 2/1 3 kr., podzim
- doc. Mgr. Jan Obdržálek, PhD.
- Prerequisities:
MB005 ||( MB101 && MB102 )||( MB201 && MB102 )||( MB101 && MB202 )||( MB201 && MB202 )||( PřF:M1120 )|| PROGRAM ( N - IN )|| PROGRAM ( N - AP )
Knowledge of basic graph algorithms and datastructures. Specifically, students should already understand the following datastructures and algorithms: Graphs searching: DFS, BFS. Network flows: Ford-Fulkerson. Minimum spanning trees: at least one of Boruvka, Jarnik (Prim), Kruskal. Shortest paths: Bellman-Ford, Dijkstra. Datastructures: priority queues, heaps (incl. Fibonacci), disjoint set (union-find). - Goals: The course surveys important graph algorithms beyond those typically covered in basic algorithms and data structures courses. Chosen algorithms span most of the important application areas of graphs algorithms.
- Learning outcomes:
At the end of the course students will:
- know and understand efficient algorithms for various graph problems, including: minimum spanning trees, network flows, (globally) minimum cuts, matchings (including the assignment problem);
- be able to prove correctness and complexity of these algorithms;
- be able to use dynamic programming to solve problems on tree-like graphs;
- learn a range of techniques useful for designing efficient algorithms and deriving their complexity. - Syllabus:
Minimum Spanning Trees.
Quick overview of basic algorithms (Kruskal, Jarník [Prim], Borůvka) and their modifications. Advanced algorithms: Fredman-Tarjan, Gabow et al. Randomized algorithms: Karger-Klein-Tarjan. Arborescenses of directed graphs, Edmond's branching algorithm.
Flows in Networks. Revision - Ford-Fulkerson. Edmonds-Karp, Dinic's algorithm (and its variants), MPM (three Indians) algorithm. Modifications for restricted networks.
Minimum Cuts in Undirected Graphs. All pairs flows/cuts: Gomory-Hu trees. Global minimum cut: node identification algorithm (Nagamochi-Ibaraki), random algorithms (Karger, Karger-Stein)
Matchings in General Graphs. Basic algorithm using augmenting paths. Perfect matchings: Edmond's blossom algorithm. Maximum matchings. Min-cost perfect matching: Hungarian algorithm.
Dynamic Algorithms for Hard Problems. Dynamic programming on trees and circular-arc graphs. Tree-width; dynamic programming on tree-decompositions.
Graph Isomorphism. Colour refinement. Individualisation-refinement algorithms. Tractable classes of graphs.
MA017 Geometric Algorithms
zk 2/0 2 kr., podzim
- doc. John Denis Bourke, PhD
- Prerequisities: Basic course on algorithms, high school geometry.
- Goals: The aim of the course is to introduce the principles of basic algorithms in computational geometry. This course can be followed by the PA093 Computational Geometry Project where the students are implemented selected algorithms in practice.
- Learning outcomes: Students will gain knowledge about state-of-the-art algorithmic methods in this field, along with their complexity and underlying data and searching structures.
- Syllabus: 1. Algorithms for construction of convex hulls in two-dimensional space 2. Line segment intersections 3. Triangulations 4. Linear programming in two-dimensional space 5. Range searching (kd-trees, range trees) 6. Point localization 7. Voronoi diagrams 8. Duality and arrangements 9. Delaunay triangulation 10. Convex hulls in in three-dimensional space
MA018 Numerical Methods
zk 2/2 3 kr., podzim
- RNDr. Veronika Eclerová, Ph.D.
- Prerequisities: Differential and integral calculus of functions of one and more variables. Basic knowledge of linear algebra, theory of matrices and solving systems of linear equations. Basics of programing.
- Goals: This course provides explanation of numerical mathematics as the separate scientific discipline. The emphasis is given to the algorithmization and computer implementation. Examples with graphical outputs help to explain even some difficult parts.
- Learning outcomes: At the end of course students should be able to apply numerical methods for solving practical problems and use these methods in other disciplines.
- Syllabus:
1. Error analysis: absolute and relative error, representation of numbers, error propagation
2. Iterative methods for solving of nonlinear equations: general iterative method, order of the convergence, Newton method and its modifications
3. Direct methods for solving systems of linear equations: methods based on Gaussian elimination, methods for special matrices
4. Iterative methods for solving of systems of linear equations: general construction of iterative methods, Jacobi method, Gauss-Seidel method
5. Solving of systems of nonlinear equations: Newton method
6. Interpolation and approximation: polynomial and piece-wise polynomial interpolation, curve approximations, subdivision schemes, least squares method
7. Numerical differentiation: differentiation schemes
8. Numerical integration: methods based on interpolation, Monte Carlo integration
MA026 Advanced Combinatorics
zk 2/1 3 kr., jaro
- prof. RNDr. Petr Hliněný, Ph.D.
- Prerequisities:
MA010
- Syllabus:
Advanced structural graph theory:
graph minors and well-quasi-ordering, width parameters, matching in general graphs, list coloring, intersection graphs
Topological graph theory: planarity testing and SPQR trees, MAXCUT algorithm in planar graphs, graphs on surfaces of higher genus, crossing numbers
Probabilistic method: review of tools - linearity of expectation and concentration bounds, lower bounds on Ramsey number, crossing number, and list chromatic number, Lovász Local Lemma
Regularity method: regularity decompositions, removal lemma, property testing algorithms
Extremal Combinatorics: Hales-Jewett Theorem, Van der Waerden Theorem, Gallai-Witt Theorem
MV008 Algebra I
zk 2/2 3 kr., podzim
- doc. Mgr. Michal Kunc, Ph.D.
- Prerequisities:
( MB005 || MB101 || MB201 || MB151 ) && ! MB008
- Goals: The aim of the course is to become familiar with basic algebraic terminology, demonstrated on monoids, groups and rings, and with its usage for instance in modular arithmetics or for calculations with permutations and numbers.
- Learning outcomes: After passing the course, students will be able to: use the basic notions of the theory of monoids, groups and rings; define and understand basic properties of these structures; verify simple algebraic statements; apply theoretical results to algorithmic calculations with numbers, mappings and polynomials.
- Syllabus:
Semigroups: monoids, subsemigroups and submonoids, homomorphisms and isomorphisms, Cayley's representation, transition monoids of automata, direct products of semigroups, invertible elements.
Groups: basic properties, subgroups, homomorphisms and isomorphisms, cyclic groups, Cayley's representation, direct products of groups, cosets of a subgroup, Lagrange's theorem, normal subgroups, quotient groups.
Polynomials: polynomials over complex, real, rational and integer numbers, polynomials over residue classes, divisibility, irreducible polynomials, roots, minimal polynomials of numbers.
Rings: basic properties, subrings, homomorphisms and isomorphisms, direct products of rings, integral domains, fields, fields of fractions, divisibility, polynomials over a field, ideals, quotient rings, field extensions, finite fields.
MV013 Statistics for Computer Science
zk 2/2 3 kr., jaro
- RNDr. Radim Navrátil, Ph.D.
- Prerequisities:
Basic knowledge of mathematical analysis: functions, limits of sequences and functions, derivatives and integrals of real and multidimensional functions.
Basic knowledge of linear algebra: matrices and determinants, eigenvalues and eigenvectors.
Basic knowledge of probability theory: probability, random variables and vectors, limit theorems. - Goals: The main goal of the course is to become familiar with some basic principles of statistics, with writing about numbers (presenting data using basic characteristics and statistical graphics), some basic principles of likelihood and statistical inference; to understand basic probabilistic and statistical models; to understand and explain basic principles of parametric statistical inference for continuous and categorical data; to implement these techniques to R language; to be able to apply them to real data.
- Learning outcomes:
Student will be able:
- to understand principles of likelihood and statistical inference for continuous and discrete data;
- to select suitable probabilistic and statistical model for continous and discrete data;
- to use suitable basic characteristics and statistical graphics for continous and discrete data;
- to build up and explain suitable statistical test for continuous and discrete data;
- to apply statistical inference on real continuous and discrete data;
- to apply simple linear regression model including ANOVA on real continuous data;
- to implement statistical methods of continuous and discrete data to R. - Syllabus:
What is statistics? Motivation and examples.
Exploratory data analysis
Revision of probability theory
Parametric models - methods for parameter estimation
Confidence intervals and hypothesis testing
Testing hypotheses about one-sample
Testing hypotheses about two-samples
ANOVA
Testing for independence
Nonparametric tests
Linear regression models
IB000 Mathematical Foundations of Computer Science
zk 2/2 4 kr., podzim
- prof. RNDr. Petr Hliněný, Ph.D.
- Goals: This course is focused on understanding basic mathematical concepts necessary for study of computer science. This is essential for building up a set of basic concepts and formalisms needed for other theoretical courses in computer science. At the end of this course the successful students should: know the basic mathematical notions; understand the logical structure of mathematical statements and mathematical proofs, specially mathematical induction; know discrete mathematical structures such as finite sets, relations, functions, and graph; be able to precisely formulate their claims, algorithms, and relevant proofs; and apply acquired knowledge in other CS courses as well as in practice later on.
- Learning outcomes: After finishing the course the student will be able to: understand the logical structure of mathematical statements and mathematical proofs, deal with and explain basic structures of discrete mathematics, precisely formulate their claims, algorithms, and relevant proofs.
- Syllabus:
The course focuses on understanding basic mathematical tools:
Basic formalisms - statements, proofs, and propositional logic.
Sets, relations, and functions.
Proof techniques, mathematical induction.
Recursion, structural induction.
Binary relations, closure, transitivity.
Equivalence and partial orders.
Composition of relations and functions.
Basics of graphs, isomorphism, connectivity, trees.
Graph distance, spanning trees. Directed graphs.
Proof techniques for algorithms.
Infinite sets and the halting problem.
IB002 Algorithms and data structures I
zk 2/2 4 kr., jaro
- prof. RNDr. Ivana Černá, CSc.
- Prerequisities:
IB015 || IB111
The students should comprehend the basic notions on the level of IB111 Introduction to Programming and IB000 Mathematical Foundations of Computer Science Students should be able to: understand and apply basic constructs of programming languages (e.g., conditions, loops, functions, basic data types) in Python, know principles of recursion, and several basic algorithms. Students should know the basic mathematical notions; understand the logical structure of mathematical statements and mathematical proofs, specially mathematical induction; know discrete mathematical structures such as finite sets, relations, functions, and graph including their applications in informatics. - Goals: The course presents basic techniques of the analysis of algorithms, data structures, and operations. Students should correctly apply the basic data structures and algorithms as well as apply the algorithm design and analysis techniques when designing new algorithms. Students implement their algorithms in programming language Python.
