# Study Programmes and Branches of Master Studies

The majority of fields of study are traditionally offered in two forms: full-time and combined studies. More information about the forms of study can be found on the following pages.

## Study Programme *Computer Science*

**Artificial
Intelligence**

*Form of study*: full-time

*Possible acceptance without taking the entrance examination, for
requirements, see Admission Requirements for
Master's Programmes in English*.

*Outline of study*: The study branch
Artificial Intelligence provides an education in the area of theoretical and
applied knowledge for the design of intelligent systems in various areas
including data analysis, automated problem solving, and robotic applications. An
emphasis is put on a deep understanding of formal theoretical foundations and
their practical applicability. Students will gain knowledge about the design of
efficient data structures; about the formal modelling of problems using
techniques of mathematical logic and probability theory; about algorithms
(classical and nature-inspired) for problem solving, the control of autonomous
agents, machine learning, and data mining; and about complexity analysis of
computational methods. Students will learn how to apply these techniques and how
to extend them both to abstract (data) and physical (robotic) worlds in
single-agent and multi-agent environments. The study branch Artificial
Intelligence can be studied in three core areas: intelligent agents, machine
learning, and robotics.

*Prospects for graduates*: Graduates can
apply and further extend techniques for the design of intelligent systems,
including knowledge modelling and formal modelling of complex systems by means
of mathematical logic and probability theory, automated problem solving,
planning and scheduling, control of autonomous agents (both virtual and
physical), machine learning, and data mining. They are also able to analyse and
formally model a complex decision problem, propose an appropriate solving
technique, and implement it. Graduates can work in research and development in
either academia or industry in any position requiring logical reasoning,
analytical capabilities, an algorithmic approach, and the exploitation of modern
methods of computer science (declarative and nature-inspired
programming).

*Details of study:*

**Computational Linguistics**

*Form of study*: full-time

*Possible acceptance without taking the entrance examination, for
requirements, see Admission Requirements for
Master's Programmes in English*.

*Outline of study*: The aim of the
Computational Linguistics programme is prepare students for research in the area
of natural language processing and the development of applications dealing with
both written and spoken language. Examples of such applications are systems of
information retrieval, machine translation, grammar checking, text summarization
and information extraction, automatic speech recognition, voice control, spoken
dialogue systems, and speech synthesis.

*Prospects for graduates*: The graduate
student is an expert in the application of state-of-the-art statistical as well
as rule-based methods in the area of natural language processing. The student is
prepared for doctoral studies in this area and for development of software
applications of natural language processing such as information retrieval,
question answering, summarization and information extraction, machine
translation, automatic construction of dictionaries, speech processing (in Czech
and other natural languages). Given the general applicability of machine
learning and data-driven methods, the graduate is also well-equipped to use
these methods in other domains, such as finance, medicine, and other areas where
large quantities of both structured and unstructured data are analysed. The
graduate has also extensive programming skills.

*Details of study:*

**Computer Graphics and Game Development**

*Form of study*: full-time

*Possible acceptance without taking the entrance examination, for
requirements, see Admission Requirements for
Master's Programmes in English*.

*Outline of study*: This study branch
consists of two closely related specializations, Computer Graphics and Computer
Game Development. The Computer Graphics specialization offers training in
a wide range of visual sciences, including geometric modeling, rendering (image
synthesis) as well as the basics of image analysis and computer vision. The
Computer Game Development specialization focuses mainly on – apart from
computer graphics techniques – artificial intelligence and intelligent agent
systems, as well as on software engineering skills necessary for the development
of large-scale gaming projects. Both specializations place emphasis on general
programming skills, both at the system level closer to the hardware, as well as
at the higher level of modern programming languages.

*Prospects for graduates*: Graduates have
expertise in the design and development of graphical systems and computer games,
but they can work in any position which requires logical thinking, analytic and
algorithmic approaches or the use of methods of computer science. Depending on
the chosen specialization, graduates have a deep knowledge of computer graphics
and image analysis, and their expertise covers the development of large-scale
gaming projects, real-time applications, programming of portable devices, as
well as the foundations of artificial intelligence and computer graphics in the
context of computer games. Graduates can apply this knowledge to solve specific
practical tasks. They can work in research and development both in the private
sector and in academia.