- Learning outcomes:
After enrolling the course students are able to:
- actively use and modify basic sorting algorithms and graph algorithms,
- actively used basic techniques for designing algorithms (divide et impera, recursion) and design simple algorithms,
- actively used and modify basic static and dynamic data structures,
- employ time complexity and correctness of algorithms,
- analyze time complexity and prove the correctness of simple iterative and recursive algorithms,
- implement algorithms in the selected programming language (Python). - Syllabus:
Basic analysis of algorithms:
The correctness of algorithms, input and output conditions, partial correctness, convergence, verification.
Length of computation, algorithm complexity, problem complexity. Asymptotical analysis of time and space complexity, growth of functions.
Algorithm design techniques. Divide et impera and recursive algorithms.
Fundamental data structures: lists, queues. Representation of sets, hash tables. Binary heaps. Binary search trees, balanced trees (B trees, Red-black trees).
Sorting algorithms: quicksort, mergesort, heapsort, lower bound for the time complexity of sorting.
Graphs and their representation. Graph search. Depth-first traversal, topological sort, strongly connected components. Breadth-first traversal, bipartite graphs. Shortest paths, algorithm Bellman-Ford, Dijkstra's algorithm.
IB005 Formal Languages and Automata
zk 2/2 4 kr., jaro
- prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D.
- Prerequisities:
IB000 && ! IB102
Knowlegde corresponding to the courses IB000 Mathematical Foundations of Computer Science - Goals: Students should be able to understand and explain the rich heritage of models and abstractions that have arisen over the years, and to develop the students' capacity to form abstractions of their own and reason in terms of them.
- Learning outcomes:
At the end of the course students should be able to:
Demonstrate an in-depth understanding of theories, concepts and techniques in automata and their link to computation.
Develop abstract machines that demonstrate the properties of physical/SW systems and be able to specify the possible inputs, processes and outputs of these machines. Analyze the computational strengths and weaknesses of these machines.
Understand the concept of computability by manipulating these machines in order to demonstrate the properties of computational processes.
Practice techniques of program design and development by using abstract machines. Apply automata concepts and techniques in designing systems that address real world problems - Syllabus:
Languages and grammars. Chomsky hierarchy.
Finite automata and regular grammars.
Properties of regular languages. Applications.
Context-free grammars and pushdown automata.
Properties of context-free languages.
Turing machines (TM). Computable languages and functions, LBA. Properties of recursive and recursive enumerable languages.
Undecidability, halting problem for TM, Reduction, Post Correspondece Problem, undecidable problems from language theory.
IB015 Non-Imperative Programming
zk 2/1 4 kr., podzim
- prof. RNDr. Jiří Barnat, Ph.D.
- Prerequisities: There are no special prerequisities apart from the basic math skills (on the secondary-school level), and certain aptitude for abstract reasoning.
- Goals: On successful completion of the course, students will understand functional and logic programming paradigms. Programming languages enforcing declarative way of description of an algorithm bring on programming habits that the students will be able to use in practice later on when implementing large applications using even imperative languages.
- Learning outcomes: After graduation students will: - understand fundaments of functional programming, - be able to decompose computational problems to individual functions and apply this ability for design and implementation of programs even in imperative programming languages, - have basic knowledge of Haskell programming language - be able to design and implement recursive functions, - be able to work with recursively defined data structures.
- Syllabus:
Functional computational paradigm and Haskell
Functions in programming;
Lists, Types and Recursion
Functions of higher rank, Lambda functions
Accumulators, Type definitions, Input/Output
Reduction strategy, Infinite lists
Relation of recursion and induction, Recursive data types
Time complexity of computation, Type classes, Modules
Functional solutions od some problems
Logical computational paradigm and Prolog
Non-imperative programming in Prologu
Lists, Arithmetics, Tail rekursion in Prologu
Cuts, Input-Output, All solutions
An Introduction to Constraint Solving Programming
IB016 Seminar on Functional Programming
z 1/1 2 kr., jaro
- RNDr. Martin Jonáš, Ph.D.
- Prerequisities:
IB015
Pre-requisities for enrolling in the course are to be familiar with Haskell in the scope of the IB015 Non-Imperative Programming course and to have a positive attitude towards functional programming. - Goals: Students will significantly extend their knowledge of functional programming. At the end of the course, they should be able to solve non-trivial programming problems using Haskell and be familiar with practical use of this functional language.
- Learning outcomes:
After finishing the course, the student will be able to:
— write a Haskell program with approximatelly 100 to 200 lines;
— perform analysis and functional decompisition of given problem;
— use supportive tools for Haskell developers such as the Cabal package manager, the Hackage package repository, the HLint linter, and the QuickCheck testing framework;
— describe theoretical functional concepts;
— have an idea about some more advanced functional techniques used in practice. - Syllabus:
Advanced syntax, modules, custom type classes, advanced data structures.
Package system (Hackage/Stackage), support tools (Cabal, HLint, Haddock).
Functors, applicative functors, monads.
Automatic generation of tests according to program specification (QuickCheck).
Input and output in Haskell, processing errors and exceptions (Maybe, Either, exceptions, error states).
Semigroups, monoids, the Foldable and Traversable classes.
Evaluation strategies (laziness vs. strictness).
Monadic parsing (Parsec).
Monads for shared writing, shared reading and keeping the state (Writer, Reader, State).
Monad transformers (MaybeT, ErrorT).
Processing strings and other useful GHC extensions.
Haskell in real world projects.
IB030 Introduction to Natural Language Processing
zk 2/0 2 kr., jaro
- doc. RNDr. Aleš Horák, Ph.D.
- Goals: In this course the main principles of natural language processing are presented. The algorithmic description of the main language analysis levels will be discussed - morphology, syntax, semantics and pragmatics. Also the resources of natural language data, corpora, will be presented. The role of knowledge representation, inference and relations to artificial intelligence will be touched as well.
- Learning outcomes:
Students will be able to:
- identify and summarize the main phases of computer natural language analysis;
- describe principles of algorithms used for speech analysis;
- explain the main approaches to analysis at the morphological and syntactic level of language;
- provide an overview of main language resources, their formats and processing;
- understand approaches to computational semantics and its applications. - Syllabus:
Introduction to Computational Linguistics (Natural Language Processing, NLP).
Levels of description: phonetics and phonology, morphology, syntax, semantics and pragmatics.
Representation of morphological and syntactic structures.
Analysis and synthesis: speech, morphological, syntactic, semantic.
Knowledge representation forms with regard to lexical units.
Language understanding: sentence meaning representation, logical inference.
IB031 Introduction to Machine Learning
zk 2/2 3 kr., jaro
- doc. RNDr. Tomáš Brázdil, Ph.D. - doc. RNDr. Lubomír Popelínský, Ph.D.
- Prerequisities: Recommended courses are MB102 a MB103.
- Goals: By the end of the course, students should know basic methods of machine learning and understand their basic theoretical properties, implementation details, and key practical applications. Also, students should understand the relationship among machine learning and other sub-areas of mathematics and computer science such as statistics, logic, artificial intelligence and optimization.
- Learning outcomes:
By the end of the course, students
- will know basic methods of machine learning;
- will understand their basic theoretical properties, implementation details, and key practical applications;
- will understand the relationship among machine learning and other sub-areas of mathematics and computer science such as statistics, logic, artificial intelligence and optimization;
- will be able to implement and validate a simple machine learning method. - Syllabus:
Basic machine learning: classification and regression, clustering,
(un)supervised learning, simple examples
Decision trees: learning of decision trees and rules
Logic and machine learning: specialization and generalization, logical entailment
Evaluation: training and test sets, overfitting, cross-validation, confusion matrix, learning curve, ROC curve; sampling, normalisation
Probabilistic models: Bayes rule, MAP, MLE, naive Bayes; introduction to Bayes networks
Linear regression (classification): least squares, relationship wih MLE, regression trees
Kernel methods: SVM, kernel transformation, kernel trick, kernel SVM
Neural networks: multilayer perceptron, backpropagation, non-linear regression, bias vs variance, regularization
Lazy learning: nearest neighbor method; Clustering: k-means, hierarchical clustering, EM
Practical machine learning: Data pre-processing: attribute selection and construction, sampling. Ensemble methods. Bagging. Boosting. Tools for machine learning.
Advanced methods: Inductive logic programming, deep learning.
IB047 Introduction to Corpus Linguistics and Computer Lexicography
zk 2/0 2 kr., jaro
- doc. Mgr. Pavel Rychlý, Ph.D.
- Goals: A basic introduction to the field of corpus linguistics and computational lexicography. Students will study types of corpora, corpus building and usage, especially in the sake of dictionaries building.
- Learning outcomes: Student will be able to: choose the right korpus type for specific purpose; interpret all layers of corpus annotation; use statistical methods on text corpora; design the structure of a dictionary; use free tools for dictionary writing.
- Syllabus:
Information technologies and language (text) corpora.
Beginning of corpus linguistics, purpose of corpora.
Corpus data, corpus types and their standardization, SGML, XML, TEI, CES. Annotated corpora, tagging on various levels: structural tagging, grammatical tagging -- POS, lemmata, word forms. Syntactic tagging, treebanks, skeleton analysis. Parallel corpora, alignment. Tools for automatic and semi-automatic annotation, disambiguation.
Building corpora, maintenance. Corpus tools: corpus manager. Concordance programmes. Queries, regular expressions and their use. Statistical programmes, absolute and relative frequencies, MI and T-score. Work with corpus attributes and tags.
Working with corpora -- CNC, SUSANNE, Prague Dependency Treebank
Words, constructions, collocations.
Computational lexicography, lexicology.
Descripton of meanings (semantic features).
Types of computer dictionaries. Lexicography standards.
Data for dictionary building -- corpora.
Lexicography Software tools. Lemmatizers.
IB107 Computability and Complexity
zk 2/1 3 kr., podzim
- prof. RNDr. Jan Strejček, Ph.D.
- Prerequisities:
IB005 || IB102
- Goals:
The course introduces basic approaches and methods for classification of problems with respect to their algorithmic solvability. It explores theoretical and practical limits of computers usage and consequences these limitations have for advancing information technologies.
At the end of the course the students will be able: to understand basic notions of computability and complexity; to understand the main techniques used to classify problems (reductions, diagonalisation, closure properties), and to apply them in some simple cases. - Learning outcomes:
After enrolling the course student will be able to:
- use asymptotic notation, both actively and passively;
- explain difference between complexity of an algorithm and of a problem;
- independently decide to which complexity class a given problem belongs;
- do practical decisions based on a complexity classification of a particular problem;
- explain that some problems are not computable, give examples of such problems;
- explain the difference between various classes of not-computable problems; - Syllabus:
Algorithms and models of computation.
Church thesis.
Classification of problems. Decidable, undecidable, and partially decidable problems. Computable functions.
Closure properties. Rice theorems.
Computational complexity. Feasible and unfeasible problems.
Reduction and completeness in problem classes. Many-one reduction and polynomial reduction. Complete problems with respect to decidability, NP-complete problems. Applications.
IB109 Design and Implementation of Parallel Systems
zk 2/0 2 kr., jaro
- prof. RNDr. Jiří Barnat, Ph.D.
- Prerequisities: The knowledge of low-level programming in C is expected at the level PB071.
- Goals: The goal of this course is to introduce to students the principles of design and implementation of parallel systems and get them acquainted with the programmer's means for their development.
- Learning outcomes: On successful completion, students should understand the principles of design and implementation of parallel algorithms and should have limited experience with programmer's means for their development. In particular, students should be able to design and implement their own parallel applications, they should know how to use selected libraries supporting the development of parallel applications, and should be able to explain what is behind the API calls to such libraries.
- Syllabus: Motivation for parallel computing. Parallel algorithm design -- decomposition and communication. Analyzes of parallel algorithms. Parallel algorithms in shared-memory.OpenMP, Intel TBB. POSIX Threads. Lock-free algorithmics. Parallel algorithms in distributed-memory. Message Passing Interface (MPI). Examples of parallel graph algorithms. Parallel algorithms for many-core platforms.
IB110 Introduction to Informatics
zk 2/2 3 kr., jaro
- RNDr. Petr Novotný, Ph.D.
- Prerequisities:
! IB005 || ! IB107
none - Goals: The main objective of the course is to acquaint the students with basic abstract computational models and their use in analysis of algorithms and computational problems. At the end of the course, the students will understand fundamental concepts in the theory of finite automata, computability and complexity theory. They will be able to leverage the knowledge of these concepts for deeper understanding of concepts appearing in a practice of programming.
- Learning outcomes:
Successful course graduates will be able to:
- explain the notion of a finite automaton and construct finite automata for simple regular languages
- explain the notion of a regular expression and construct REs for simple regular languages
- explain the concept of non-determinism and use non-determinism to simplify the construction of finite automata
- use the basic algorithms for handling of finite automata (determinisation etc.)
- understand the notion of decidability and explain the existence of undecidable problems
- explain the concept of a Turing machine and construct TMs for simple problems
- understand the concept of reduction between computational problems
- understand the concept of computational complexity, the basic complexity classes and relationships between them - Syllabus:
Finite automata and regular languages. Construction of finite automata.
Non-deterministic automata, the use of non-determinism, determinisation, minimalisation.
Regular expressions and regular grammars. Examples of non-regular languages.
Computational problems and algorithms. Turing machines. Decidable and undecidable problems, diagonalisation.
Reductions between computational problems.
Time and space complexity of algorithms and problems. Classes P and NP. NP-complete problems. Examples of complexity classes and relationships between them.
IB111 Foundations of Programming
zk 2/2 5 kr., podzim
- RNDr. Nikola Beneš, Ph.D.
- Prerequisities:
! IB113 && ! NOW ( IB113 )
- Goals: The course is an introduction to programming and algorithmic style of thinking.
- Learning outcomes: At the end of the course students should be able to: understand and apply basic constructs of programming languages (e.g., conditions, loops, functions, basic data types); write and debug a program in Python; use basic data types and structures (strings, lists, dictionaries); describe several basic algorithms; describe main conventions and recommended programming style.
- Syllabus:
The course shows the basic elements of imperative programming and algorithmic thinking using the high-level programming language Python as an example.
Basic notions of imperative programming languages: variables and their semantics, expressions and statements, branching, cycles; subroutines (functions), passing parameters (calling functions), pure functions, predicates.
Numerical computation, basic data types, using the random generator.
Data structures, ADT, lists, strings, multidimensional arrays, sets, dictionaries, the basic of using objects to create user-defined data structures.
The basics of testing and debugging, preconditions and postconditions, type annotation.
Examples of basic algorithms: greatest common divisor, prime numbers, sorting algorithms, searching.
The efficiency of algorithms, the basics of complexity, the complexity of basic data structures operations.
Recursion and its specifics in the imperative paradigm, tail recursion; using recursion to work with tree data structures and to solve constraint satisfaction problems (the basics of the backtracking technique).
Interaction with the environment (I/O), turtle graphics, bitmap graphics, text processing.
Program design, programming styles and conventions, readability and maintainability of code, documentation and comments.
IB113 Introduction to Programming and Algorithms
zk 2/2 4 kr., podzim
- doc. Mgr. Radek Pelánek, Ph.D.
- Prerequisities:
! NOW ( IB111 ) && ! IB111 && ! PB162 && ! PB161 && ! PB071 && ! IB001
- Goals: The course is an introduction to programming and algorithmic style of thinking. At the end of the course students should be able to: understand and apply basic constructs of programming languages (e.g., conditions, loops, functions, basic data types) and know several basic algorithms.
- Learning outcomes:
After finishing this course, a student should be able to:
- use basic tools of structured imperative programming languages (variables, conditions, loops, functions, record data types);
- write and debug a simple Python program and adhere to recommended principles of programming style;
- use basic data types and structures (strings, lists, dictionaries);
- explain several classical algorithms. - Syllabus:
Basic constructions of imperative programming languages: conditions, loops, data types, functions, input, output.
Number types, randomness, algorithms with numbers.
Data types, lists, dictionaries, objects.
Basic algorithms: prime numbers, sorting, searching. Complexity of algorithms (basics).
Turtle graphics, bitmap graphics, regular expressions, text processing.
IB114 Introduction to Programming and Algorithms II
zk 2/1 3 kr., jaro
- prof. RNDr. Ivana Černá, CSc.
- Prerequisities:
( IB111 || IB113 ) && ! IB002 && ! NOW ( IB002 )
This course is intended for the study program Cybersecurity. Students enrolled in programs Informatics and Programming and Application Development are recommended IB002 instead. - Goals: The course presents basic data structures and algorithms. Students should correctly apply the basic data structures and algorithms as well as apply the algorithm design and analysis techniques when designing new algorithms. Students implement their algorithms in programming language Python.
- Learning outcomes:
After enrolling the course students are able to:
- actively use basic sorting algorithms and graph algorithms,
- actively design simple algorithms,
- actively used basic static and dynamic data structures,
- employ time complexity and correctness of algorithms,
- implement simple algorithms in the selected programming language (Python). - Syllabus:
Basic analysis of algorithms.
The correctness of algorithms, input and output conditions, partial correctness, convergence, verification.
Length of computation, algorithm complexity, problem complexity. Asymptotical analysis of time and space complexity, growth of functions.
Fundamental data structures. Lists, queues. Representation of sets, hash tables. Binary heaps. Binary search trees.
Sorting algorithms. Quicksort, Mergesort, Heapsort.
Graphs and their representation. Graph search. Depth-first traversal and Breadth-first traversal, applications.
IA006 Selected topics on automata theory
zk 2/1 3 kr., podzim
- prof. RNDr. Mojmír Křetínský, CSc.
- Prerequisities: Knowlegde corresponding to the courses IB005 - Formal languages and automata and IB107 - Computability and complexity
- Goals: The main aim is to understand and explain selected advanced parts of automata theory, including parsing techniques for deterministic contex-free languages, relationship between finite-state automata and MSO logic, automata on infinite words, and process specifications. Further, students should be able to make reasoned decisions about computational models appropriate for the respective areas and to understand methods and techniques of their applications.
- Learning outcomes: At the end of the course students should be able to understand and explain selected advanced parts of automata theory, and to make reasoned decisions about computational models appropriate for the respective area and to understand methods and techniques of their applications.
- Syllabus:
Methods of syntactic analyses of detCFLs.
LL(k) grammars and languages, properties and analyzers.
LR(k) grammars and languages, properties and analyzers.
Relationships between LL, LR and detCFL.
Infinite=state transition systems and nondeterminism - bisimulation. Selected decidable problems related to process verification.
Finite-state automata and monadic second-order logic
Automata and infinite words: infinite words, regular (rational) sets of infinite words.
Automata: deterministic and nondeterministic Buchi automata, Muller, Rabin, and Street automata. McNaughton theorem. Relationships.
IA008 Computational Logic
zk 2/2 3 kr., jaro
- Dr. rer. nat. Achim Blumensath
- Goals: At the end of the course students should be familiar with main research and applications in computational logic; They will be able to use automatic provers for propositional and predicate logic and also for its extensions; They will be familiar with, and able to use, methods for inductive inference in those logics;
- Learning outcomes: After successfully completing this course students should be familiar with several logics, including propositional logic, first-order logic, and modal logic. They should be familiar with various proof calculi for these logics and be able to use such calculi to test formulae for satisfiability and or validity. In addition, they should have basic knowledge about automatic theorem provers and they way these work.
- Syllabus:
Resolution for propositional logic.
Resolution for first-order logic.
Prolog.
Fundamentals of database theory.
Tableaux proofs for first-oder logic.
Natural deduction.
Induction.
Modal logic.
Many-valued logics.
IA010 Principles of Programming Languages
zk 2/0 2 kr., podzim
- Dr. rer. nat. Achim Blumensath
- Prerequisities: Knowledge of at least one imperative (e.g. C/C++/Java) and one functional language (e.g. Haskell). Knowledge of additional programming languages is an advantage.
- Goals:
By the end of the course, the student will be able:
to understand the various features of a given programming language , including their advantages and disadvantages;
to choose a programming language and programming paradigm suitable for a given problem domain;
to analyse both strong and weak aspects of a given programming language;
to quickly obtain an in-depth understanding a of new programming language; - Learning outcomes: After successfully completing this course students will be familiar with the most common features of programming languages. They will know how these features can be used. They will be able to discuss which features can be used to solve a given programming problem and the advantages and disadvantages of the various options.
- Syllabus:
Brief history of programming languages.
Expressions and functions. Scoping. Functional programming.
Types and type checking. Polymorphism. Type inference.
State and side effects. Imperative Programming.
Modules. Abstract data types.
Control flow. Continuations. Generators. Exceptions. Algebraic effects.
Declarative Programming. Single assignment variables. Unification. Backtracking.
Object oriented programming. Dynamic Dispatch. Subtyping. Encapsulated state. Inheritance.