*Details of study:*

**Discrete Models and Algorithms**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The study plans
Discrete Mathematics and Combinatorial Optimization and Mathematical Structures
in Computer Science provide advanced knowledge in the fields of applied
mathematics and computer science. An emphasize is put on up-to-date theoretical
and applied questions in the area. The study plans Optimization and Mathematical
Economics provide skills to solve difficult technical and economical problems
with the use of optimization methods and suitable methods from mathematical
economics.

*Prospects for graduates*: Graduates have
a broad range of possibilities to work in areas connected with applied
mathematics and computer science. Graduates are able to solve complicated
technical and economic decision problems. Solutions of these problems are based
on methods of mathematical optimization and on methods solving conflict
situations. A deep knowledge of modern mathematical methods enables the
graduate to design mathematical models in complicated economic situations. An
education in computer science provides skills to effectively implement the
solutions with the use of fast computers.

*Details of study:*

**Software and Data Engineering**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The study branch
Software and Data Engineering aims at expertise in the analysis, design and
development of complex software solutions, and systems focused on big data
processing. The portfolio of courses provided in the study covers a number of
technological platforms, from classic, web-based, to modern cloud and
distributed solutions. Required as part of the course is work on a large
software project where students apply not only theoretical knowledge and
technological skills but also team work abilities.

*Prospects for graduates*: The graduate
gains a deep knowledge of software and data engineering based on her/his
specialization. With the specialization Software Engineering the graduate is
able to analyse requirements for software solutions, to design architectures,
and to lead the development process. The specialization Software Development
prepares the graduate for leading a team of SW developers. The development of
internet applications is covered by the specialization Web Engineering. The
graduate of Database Systems is able to design schemas of databases and to
implement complex database applications. With the Big Data Processing
specialization the graduate is prepared for the role of data scientist with
abilities in data mining and related data analytics knowledge.

*Details of study:*

**Software
Systems**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The study branch
Software Systems puts an emphasis on system-oriented programming in one of three
focus domains. The System Programming domain focuses on coding the basic layers
of a computer system (middleware, operating system). In the Dependable Systems
domain, the curriculum deals with the systematic construction of systems with
high reliability, such as embedded and real-time systems. The High Performance
Computing branch introduces techniques for software development on high
performance computing systems (highly parallel systems, distributed systems,
clouds). All focus domains pay attention to both the programming tools and
methods and the associated architectural knowledge.

*Prospects for graduates*: Graduates have
an expertise in the team development of software systems, their analysis,
design, implementation and deployment in the real world, including evaluation.
They acquire during their studies the ability to react flexibly to the continual
advancement of new technologies. They gain knowledge of database systems,
architectures and principles of system environments and software systems, modern
internet technologies, computer graphics etc.

*Details of study:*

**Theoretical Computer Science**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The goal of the study
programme Theoretical Computer Science is to prepare graduates with a deep and
sufficiently broad background in computer science which is based on mastering
its theoretical foundations. These foundations are extended by specialized
courses giving graduates a good overview of areas of computer science such as
complexity and computability, design and analysis of algorithms, and artificial
intelligence. This deep theoretical knowledge then allows graduates to more
quickly absorb new findings in the developing areas of computer science and to
actively contribute to the advancement of the state-of-the-art.

*Prospects for graduates*: Graduates may
work in research and development in the area of software production for
industrial applications, state administration, and in consulting companies. They
can work in any position that requires logical thinking, analytical
capabilities, an algorithmic approach to problem solving, and the exploitation
of modern methods of computer science (artificial intelligence, knowledge
representation, declarative programming, machine learning, biologically inspired
paradigms, and multi-agent systems). Graduates may also work at a university
and continue studies for a PhD. The education acquired also permits graduates
to work as programmers in any position.

*Details of study:*

## Study Programme *Mathematics*

**Financial and Insurance Mathematics**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: This programme
provides theoretical and applied education in financial and insurance
mathematics. A solid mathematical background provides the foundations for
developing disciplines of mathematical modelling in the insurance and banking
industries and other financial areas. The graduate is able to develop financial
and insurance products and analyse their profitability and risk.

*Prospects for graduates*: The graduate
has deeper knowledge of basic mathematical disciplines (mathematical analysis,
algebra) and special knowledge in the fields of probability and statistics,
stochastic processes, mathematical methods in finance, life and non-life
insurance, advanced financial management, risk theory, accounting, and modelling
with progressive systems (mathematica). The knowledge provides tools for
effective modelling of financial and insurance products, analysis of their
profitability and risk, and other characteristics important for effective
financial management.