Concurrency. Fibres. Message passing. Shared memory.
IA011 Programming Language Semantics
zk 2/1 3 kr., jaro
- prof. RNDr. Antonín Kučera, Ph.D.
- Prerequisities: Students should be familiar with basic notions of set theory and formal logic (validity and provability, correctness and completeness of deductive systems, etc.)
- Goals: An introduction to the theory of formal semantics of programming languages (operational, denotational, and axiomatic semantics).
- Learning outcomes:
After graduation, student will:
understand basic types of formal semantics of programming languages;
be able to reason about properties of programs using formal semantics;
understand basic notions of temporal logics. - Syllabus:
Formal semantics of programming languages, basic paradigms
(operational, denotational, and axiomatic approach).
Structural operational semantics and its variants (small-step and big-step semantics).
Denotational semantics. Complete partial orders, continuous functions. The fixed-point theorem and its applications, semantics of recursion. Equivalence of operational and denotational semantics.
Axiomatic semantics. Hoare's deductive system, its correctness and completeness.
Temporal logics; the semantics of non-terminating and parallel programs.
IA012 Complexity
zk 2/0 3 kr., podzim
- prof. RNDr. Ivana Černá, CSc.
- Prerequisities: The course expands on course IB107 Computability and Complexity.
- Goals: Theory of computational complexity is about quantitative laws and limitations that govern computing. The course explores the structure of the space of of computable problems and develops techniques to reduce the search for efficient methods for the whole class of algorithmic problems to the search for efficient methods for a few key algorithmic problems. The theory classifies problems according to their computational complexity into feasible and unfeasible problems. Finally, the course tries to understand unfeasability can be coped with the help of techniques like randomization, approximation and parallelization. The main goal of the course is to provide a comfortable introduction to moder complexity theory. While choosing the relevant topics, it places premium on choosing topics that have a concrete relationship to algorithmic problems. Students should understand and analyze complexity issues of basic algorithmic problems and compare different computing approaches.
- Learning outcomes:
After enrolling the course students are able to:
- actively work with computational complexity of problems and algorithms,
- analyse upper and lower bounds of computational complexity,
- differentiate between tractable and untractable problems,
- define basic complexity classes and analyze their relationships,
- explain (NP) hardness and prove hardness of computational problems,
- describe limits of determicnistic, nondeterministic, alternating, randomized, and parallel computing paragigms. - Syllabus:
The structure and properties of time complexity classes. Relation
between determinism and nondeterminism.
The structure and properties of space complexity classes. Relation between determinism and nondeterminism. closure properties of space complexity classes.
Unfeasible problems. Hierarchy of complexity classes. Polynomial hierarchy. Relativization. Non-uniform computational complexity.
Randomized complexity classes and their structure. Approximative complexity classes and non-approximability.
Alternation and games. Interactive protocols and interactive proof systems.
Lower bounds techniques. Kolmogorov complexity.
Descriptive complexity.
IA014 Advanced Functional Programming
zk 2/0 2 kr., jaro
- doc. Mgr. Jan Obdržálek, PhD.
- Prerequisities: Previous experience with functional programming, at least to the extent covered by the course IB015 - Non-imperative programming.
- Goals: Introduce the theoretical concepts behind the functional programming paradigm, i.e. lambda-calculus and various type systems. Present some of the modern advanced functional programming concepts (typeclasses, monads, monad transformers, GADTs, dependent types...).
- Learning outcomes:
By the end of the course, students will:
understand the theoretical foundations of functional programming, e, g, lambda calculi and type theory;
understand and be able to efficiently use modern/advanced concepts of functional programming languages (e.g. typeclasses, monads, monad transformers...);
know the limits of the functional programming paradigm;
be able to evaluate and use FP-based concepts in modern mainstream (non-FP) languages. - Syllabus:
History of functional programming languages.
Untyped lambda calculus.
Simply typed lambda calculus.
Polymorphism add type inference (Hindley-Milner, System F)
Type classes.
Functors, Applicatives.
Monads.
Monad tranformers.
GADTs - Generalized Algebraic Data Types
Dependent types.
IA023 Petri Nets
zk 2/0 2 kr., jaro
- prof. RNDr. Antonín Kučera, Ph.D.
- Prerequisities: Students should be familiar with basic notions of computability, complexity, and automata theory.
- Goals: An introduction to Petri nets; the course covers both "classical" results (about boundedness, liveness, reachability, coverability, etc.) and "modern" results (the (un)decidability of equivalence-checking and model-checking, etc.)
- Learning outcomes: At the end of the course, students should be able to: understand the language of Petri nets; model various classes of systems using Petri nets; apply specific analytical techniques developed for Petri nets; prove properties of discrete systems using Petri nets and appropriate specification formalisms.
- Syllabus:
The theory of Petri nets provides a formal basis for modelling,
design, simulation and analysis of complex distributed
(concurrent, parallel) systems, which found its way to
many applications in the area of computer software, communication protocols, flexible manufacturing systems, software engineering, etc.
Principles of modelling with Petri nets.
Classical results for place/transition nets. Boundedness, coverability, Karp-Miler tree, weak Petri computer; reachability and liveness.
(Un)decidability of equivalence-checking and model-checking with place/transition nets.
S-systems, T-systems. Reachability, liveness, S-invariants, T-invariants.
Free-choice Petri nets. Liveness, Commoner's theorem.
IA041 Concurrency Theory
k 0/2 2 kr., jaro
- prof. RNDr. Mojmír Křetínský, CSc.
- Prerequisities:
IA006
Knowlegde corresponding to the courses IA006 - Automata IB107 - Computability and complexity - Goals: Students should study, understand, present and to work with the basic concepts and techniques used for modelling, analysis and verification of concurrent processes.
- Learning outcomes:
At the end of the course students should be able:
to understand and to work with the basic techniques used for modelling, analysis and verification of concurrent processes;
to make deductions based on acquired knowledge on actual topics and results of concurrent processes and their formal verification. - Syllabus:
Processes, labelled transition systems and their (finite) specifications.
Operational semantics. Caucal a Mayr hierarchies.
Selected sematic equivalencies (and preorders) for processes and their relationships (linear time - branching time spectrum).
Boundaries of algorithmic verification (equivalence checking) -- undecidability, decidability and complexity of some semantic equivalencies on selected classes of infinite state processes.
IA062 Randomized Algorithms and Computations
zk 2/2 3 kr., podzim
- prof. RNDr. Daniel Kráľ, Ph.D., DSc.
- Prerequisities: No special requirements are needed.
- Goals: The aim: randomized algorithms and methods are becoming one of the key tools for an effective solution of a variety of problems in informatics and its aplications practically in all theoretical and aplication areas.
- Learning outcomes: After finishing the lecture student will be able: To manage basic techniques to design randomized algorithms; to understand differences concerning power of deterministic and randomized algorithms; to manage basic tools for analysis of randomized algorithms; to work with tail inequalities; to understand power and use of the probabilistic method; to understand power of random walks; to understand power of randomized proofs; to understand basic principles of randomized cryptographic protocols.
- Syllabus:
Randomized algorithms and methods.
Examples of randomized algorithms.
Methods of game theory.
Main types of randomized algorithms.
Randomized complexity classes.
Chernoff's bounds.
Moments and deviations.
Probabilistic methods.
Markov chains and random walks.
Algebraic methods.
Aplications:
Linear programming.
Parallel and distributed algoritms.
Randomization in cryptography.
Randomized methods in theory of numbers.
IA066 Introduction to Quantum Computing
zk 2/0 2 kr., podzim
- RNDr. Vít Musil, Ph.D.
- Prerequisities: linear algebra, automata and languages, no quantum physics is necessary, algorithm design
- Goals: Quantum computing in particular and quantum information processing in general are one of the hotest subjects in science in general and in informatics in particular. The goal of this introductory course is to present basic aims, concepts, methods and result in this fascinating area.
- Learning outcomes: After completing the course student will be able: to understand principles of the design of quantum algorithms; to understand basic ideas of Shor's and Grover's algorithms; to design simple quantum circuits; to understand recognition power of several quantum automata; to understand basic principles of quantum cryptography - theory, experiment and practical systems; to design quantum error-correcting codes.
- Syllabus:
Motivácie, historia, základné kvantové experimenty,
ohraničenia a paradoxy kvantového spracovania informácie
Hilbertové priestory, kvantové bity, registre, hradla a obvody
kvantové výpočtové primitíva
kvantové entanglovanie a nelokálnost
jednoduché kvantové algoritmy, Shorove kvantové algoritmy, algoritmus Grovera a jeho aplikácie
kvantové konečné automaty
kvantové samoopravujúce kody a kvantové fault-tolerantné hradla.
kvantová krzptografia
vesmír ako kvantový systém
IA067 Informatics Colloquium
z 1/0 1 kr., podzim
- prof. RNDr. Daniel Kráľ, Ph.D., DSc. - doc. RNDr. Barbora Kozlíková, Ph.D. - doc. RNDr. Petr Švenda, Ph.D.
- Goals: The aim of the colloquium is to present new directions, methods and results in informatics, broadly understood. Talks will cover all areas of informatics and related areas and will be given by well-known specialists, especially outside of Brno and from abroad.
- Learning outcomes: After finishing the course students will have updated information about recent research provided by faculties and also by specialists from other academic instituition, also from abroad. For each presented area student will be able to decide whether its techniques can be used to solve a particular theoretical or application problem.
- Syllabus: The aim of the colloquium is to present new directions, methods and results in informatics, broadly understood. Talks will cover all areas of informatics and related areas and will be given by well-known specialists, especially outside of Brno and from abroad.
IA067 Informatics Colloquium
z 1/0 1 kr., jaro
- prof. RNDr. Daniel Kráľ, Ph.D., DSc. - doc. RNDr. Barbora Kozlíková, Ph.D. - doc. RNDr. Petr Švenda, Ph.D.
- Goals: The aim of the colloquium is to present new directions, methods and results in informatics, broadly understood. Talks will cover all areas of informatics and related areas and will be given by well-known specialists, especially outside of Brno and from abroad.
- Learning outcomes: After finishing the course students will have updated information about recent research provided by faculties and also by specialists from other academic instituition, also from abroad. For each presented area student will be able to decide whether its techniques can be used to solve a particular theoretical or application problem.
- Syllabus: The aim of the colloquium is to present new directions, methods and results in informatics, broadly understood. Talks will cover all areas of informatics and related areas and will be given by well-known specialists, especially outside of Brno and from abroad.
IA072 Seminar on Verification
z 0/2 2 kr., podzim
- prof. RNDr. Jan Strejček, Ph.D.
- Prerequisities:
souhlas
for postgraduate students; undergraduate students interested in formal methods may ask for an exception, especially if they are interested in program analysis or automata theory. - Goals:
The aim of the course is to
introduce students to selected research areas;
check their ability to understand a scientific paper;
check and improve their skill of presenting a scientific paper; - Learning outcomes:
At the end of the course students should be able to:
understand a theoretical scientific text;
make a presentation that explains main ideas of such a text;
potentially apply gathered knowledge in an original research; - Syllabus:
Presentations of results from the following areas:
Analysis and verification of software.
Automata and logics over infinite words.
Satisfiability and theorem proving.
IA072 Seminar on Verification
z 0/2 2 kr., jaro
- prof. RNDr. Jan Strejček, Ph.D. - Mgr. Marek Trtík, Ph.D.
- Prerequisities:
souhlas
for postgraduate students; undergraduate students interested in formal methods may ask for an exception, especially if they are interested in program analysis or automata theory. - Goals:
The aim of the course is to
introduce students to selected research areas;
check their ability to understand a scientific paper;
check and improve their skill of presenting a scientific paper; - Learning outcomes:
At the end of the course students should be able to:
understand a theoretical scientific text;
make a presentation that explains main ideas of such a text;
potentially apply gathered knowledge in an original research; - Syllabus:
Presentations of results from the following areas:
Analysis and verification of software.
Automata and logics over infinite words.
Satisfiability and theorem proving.
IA080 Seminar on Knowledge Discovery
k 0/2 2 kr., podzim
- doc. RNDr. Lubomír Popelínský, Ph.D.
- Goals: At the end of the course students should be able to understand scientific works in the area of machine learning and knowledge discovery in data and use it in their work. They will be able to evaluate contributions of such research studies.
- Learning outcomes:
A student will be able
- to understand research papers from machine learning and data mining;
- of critical reading of such papers;
- to prepare and present a lecture on advanced methods of data science. - Syllabus: The seminar is focused on machine learning and theory and practice of knowledge discovery in various data sources. Program of the seminar contains also contributions of teachers and PhD. students of the Knowldge Discovery Laboratory, as well as other laboratories, on advanced topics of knowledge discovery.
IA080 Seminar on Knowledge Discovery
k 0/2 2 kr., jaro
- doc. RNDr. Lubomír Popelínský, Ph.D.
- Prerequisities: Prerequisite for enrollment in the subject is 1) being familiar with advanced machine learning 2) approval of the application by the teacher
- Goals: At the end of the course students should be able to build and evaluate advanced machine learning systems and to understand scientific works in the area of machine learning and data science and use it in their work. They will be able to evaluate contributions of such research studies.
- Learning outcomes:
A student will be able
- to understand research papers from machine learning and data mining;
- of critical reading of such papers;
- to prepare and present a lecture on advanced methods of data science. - Syllabus: The seminar is focused on machine learning and theory and practice of knowledge discovery in various data sources. Program of the seminar contains also contributions of teachers and PhD. students of the Knowldge Discovery Laboratory, as well as other laboratories, on advanced topics of knowledge discovery.
IA081 Lambda calculus
zk 2/0 2 kr., jaro
- prof. RNDr. Jiří Zlatuška, CSc.
- Goals: The goal is to introduce lambda-calculus to students and to demonstrate expressive power of lambda-caluclus on a couple of general computation concepts.
- Learning outcomes: At the end of this cource, students shall learnd and understand basic techniques and results of the theory of sequential functions as described by the lambda-calculus and combinatoru logic; will understand the basics of the typed and untyped version of the formalism; shall learn basic elements of model construction for of lambda-calulus; shall be able to employ recursive constructs used in programming as well in the corresponding semantics constructs; will be abble to use it as a reference formalism useful for variaous applications.
- Syllabus:
Pure lambda-calculus: lambda-terms, structure of terms,
equational theories.
Reductions: one-way transformations, general reductions, beta-reduction.
Lambda-calculus and computations: coding, recursive definitions, lambda-computability, fixed-point combinators, undecidable properties.
Modification of the theory: combinatory logic, extensionality, eta-reduction.
Typed lambda-calculus: types and terms, normal forms, set models, strong normalization, types as formulae.
Domain models: complete partial orders, domains, least fixed points, partiality.
Domain construction: compound domains, recursive domain construction, limit domains.
IA082 Physical concepts of quantum information processing
zk 2/0 2 kr., jaro
- RNDr. Daniel Reitzner, PhD. - doc. Mgr. Mário Ziman, Ph.D.
- Prerequisities:
PV275 || SOUHLAS
- Goals: Introduction to quantum physics and quantum information theory.
- Learning outcomes:
After this course students should:
understand basic principles of quantum physics;
apply the learned concepts in the subsequent study of quantum information theory;
self-study quantum theory books. - Syllabus:
1. Security and computation with photons
- photon's polarization and polarizers, Vernam cipher, quantum key "distribution" protocol B92, polarizing beam-splitter, √NOT logic gate,
2. Quantum interference and superposition - Mach-Zender interferometer, concept of quantum state, quantum probabilities and amplitudes, Hilbert space and operators,
3. Measuring quantum properties - description of quantum measurement devices (POVM), tomography of polarization, uncertainty relations, no information without disturbance
4. Hydrogen atom - emission spectrum, Bohr's model, position and momentum, quantum solution, Zeeman effects, spin of electron,
5. Schrodinger equation - time and evolution, unitary operators, energy conservation and system's Hamiltonian,
6. Quantum bit - two-level quantum system (polarization and spin-1/2), Stern-Gerlach experiments, Bloch sphere, orthogonality and information, no-cloning theorem, quantum NOT gate, qubit implementations
7. Quantum sources and randomness - mixed states, quantum commpression, von Neumann entropy, capacity of noiseless quantum channel, randomness sources, min-entropy
8. Einstein-Podolski-Rosen paradox - composite quantum systems, tensor product, quantum steering, EPR paradox, local hidden variable model, CHSH inequalities, experiments and loopholes
9. Quantum one-time pad protocols - one-time pad, super-dense coding and teleportation
10. Quantum entanglement - correlated and separable states, definition of entanglement, entanglement distilation,
11. Quantum cryptography - QKD protocols BB84, E91, no-quantum bit commitment theorem, quantum secret sharing protocols,
12. Elementary particles - fermions and bosons and tensor products, standard model, Higg's boson
IA085 Satisfiability and Automated Reasoning
zk 2/1 4 kr., jaro
- RNDr. Martin Jonáš, Ph.D.
- Goals:
At the end of the course, students should:
- have working knowledge of propositional logic and first-order logic,
- be able to express real-world problems in a suitable logical formalism,
- be able to explain principles, algorithms, and underlying theoretical concepts of modern satisfiability solvers and theorem provers,
- be able to apply to asses what kind of tool is relevant for their problem and apply an existing satisfiability solver or theorem prover to the problem,
- understand strengths and weaknesses of existing satisfiability solvers and theorem provers. - Learning outcomes:
At the end of the course, students should:
- have working knowledge of propositional logic and first-order logic,
- be able to express real-world problems in a suitable logical formalism,
- be able to explain principles, algorithms, and underlying theoretical concepts of modern satisfiability solvers and theorem provers,
- be able to apply to asses what kind of tool is relevant for their problem and apply an existing satisfiability solver or theorem prover to the problem,
- understand strengths and weaknesses of existing satisfiability solvers and theorem provers. - Syllabus:
Propositional satisfiability: syntax and semantics of propositional logic
, encoding of real-world problems, historical and modern satisfiability decision procedures, design and usage of modern satisfiability solvers, preprocessing techniques, proofs of unsatisfiability.
Satisfiability Modulo Theories: syntax and semantics of first-order logic without quantifiers; first-order theories relevant for description of systems, their decidability and complexity; CDCL(T) algorithm and theory solvers for selected first-order theories.
Reasoning with Quantifiers: syntax and semantics of first-order logic with quantifiers; encoding of real-world problems; first-order resolution, superposition, E-matching; implementation of proof search in modern theorem provers; quantifier elimination; quantifier instantiation.
Interactive Theorem Proving: formal foundations; practical usage of a state-of-the art theorem prover.
IA101 Algorithmics for Hard Problems
zk 2/0 2 kr., podzim
- prof. RNDr. Ivana Černá, CSc.
- Prerequisities: Experience with basic techniques for design and analysis of algorithms (recursion, dynamic programming, greedy approach) as well as with basic data structures and algorithms are required.
- Goals: The course expands on courses IB002 Algorithms and Data Structures I and IV003 Algorithms and Data Structures II. It focuses on design of algorithms for hard computing tasks. The course systematically explains, combines, and compares the main possibilities for attacking hard algorithmic problems like randomization, heuristics, approximation and local search.
- Learning outcomes:
After enrolling the course students are able to :
- identify algorithmically hard problems,
- identify applications where pseudopolynomial, approximative, randomized, and heuristic algorithms can be succesfully used,
- actively used published pseudopolynomial, approximative, and randomized algorithms and correctly interpret their outcomes,
- design simple pseudopolynomial, approximative, and randomized, algorithms,
- experimentally evaluate heuristic algorithms. - Syllabus:
Deterministic approaches: pseudo-polynomial-time algorithms,
parametrized complexity, branch-and-bound, lowering worst case
complexity of exponential algorithms.
Approximation approaches: concept of approximation algorithms, classification of optimization problems, stability of approximation, inapproximability, algorithms design. Linear programming as a method for construction of approximative algorithms.
Randomized approaches: classification of randomized algorithms and design paradigms, design of randomized algorithms, derandomization, randomization and approximation.
Heuristics: local search, simulated annealing, genetic algorithms.
IA158 Real Time Systems
zk 1/0 2 kr., jaro
- doc. RNDr. Tomáš Brázdil, Ph.D.
- Prerequisities: Basic programming skill in C is expected.
- Goals: At the end of the course students should: know specific aspects of real-time systems; understand main problems of the design of real-time systems and know some solutions; be able to use formal reasoning about real-time systems.
- Learning outcomes: At the end of the course student will have a comprehensive knowledge of real time systems and related areas. Will be able to distinguish basic types of real-time systems. Will be aware of typical design errors in real-time and embedded systems and their standard solutions. Will understand fundamental real-time scheduling and resource management algorithms. Will have a basic knowledge of implementation details of these algorithms in standard programming environments.
- Syllabus:
Real-time aspects of embedded systems; examples of real-time systems. Soft and hard real-time systems.
Real-time scheduling: periodic and aperiodic tasks, priority-driven scheduling, resource access control.