*Details of study:*

**Mathematical
Analysis**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The programme in
Mathematical Analysis offers students advanced knowledge of traditional fields
of mathematical analysis (real function theory, complex analysis, functional
analysis, ordinary and partial differential equations). It is characterized by
a depth of insight into individual topics and an emphasis on their mutual
interconnections. Basic knowledge of these topics at an advanced level is
provided by the set of compulsory courses. Elective courses deepen the knowledge
of selected fields, especially those related to the topic of the diploma thesis.
Seminars provide contact with contemporary mathematical research. Mathematical
analysis has close relationships with other mathematical disciplines, such as
probability theory, numerical analysis and mathematical modelling. Students
become familiar with these relationships in some of the elective courses. The
programme prepares students for doctoral studies in mathematical analysis and
related subjects. Applications of mathematical theory, theorems and methods to
applied problems broaden the qualification to employment in a non-research
environment.

*Prospects for graduates*: The graduate
has acquired advanced knowledge in the principal fields of mathematical analysis
(real function theory, complex analysis, functional analysis, ordinary and
partial differential equations), understands their interconnections and
relations to other mathematical disciplines. He/she is able to apply advanced
theoretical methods to real problems. The programme prepares students for
doctoral studies but the knowledge and abilities acquired can be put to use in
practical occupations too.

*Details of study:*

**Mathematical Modelling in Physics and
Technology**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: Mathematical modelling
is an interdisciplinary field connecting mathematical analysis, numerical
mathematics, and physics. The curriculum is designed to provide excellent basic
knowledge in all these disciplines and to allow a flexible widening of
knowledge by studying specialized literature when the need arises. All students
take compulsory courses in continuum mechanics, partial differential equations,
and numerical mathematics. Students acquire the ability to design mathematical
models of natural phenomena (especially related to continuum mechanics and
thermodynamics), analyse them, and conduct numerical simulations. After passing
the compulsory classes, students get more closely involved with the physical
aspects of mathematical modelling (model design), with mathematical analysis of
partial differential equations, or with methods for computing mathematical
models. The grasp of all levels of mathematical modelling (model, analysis,
simulations) allows students to use modern results from all relevant fields to
address problems in physics, technology, biology, and medicine, surpassing the
scope of each individual field. Graduates can pursue academic or commercial
careers in applied mathematics, physics and technology.

*Prospects for graduates*: The graduate
has mastered methods and results in continuum mechanics and thermodynamics,
mathematical analysis of partial differential equations, and numerical
mathematics and is ready to widen his/her knowledge by studying specialized
literature. He/she can formulate questions regarding the physical substance of
natural phenomena, especially those related to the behaviour of fluids and solid
matter in the framework of classical physics, with applications to technology,
medicine, biology, geophysics, and meteorology. He/she can choose appropriate
mathematical models for such phenomena, perform its mathematical analysis, and
conduct numerical simulations with suitable methods. He/she can critically
analyse, evaluate, and tie in the whole modelling process. In simpler cases,
he/she is able to assess the errors in the modelling process and predict the
agreement between numerical results and the physical process. The graduate is
ready to work in interdisciplinary teams. He/she can pose interesting questions
in a format ready for mathematical investigation and use abstract mathematical
results for addressing applied problems.

*Details of study:*

**Mathematical
Structures**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The programme is
focused on extending a general mathematical background (algebraic geometry and
topology, Riemann geometry, universal algebra and model theory) to a deeper
knowledge in selected topics of algebra, geometry, logic, and combinatorics. The
aim is to provide sufficient general knowledge of modern structural mathematics
and to bring the students to the threshold of independent research activity. An
emphasis is put on topics taught by instructors who have reached worldwide
recognition in their fields of research.

*Prospects for graduates*: The graduate
has advanced knowledge of algebra, geometry, combinatorics and logic. He/she is
in close contact with the latest results of contemporary research in the
selected field. The abstract approach, extensiveness and intensiveness of the
programme result in the development of an ability to analyse, structure and
solve complex and difficult problems. The graduate may pursue an academic career
or realize him/herself in jobs that involve mastering new knowledge and the
control of complex systems.

*Details of study:*

**Mathematics for Information
Technologies**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: This
master's programme focuses on deeper knowledge of various mathematical
disciplines and their algorithmic aspects. The student can specialize either in
Mathematics for Information Security or in Computer Geometry.