Basic information about real-time operating systems and programming.
IA159 Formal Methods for Software Analysis
zk 2/0 2 kr., podzim
- prof. RNDr. Jan Strejček, Ph.D.
- Prerequisities:
IA169
- Goals:
At the end of this course, students should understand and be able to explain principles, advantages, and disadvantages of selected methods from the area of formal verification, namely model checking methods, abstraction, static analysis via abstract interpretation, and shape analysis;
make reasoned decisions about suitability of various methods for verification of specific systems; - Learning outcomes:
At the end of this course, students should understand and be able to explain principles, advantages, and disadvantages of selected methods from the area of formal verification, namely model checking methods, abstraction, static analysis via abstract interpretation, and shape analysis;
make reasoned decisions about suitability of various methods for verification of specific systems; - Syllabus:
Overview of formal verification methods.
LTL model checking of finite and infinite-state systems including partial order reduction.
Abstraction.
Counterexample-guided abstraction refinement (CEGAR).
Static analysis, abstract interpretation.
Shape analysis.
Software verification via automata, symbolic execution, and interpolation.
Property-Directed Reachability (PDR/IC3).
IA161 Natural Language Processing in Practice
k 1/1 2 kr., podzim
- doc. RNDr. Aleš Horák, Ph.D. - RNDr. Miloš Jakubíček, Ph.D. - RNDr. Marek Medveď - RNDr. Zuzana Nevěřilová, Ph.D. - RNDr. Adam Rambousek, Ph.D. - doc. Mgr. Pavel Rychlý, Ph.D. - RNDr. Vít Suchomel, Ph.D.
- Prerequisities: All students should have basic practical knowledge of programming in Python. Overview knowledge of the natural language processing field at the level of introductory courses such as IB030 Introduction to Natural Language Processing or PA153 Natural Language Processing is expected. The seminar is given in English. Task solutions can be in English, Czech or Slovak.
- Goals: The course participants will have the opportunity to learn about, test and experiment with advanced techniques of natural language processing (NLP) and to develop an understanding of the limits of those techniques. The course aims to introduce current research issues, and to meet in practice with particular programming techniques used in language technology applications.
- Learning outcomes:
After studying the course, the students will be able to:
- explain a selected NLP problem and list its main aspects;
- implement a basic or intermediate application for complex tasks in language processing, typically for Czech, Slovak, or English;
- create data resources (models, test sets) for a selected NLP problem and evaluate their assets;
- compare selected available tools for complex NLP tasks and apply them to chosen data resources with possible adaptations to particular purposes. - Syllabus:
The presented NLP problems will concentrate on practical problems connected with processing human-produced textual data. Particular topics include:
- Opinion mining, sentiment analysis
- Machine translation
- Parsing of Czech: Between Rules and Statistics
- Named Entity Recognition
- Building Language Resources from the Web (effective crawling, boilerplate removal, tokenisation, near duplicates identification)
- Language modelling
- Topic identification, topic modelling
- Extracting structured information from text
- Automatic relation extraction (hypernyms, synonyms, ...)
- Adaptive electronic dictionaries
- Terminology identification (keywords, key phrases)
- Anaphora resolution
- Stylometry
- Automatic language corrections
IA168 Algorithmic game theory
zk 2/0 3 kr., podzim
- doc. RNDr. Tomáš Brázdil, Ph.D.
- Prerequisities: basic linear algebra, basic probability theory (mostly discrete probability), elementary complexity theory, some calculus
- Goals: In recent years, huge amount of research has been done at the borderline between game theory and computer science, largely motivated by the emergence of the Internet. The aim of the course is to provide students with basic knowledge of fundamental game theoretic notions and results relevant to applications in computer science. The course will cover classical topics, such as general equilibrium theory and mechanism design, together with modern applications to network routing, scheduling, online auctions etc. We will mostly concentrate on computational aspects of game theory such as complexity of computing equilibria and connections with machine learning.
- Learning outcomes: Student knows the basics types of models of games and algorithms for searching winning strategies.
- Syllabus:
Basic definitions: Games in normal form, dominant strategies, Nash
equilibria in pure and mixed strategies, existence of Nash equilibria, basic examples
Computing Nash equilibria: Lemke-Howson algorithm, support enumeration, sampling methods, PPAD-completeness of Nash equilibria,
Quantifying the inefficiency of equilibria and related games: Congestion and potential games, price of anarchy and price of stability, routing games, network formation games, load balancing games
Learning in games: Regret minimization algorithms, correlated equilibria and connection to learning in games, regret minimization in routing games
Auctions and mechanism design: First price auctions, Vickrey auctions, truthfulness, Vickrey-Clark-Groves mechanism, Bayesian games, Bayesian Nash equilibria, formal framework for mechanism design, revelation principle, auctions on Google
Games with multiple moves: Games in extensive form, games on graphs, Markov decision processes, stochastic games
IA169 Model Checking
zk 2/1 3 kr., jaro
- prof. RNDr. Jan Strejček, Ph.D.
- Prerequisities:
(! IV113 ) && (! NOW ( IV113 ))
User-level familiarity with Unix/Linux operating system. Basic programming skills (Python). Some degree of abstract math reasoning. - Goals: The student will understand the necessary theoretic background as well as acquire hands-on experience with relevant tools for bug finding and formal verification techniques. Students will get acquainted with a number of concrete software verification tools for analysis of concurrent systems, real-time systems, hybrid systems, cryptographic systems, and systems with probabilities.
- Learning outcomes:
Students will:
be aware of fundaments of black-box testing;
understand priciples of deductive verification;
understand the theory and application of model checking;
have hand-on experince with a couple of verification tools. - Syllabus: This course will provide the necessary theoretic background as well as hands-on experience with relevant tools for bug finding and formal verification techniques. The core topics of this course will include testing, symbolic execution, abstract interpretation, static analysis, theorem proving, automated formal verification as well as an introduction to model-based verification. Students will get acquainted with a number of concrete software verification tools for analysis of concurrent systems, real-time systems, hybrid systems, cryptographic systems, and systems with probabilities. An introductory insight into security standards like Common Criteria for Information Technology Security Evaluation and FIPS 140 shall be provided as well.
IA174 Fundaments of Cryptography
zk 2/0 3 kr., podzim
- RNDr. Petr Novotný, Ph.D.
- Prerequisities: Grasp of basic concepts from discrete mathematics (e.g. groups, see the MB154 and MV008 courses). Awareness of basic aims and building blocks of cryptography, corresponding to the respective parts of the PV080 course.
- Goals: The course covers theoretical foundations of cryptography, ranging from encryption and hashing primitives to more modern topics such as post-quantum cryptography. We will learn why are the state-of-the-art cryptographic algorithms constructed in the way they are, and how to reason about their mechanics and security guarantees via the language of mathematics.
- Learning outcomes:
Upon a successful completion of the course, the student will be able to:
*Explain and understand the mechanics of basic primitives of both symmetric and asymmetric cryptography, including the underlying mathematics.
*Explain and understand the function, construction, and the use of cryptographic hash functions.
*Explain and understand cryptographic techniques for ensuring data authenticity and integrity, including digital signature schemes.
*Understand, at an abstract level, the purpose and foundations of post-quantum cryptography and zero-knowledge proofs, so as to be able to learn further details of these topics on her/his own.
*Understand possible weaknesses of cryptosystems and various trade-offs in their design.
*Analyse weaknesses of simple cryptosystems. - Syllabus:
Symmetric cryptography:
*Symmetric block ciphers: design principles and basic notions (boolean functions, random permutations, confusion, diffusion, non-linearity); design of iterated block ciphers, rounds, key schedules; AES; modes of operations of block ciphers.
*Symmetric stream ciphers: General principles, ChaCha cipher, relation to pseudorandom number generators.
Asymmetric cryptography:
*General principles and design elements, "reductions" to hard problems.
*RSA algorithm: math foundations (modular arithmetic, multiplicative Z_n^x groups, Euler's theorem, Chinese remainder theorem, extended Euclidean algorithm); RSA encryption, possible attacks, relationship to integer factorization.
*Cryptography based on discrete logarithm (DL): refresher of basic group theory; DL in (Z_n )^x groups, Diffie-Hellman key exchange, DSA; discrete logarithm on elliptic curve groups, elliptic curve cryptography, ECDSA.
Cryptographic hash functions: Design principles, Merkle–Damgård construction, sponge construction, collision-resistant CHFs, Keccak CHF, attacks against CHFs.
Data integrity, message authentication, signatures (2 lectures):
*Message authentication codes (MACs): integrity, authenticity, construction from block ciphers, construction from hash functions; authenticated encryption, AEAD.
*Digital signatures: non-repudiation, signature schemes (RSA, DSA, ElGamal), attacks against dig. signature schemes, blind signatures.
*Integrity of data structures: hash trees, their use in Bitcoin.
Post-quantum cryptography: Quantum-computer attacks on RSA and discrete logarithm schemes, overview of candidate techniques for post-quantum cryptography, standardization of post-quantum cryptography.
Zero-knowledge proofs: mathematical foundations, connection to complexity classes, illustration on concrete problems.
IA175 Algorithms for Quantitative Verification
zk 2/1 4 kr., podzim
- prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D.
- Prerequisities:
IB005
acquaintance with basic probability theory - Goals:
The course introduces
(1) several fundamental mathematical structures for modelling dynamic systems, where quantities such as probability, time, or cost are essential, and
(2) algorithms for their analysis, in particular their verification with respect to typical types of correctness requirements.
Besides, the course offers also a more practical experience with modelling and analysis tools. - Learning outcomes:
The student can:
- model systems and their properties in appropriate mathematical formalisms
- can analyze the systems with respect to the properties using the discussed algorithms
- can choose appropriate algorithms for the analysis
- can design modifications of these algorithms and can rigorously argue about their correctness, complexity, and (dis)advantages - Syllabus:
Motivation: verification, temporal logics, quantitative systems
Timed automata: modelling, semantics; reachability, region construction; zones, timed CTL
Markov chains: reachability, rewards, probabilistic LTL and CTL
Markov decision processes: modelling, semantics; reachability (linear programming, value iteration, strategy iteration; interval iteration, bounded real-time dynamic programming), rewards, probabilistic LTL and CTL; reinforcement learning and approximate dynamic programming; multi-objective optimization
Stochastic games: reachability (quadratic programing, value iteration, strategy iteration)
Systems with continuous time and space
IV003 Algorithms and Data Structures II
zk 2/2 3 kr., jaro
- prof. RNDr. Ivana Černá, CSc.