Mathematics for Information Security focuses on deepening theoretical knowledge of number theory, probability theory, theory of error correcting codes, complexity theory, theory of elliptic curves, and computer algebra applied to some of these subjects. Attention is also given to practical aspects such as internet security, standards in cryptography, and legal aspects of data security.

Computer Geometry deepens theoretical knowledge in various algebraic and geometric subjects together with their applications in geometry of computer vision and robotics, computer graphics and image processing, optimization methods, and numerical linear algebra.*Prospects for graduates*: Graduates have
a broad knowledge of advanced algebra, geometry and logic, and can apply it to
solve advanced problems of mathematical information security and computer
geometry.

Graduates specializing in Mathematics for Information Security are well-acquainted with both present and prospective systems of data security and encryption, including their mathematical principles, practical applications and standards. The mathematical knowledge covers the theoretical background of cryptography in full breadth (number theory, self-correcting codes, complexity of algorithms, elliptic curves, one-way functions). Graduates also understand the structure of cryptographic protocols and are aware of basic legal aspects of data security.

Graduates specializing in Computer Geometry have a deep knowledge of algebra and geometry, subjects that are applied in information technologies processing geometric information and data.

The graduates are well-prepared for various jobs in information technologies where understanding and processing new knowledge and big data is needed. They are also prepared for an academic career.*Details of study:*

**Numerical and Computational Mathematics**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: This programme focuses
on the design, analysis, algorithmization, and implementation of methods for
computer processing of mathematical models. It represents a transition from
theoretical mathematics to obtaining practically useful results. An emphasis is
placed on the creative use of information technology and the production of
programming applications. An integral part of the programme is the verification
of methods employed. The students will study modern methods for solving partial
differential equations, the finite element method, linear and non-linear
functional analysis, and methods for matrix calculation. They will choose
elective courses according to the topic of their master’s thesis. They may
specialize in industrial mathematics, numerical analysis, or matrix
calculations.

*Prospects for graduates*: The graduate
has attained the knowledge needed for the numerical solution of practical
problems ranging from discretization through numerical analysis up to
implementation and verification. He/she can choose an appropriate numerical
method for a given problem, conduct its numerical analysis, and implement its
computation including analysis of the numerical error. The graduate can
critically examine, assess, and tune the whole process of the numerical
solution, and can assess the agreement between numerical results and reality.
He/she can carry out an analytical approach to the solution of a general
problem based on thorough and rigorous reasoning. The graduate is qualified for
doctoral studies and for employment in industry, basic or applied research, or
government institutions.

*Details of study:*

**Probability, Mathematical Statistics and
Econometrics**

*Form of study*: full-time

**for
requirements, see Admission Requirements for
Master's Programmes in English**

*Outline of study*: The programme is
targeted at students who wish to obtain theoretical and practical knowledge
about the mathematics of random events. It is primarily characterized by
a balance between rigorous mathematical theory, depth of insight into various
fields of the subject (probability, statistics, econometrics) and applications
in various areas. The students will obtain a general background by taking
compulsory courses in probability, optimization, statistical modelling and
random processes. They continue by taking elective courses to extend their
expertise and choose a specialization they would like to study more deeply. In
seminars, they learn to work independently as well as to collaborate on complex
projects. Great emphasis is placed on the development of independent analytical
thinking. Probability, statistics and econometrics have a close relationship to
other mathematical subjects (mathematical analysis, numerical mathematics,
discrete mathematics). Applications are inspired by real problems from
economics, medicine, technology, natural sciences, physics and informatics. The
primary objective of the programme is to prepare students for successful careers
in academia as well as in finance, telecommunications, marketing, medicine and
the natural sciences.

*Prospects for graduates*: The graduate is
familiar with mathematical modelling of random events and processes and its
applications. He/she understands the foundations of probability theory,
mathematical statistics, random process theory and optimization. His/her general
background has been extended to a deeper knowledge of random process theory and
stochastic analysis, modern statistical methods, or advanced optimization and
time series analysis. The graduate understands the substance of the methods,
grasps their mutual relationships, and is able to extend them actively and use
them. He/she knows how to apply theoretical knowledge to practical problems in
a creative way. The graduate’s ability to think logically, to analyse
problems, and to solve non-trivial problems can be put to use in independent and
creative jobs in the commercial sector or in academic positions.

*Details of study:*