- Prerequisities:
( IB002 || program ( PřF:N - MA )) && ! IB108
The course expands on courses IB002 Algorithms and Data Structures I. - Goals: The course expands on the introductory course Algortihm Design I. It presents algorithmic concepts without their direct connection to any particular programming language. The aim is to introduce students into design and analysis of advanced algorithms. The course presents advanced techniques of algorithm analysis and a wide spectrum of strategies together with algorithms built up on these strategies. Students are introduced into new data structures which are displayed in a row with algorithms based on them.
- Learning outcomes:
After enrolling the course students are able to:
- actively use and modify advanced graph and string algorithms,
- actively used advanced techniques for designing algorithms (dynamic programming, greedy techniques) for designing algorithms, expain their specific properties and limits,
- actively used and modify advanced dynamic data structures and use them for designing effective algorithsm,
- analyze time complexity and prove correctness of algorithms. - Syllabus:
Advanced design and analysis techniques: dynamic programming, greedy strategies,backtracking. Amortized analysis.
Advanced data structures: binomial and Fibonacci heaps, data structures for disjoint sets.
Graph algorithms: Single-Source Shortest Paths (The Bellman-Ford algorithm). All-Pairs Shortest Paths (Shortest paths and matrix multiplication, The Floyd-Warshall algorithm, Johnson's algorithm for sparse graphs). Maximum Flow (The Ford-Fulkerson method, The Push-Relabel method). Maximum bipartite matching.
String matching: the naive string-matching algorithm, Karp-Rabin algorithm, string matching with finite automata. The Knuth-Morris-Pratt algorithm.
IV010 Communication and Parallelism
zk 2/0 2 kr., jaro
- prof. RNDr. Luboš Brim, CSc.
- Goals:
The goal is to acquire basic skills that are used for formal specification and analysis of communicating systems, including the theoretical background.
By the end of the course the students should be able: to develop simple specifications and implementations of communicating systems in CCS, to check formally their equivalence and to understand various kinds of process equivalences and their limitations. - Learning outcomes: By the end of the course the students should be able: to develop simple specifications and implementations of communicating systems in CCS, to check formally their equivalence and to understand various kinds of process equivalences and their limitations.
- Syllabus:
Introduction, overview of models for concurrent systems. Modelling
communication, examples of communicating systems.
Language of CCS: synchronization, actions and transitions, internal communication, semantics of CCS.
CCS with value passing and its translation into pure CCS.
Equational laws and their applications: classification of combinators, expansion theorem, dynamic and static laws.
Bisimulation and equivalence: Strong bisimulation, weak bisimulation, weak congruence, basic properties, solving equations, other equivalences, finite state processes.
Temporal properties of processes.
IV022 Principles of elegant programming
zk 2/0 2 kr., podzim
- prof. RNDr. Luboš Brim, CSc.
- Goals: Programs are typically constructed from smaller ones, each realizing a particular function. The ability to design small perfect programs seems to be the core skill of every serious programmer. The goal is to get acquainted with methods for designing and verifying small and, at the same time, elegant sequential algorithms. The students acquire basic techniques and principles that can contribute to this goal.
- Learning outcomes: By the end of the semester, students should be able to develop small sequential algorithms and prove their correctness.
- Syllabus:
Garded command language. Skip and abort commands, composition, alternative
command, iterative command.
Verification of programs, proof outlines, verification rules for sequential composition, alternative, and loop commands. Array manipulation.
Constructive verification of programs, basic principles and strategies, developing loops from invariants and bounds, developing invarinats.
Examples of program development. Deriving of efficient algorithms, Searching and sorting.
IV029 Introduction to Transparent Intensional Logic
zk 2/0 2 kr., podzim
- prof. RNDr. Marie Duží, CSc.
- Prerequisities: Foundations of the first-order predicate logic
- Goals:
Students enrolled in the course will obtain knowledge on a rather new discipline Logical semantics and knowledge representation that belongs to the fundamentals of artificial intelligence.
Adequate analysis of the meaning of natural language expressions consists in discovering algorithmically structured procedure known as TIL construction encoded by the expression. The analysis should be as fine-grained as possible so that the inference machine is neither over-inferring nor under-inferring. At the same time it is necessary to formalize the results of an analysis so that they are computationally tractable. - Learning outcomes: The students will learn to solve relevant problems in such a way that undesirable paradoxes and inconsistencies are avoided. The formalized analysis can be used in knowledge-base systems of artificial intelligence, in automatic translation, in multi-agent systems, etc.
- Syllabus:
Deductive reasoning as the subject of logic
Paradoxes stemming from a coarse-grained analysis of premises
Frege-Church semantic schema; denotational vs. procedural semantics
Transparent Intensional Logic; constructions as procedures
Simple theory of types comprising non-procedural objects; epistemic base; intensions and extensions
Ramified theory of types comprising procedural objects
Extensional, intensional and hyperintensional context
Extensional rules: Leibniz’s law and existential quantification into
The problem of non-existence and modalities
Ontology as a logic of intensions; conceptual analysis
Logic of attitudes; hyperintensional knowledge representation
Dynamic reasoning and tense logics
Communication of agents in a multi-agent system
IV064 Information Society
zk 2/0 2 kr., podzim
- prof. RNDr. Jiří Zlatuška, CSc.
- Prerequisities:
! CORE012 && !( NOW ( CORE012 ))
- Goals: The goal of this course is to introduce the nature of wider impacts of Informatics on the society.
- Learning outcomes: At the end of this course students will be able to understand and explain the nature of wider impacts of Informatics on the society; to use information about events characteristic for the impact of the information revolution; to draw parallels with the industrial revolution; to explain and characterize events and processes associated with the formation of information society; to better comprehend the role of the information and communication technologies in the society not only as technical tools, but also as a phenomenon enabling social processes transformation; to understand newly emerging organizational structures both in business and in e-government resulting from intensification of the information processing; to understand the nature of innovative processes associated with informatics and to thing through the consequences of differencec from prevailing older paradigms; to grasp idea of the structure of policies assiciated with information society; to present thoughful analyses of nontechnical impacts of widespread availability and use of services based on information processing; to think through and creatively develop designs of new possible applications; to develop motivation for future theoretical or practical work in this area.
- Syllabus:
This course deals with the impact of Information Technologies on society,
with the nature of computer (information) revolution,
and the advent of an information society.
Informatics in historical perspective.
Computer revolution.
Productivity paradox.
The Internet and WWW.
Digital economy.
Network economy and virtual communities.
Organizational and company structure.
Organizational transformation.
Teleceoomunications and information infrastructure.
Legal aspects of an information society.
Ethical problems.
Riskc of computing technology.
Social impacts.
There is a seminar IV057 Seminar on Information Society accompanying this course for students interested in presenting up-to-date material based on literature on an information society.
IV074 Laboratory of Parallel and Distributed Systems
z 0/0 2 kr., podzim
- prof. RNDr. Jiří Barnat, Ph.D. - prof. RNDr. Ivana Černá, CSc.
- Prerequisities:
souhlas
Applicants should 1) be able to work independently 2) have interest in long-term projects (several semesters) 3) have working knowledge of English 4) be able to work in a team. The enrollment must be approved by the laboratory head (J. Barnat). - Goals: The goal of this course is to let students participate on research activities.
- Learning outcomes: On successful completion of the course students - will have practical experience with active research - should be able to read and understand scientific papers - should be able to employ gathered information to formulate and prove their own hypotheses within the relevant context.
- Syllabus: Laboratory of Parallel and Distributed Systems (ParaDiSe) is a team project focused on the development of parallel methods and tools for the design and analysis of complex systems. Students meet regularly with senior researchers to discuss research problems related to their research topics.
IV074 Laboratory for Parallel and Distributed Systems
z 0/0 2 kr., jaro
- prof. RNDr. Jiří Barnat, Ph.D. - prof. RNDr. Ivana Černá, CSc.
- Prerequisities:
souhlas
Applicants should 1) be able to work independently 2) have interest in long-term projects (several semesters) 3) have working knowledge of English 4) be able to work in a team. The enrollment must be approved by the laboratory head (J. Barnat). - Goals: The goal of this course is to let students participate on research activities.
- Learning outcomes: On successful completion of the course students - will have practical experience with active research - should be able to read and understand scientific papers - should be able to employ gathered information to formulate and prove their own hypotheses within the relevant context.
- Syllabus: Laboratory of Parallel and Distributed Systems (ParaDiSe) is a team project focused on the development of parallel methods and tools for the design and analysis of complex systems. Students meet regularly with senior researchers to discuss research problems related to their research topics.
IV105 Bionformatics seminar
k 0/1 1 kr., podzim
- Ing. Matej Lexa, Ph.D. - Mgr. Monika Čechová, Ph.D.
- Prerequisities: Those who sign up for this interdisciplinary course should be able to read and comprehend a scientific paper or book chapter written in English. Alternatively computational tools in bioinformatics will be studied (deeper knowledge of algorithm design and programming will allow the particular student to focus more on the biological side of the studied problems or vice versa). Students of non-biological fields should be concurrently enrolled in, or have previously passed IV107 Bioinformatics I. Alternatively they may frequent the course with the consent of the teacher.
- Goals: A bioinformatics course opening up the world of genes and molecules to students via external lecturers and student presentations organized as a journal club.
- Learning outcomes: Students will gain insight into problems studied in bioinformatics; they will practice presentation and discussion techniques in front of an audience.
- Syllabus:
The students will chose publications to study recent methods in genomic sequence analysis (using suggested journal articles or other material approved by the teacher) covering
Nanopore DNA sequencing methods
Tools and algorithms for processing and analysis of long/nanopore reads
Genomic and biological studies based on nanopore sequencing
IV106 Bioinformatics seminar
k 0/1 1 kr., jaro
- Mgr. Monika Čechová, Ph.D. - Ing. Matej Lexa, Ph.D.
- Prerequisities: Those who sign up for this interdisciplinary course should be able to listen to lectures and to read and comprehend a scientific paper or book chapter written in English. Deeper knowledge of algorithm design and programming will allow the particular student to focus more on the biological side of the studied problems or vice versa. Students of non-biological fields should be concurrently enrolled in, or have previously passed IV107 Bioinformatics I. Alternatively they may frequent the course with the consent of the teacher.
- Goals: Long-term the seminar covers "Biological (molecular) and biomedical data analysis". Individual runs may focus on a specific subtopic.
- Learning outcomes: Students will gain insight into problems studied in bioinformatics; they will practice presentation and discussion techniques in front of an audience.
- Syllabus: - Introduction to deep learning in bioinformatics - Lectures of invited lecturers covering the same topic - Students will chose a publication from this area to present in class in a 'journal club' format
IV107 Bioinformatics I
zk 2/1 2 kr., podzim
- Ing. Matej Lexa, Ph.D.
- Prerequisities: This is an entry course into the area of bioinformatics for students of non-biological disciplines, there are no prerequisites.
- Goals: This course will lead the students into the fascinating world of molecules, genes and proteins. Currently, bioinformatics is going through a period of unusual growth. Abilities to think and act as a bioinformatician (to work with large biological datasets using modern computer science methods) are needed in many areas of science and applied disciplines, especially biology, medicine and chemistry.
- Learning outcomes: After taking the course, the students will understand basic principles of molecular biology; they will be familiar with important biological problems that can be best handled by computers; they will understand and be able to choose basic computational methods for handling molecular data.
- Syllabus:
The history and subject of bioinformatics
Basics of molecular biology
Organization of living matter
DNA structure and function
Protein structure and function
Evolution of genes and proteins
Bioinformatic data
Data sources
Common data types
Public sequence data and their accessibility
DNA sequence analysis
Computer exercises: Data sources, similarity search, visualization of molecules
Protein sequence analysis
Structural and functional data
Similarity searches and scoring
Other types of data and their analysis
Expression data
Protein digests and mass spectra
Literature data analysis
IV108 Bioinformatics II
zk 1/1 2 kr., podzim
- Ing. Matej Lexa, Ph.D.
- Prerequisities: IV107 Bioinformatics I or consent of the teacher (not needed for biology students).
- Goals: Introduction to selected algorithms and methods of analysis used in bioinformatics.
- Learning outcomes:
At the end of the course, the students will:
understand the inner workings of selected algorithms, their advantages and disadvanteges, including knowledge of recent alternatives
be able to work with 3-D models of molecules
be able to evaluate or design methods for solving current problems in bioinformatics
understand the principles of existing DNA sequencing methods and processing sequencing data - Syllabus:
Algorithms for sequence analysis
Algorithms for prediction and analysis of structural data
Biological language
Next-generation DNA sequencing methods and data processing
Understanding protein cleavage and mass spectra
Expression profile and promoter analysis
IV109 Modeling and Simulation
zk 2/1 3 kr., jaro
- doc. Mgr. Radek Pelánek, Ph.D.
- Goals: The course offers a wide overview of computational modeling and gives students a practical experience with computational modeling.
- Learning outcomes: At the end of the course students will be able to: describe main concepts of complex systems (particularly "feedback loops"); explain main principles and applications of computational modeling; compare modeling approaches; describe well-know case studies in computational modeling; create a computational model.
- Syllabus:
Introduction, history, role of modeling and simulation in research,
applications. Computational models.
Complex systems, system thinking, feedback loops.
System dynamics approach, examples (demographics, Limits to growth).
Agent based modeling: basic principles, cellular automata, decentralized systems.
Game theory, models of cooperation. Models of adaptation (genetic algorithms, neural networks).
Modeling of networks: examples of networks and their properties, models of networks.
Analysis and evaluation of models.
Application of modeling from different areas (e.g. economics, traffic, epidemiology, biology).
IV110 Bioinformatics project I
k 1/1 2 kr., podzim
- Ing. Matej Lexa, Ph.D.
- Prerequisities: IV107 Bioinformatics I plus elementary programming skills (e.g. UNIX + C/C++/Java + Perl/Python) or teacher's consent
- Goals:
In this course the students will:
be able to select appropriate bioinformatic tools for a given problem
be able to carry out independent analysis of bioinformatic data
present their results to their colleagues - Learning outcomes:
In this course the students will:
be able to select appropriate bioinformatic tools for a given problem
be able to carry out independent analysis of bioinformatic data
present their results to their colleagues - Syllabus:
Discussion of interesting problems to solve
Preparation of student proposals
Programming phase
Student mini-conference
IV111 Probability in Computer Science
zk 2/2 3 kr., podzim
- doc. RNDr. Vojtěch Řehák, Ph.D.
- Prerequisities: Knowledge of basic discrete mathematics (e.g. as presented in the course IB000).
- Goals: At the end of the course student should have a broad knowledge and an ability of independent study of problems based on the probability theory and its computer science applications. Will be able to apply the results of the probability theory in practical examples. Should be able to learn independently new problems requiring knowledge of probability theory. Will be able to characterise basic principles of data compression and error correction. Should be able to apply information theory results in practice.
- Learning outcomes: Student is able: to define basic terms of the mentioned topics (e.g., random variable, expectation, variance, random process, Markov chain, channel capacity, code rate); to explain meaning on the terms on practical examples; to solve simple examples e.g. using linearity o expectation; to provide basic analysis on both discrete- and continuous-time Markov chains; to compute (conditional) expectation, mutual information, and entropy random variables with given probability distribution; to demonstrate basic proof mentioned during lectures.
- Syllabus:
Probability. Discrete probabilistic space.
Random variable and its applications. Expectation and variation.
Markov and Chebyshev inequalities. Chernoff bounds. Weak and strong law of large numbers.
Random processes. Markov processes.
Entropy. Information.
Applications in computer science (information theory, coding theory, cryptography etc).
IV114 Bioinformatics and Systems Biology Project
k 0/1 2 kr., podzim
- Ing. Matej Lexa, Ph.D.
- Prerequisities: The students should have finished IV107 Bioinformatics I, be acquainted with NGS/sequencing data processing tools and have elementary programming skills in any programming language/environment (optimally UNIX with C/C++/Java and Perl/Python) or consent of the lecturer
- Goals:
In this course the students will:
get acquainted with DNA nanopore sequencing
be able to select appropriate bioinformatic tools for a given problem
be able to carry out independent analysis of bioinformatic data
present their results to their colleagues - Learning outcomes:
In this course the students will:
get acquainted with DNA nanopore sequencing
be able to select appropriate bioinformatic tools for a given problem
be able to carry out independent analysis of bioinformatic data
present their results to their colleagues - Syllabus:
Familiarization with DNA sequencing using minION technology
Preparation of student proposals in pairs (selection of material for sequencing; preparation of bioinformatic tools and pipelines)
Analysis phase (DNA sequencing and data collection; data processing by filtration, mapping and assembly; visualization)
Student mini-conference and optional participation in paper writing (depending on quality of results)
IV115 Parallel and Distributed Laboratory Seminar
z 0/2 2 kr., podzim
- prof. RNDr. Jiří Barnat, Ph.D. - RNDr. Petr Ročkai, Ph.D.
- Prerequisities:
souhlas
Ability of self-education by reading latest scientific papers focused on modeling and verification of complex systems. - Goals: Students acquire experience with preparing presentations of their own research work and should be able to actively participate in research activities of the ParaDiSe laboratory.
- Learning outcomes: Experience with presentation of research results to adequately educated audience.
- Syllabus: Discussion topics and papers to be studied and presented are specified during the first two weeks of semester.
IV115 Parallel and Distributed Laboratory Seminar
z 0/2 2 kr., jaro
- prof. RNDr. Jiří Barnat, Ph.D. - RNDr. Petr Ročkai, Ph.D.
- Prerequisities:
souhlas
Ability of self-education by reading latest scientific papers focused on modeling and verification of complex systems. - Goals: Students acquire experience with preparing presentations of their own research work and should be able to actively participate in research activities of the ParaDiSe laboratory.
- Learning outcomes: Experience with presentation of research results to adequately educated audience.
- Syllabus: Discussion topics and papers to be studied and presented are specified during the first two weeks of semester.
IV119 Seminar on Discrete Mathematical Methods
k 0/2 2 kr., jaro
- prof. RNDr. Petr Hliněný, Ph.D. - prof. RNDr. Daniel Kráľ, Ph.D., DSc.
- Prerequisities: Basics of undergraduate mathematics (IB000 is enough).
- Goals: The aim of this seminar is to introduce interested students into the beauties of mathematics and of clean mathematical proofs. This will teach students "mathematical thinking" - to understand math definitions, statements, and proofs in their full depth, and to make their own new proofs in all areas of mathematics and theoretical computer science.
- Learning outcomes: After finishing this seminar, successful students should be able to understand presented mathematical proofs in their full depth, and to make their own new proofs in areas of mathematics and theoretical computer science.
- Syllabus:
Selected nice topics from "Proofs from THE BOOK"; TBA each year.
Number theory, Combinatorics, Combinatorial geometry, Graph theory.
IV123 Informatics-Driven Future
zk 2/0 2 kr., podzim
- prof. RNDr. Jozef Gruska, DrSc.
- Prerequisities: There are no special technical requirements. Main requirement is a deeper interest to know the expected role of Informatics for society in future, , as well as its main challenges and potential
- Goals: Exponentially fast developments in Informatics, especially in information storing, transmission and processing driven technologies, and in artificial intelligence, create potential for enormous impacts on society. The impact that has potential to be very positive, but also very negative, even historical. Moreover, due to that development, what can be nowadays expected as to happen in the next 50-100 years, in most of the areas of society, especially in science, technology, health care,...., if the current rate of development is sustained, can happen actually already within next 20-40 years. The goal of the course is to provide a visionary and thoughts-provoking, but well grounded, analysis of the main developments that we can, reasonably, expect, and why, in the (very) near future. Especially due to the development in all information processing and communication driven technologies, nanotechnologies, genetics, non-biological (artificial) intelligence and in fights with natural death and in explorig intelligence as a commodity. Informatics, once properly understood and developed%and sufficiently broadly and deeply understood, is to play at that a key role. Merits of the favorable future, but also ways to avoid perils, if possible, will also be discussed. The course should be of interest and importance to all those interested to find out the frameworks, tools, tasks and main challenges they and society will face in the (already quite near) future. To understand that should be for anyone not only very interesting, but actually much needed for knowing how to prepare oneself in the best way for the expected long future carrier in enormously fast changing frameworks. Contents: 1. Introduction: Why and how to foresee future? Main megachallenges. 2. Evolution - from biological to non-biological one and to their merge. 3. Exponential acceleration of all information-driven technologies. 4. New perception of Scientific Informatics and its grand challenges. 5. Impulses and roads to a new perception of Informatics 6. Technological and Applied Informatics and their grand challenges. 7. New, Informatics-driven, methodology and its grand challenges. 8. Developments in the understanding and simulation of human brains. 9. GNR-revolution - Artificial intelligence and robotics,aibeings 10. GNR revolution - Genetics and Nanotechnologies. 11. Singularity: merge of bio- and non-bio-intelligence-merits/perils. 12. Longevity - Can we fight death? Can we make life enjoyable till/after 150?!