# 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 Procedure for Master
Studies*.

*Outline of study*: The study branch
Artificial Intelligence provides education in the area of theoretical and
applied knowledge for design of intelligent systems in various areas including
data analysis, automated problem solving, and robotic applications. The emphasis
is put on deep understanding of formal theoretical foundations and their
practical applicability. Students will gain knowledge about design of efficient
data structures, about formal modeling of problems and knowledge by using
techniques of mathematical logic and probability theory, about algorithms
(classical and nature-inspired) for problem solving, for control of autonomous
agents, for machine learning, and for data mining, and about complexity analysis
of computational methods. The students will learn how to apply these techniques
and how to extent them both for 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 Procedure for Master
Studies*.

*Outline of study*: The aim of the program
is to get the students ready for research in the area of natural language
processing and 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 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 finances, medicine, and other areas
where large quantities of both structured and unstructured data are being
analyzed. 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 Procedure for Master
Studies*.

*Outline of study*: The 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 – apart from computer
graphics techniques – mainly on 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
on 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 Procedure for Master
Studies**

*Outline of study*: 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. Study plans Optimization and Mathematical economics
provide skills to solve difficult technical and economical problems with the use
of optimization methods and suitable methods in mathematical economy.

*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 economical decision problems. Solutions of these problems are
based on methods of mathematical optimization and on methods solving conflict
situations. Deep knowledge of modern mathematical methods enables the graduate
to design mathematical models in complicated economical situations. Education in
computer science provides skills to implement effectively the solutions with the
use of fast computers.

*Details of study:*

**Software and Data Engineering**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

*Outline of study*: The study branch
Software and data engineering aims at expertise in 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. A required part of the study is a work on large
software project where students apply not only the 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 Procedure for Master
Studies**

*Outline of study*: The study branch puts
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 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 will
have an expertise in the team development of software systems, their analysis,
design, implementation and deployment in the real world including an evaluation.
They will acquire during the study an ability to flexibly react to the continual
advancement of new techologies. They will have knowledge from the areas of
database systems, architectures and principles of system environments and
software systems, modern internet techologies, computer
graphics etc.

*Details of study:*

**Theoretical Computer Science**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

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

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

*Details of study:*

## Study Programme *Mathematics*

**Financial and Insurance Mathematics**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

*Outline of study*: This programme
provides theoretical and applied education in financial and insurance
mathematics. Solid mathematical background provides the foundations for
developing disciplines of mathematical modelling in insurance and banking
industry and other financial areas. The graduate is able to develop financial
and insurance products and analyze 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 Procedure for Master
Studies**

*Outline of study*: Mathematical analysis
programme offers students advanced knowledge of mathematical fields
traditionally forming mathematical analysis (real function theory, complex
analysis, functional analysis, ordinary and partial differential equations). It
is characterized by depth of insight into individual topics and emphasis on
their mutual relations and interconnections. Basic knowledge of these topics on
an advanced level is provided by a set of compulsory courses. Elective courses
deepen the knowledge of selected fields, especially those related to the diploma
thesis topic. 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 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 acquired knowledge and abilities can be put into use in
practical occupations as well.

*Details of study:*

**Mathematical Modelling in Physics and
Technology**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

*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. The students will acquire ability to design
mathematical models of natural phenomena (especially related to continuum
mechanics and thermodynamics), analyze them, and conduct numerical simulations.
After passing the compulsory classes, the students get more closely involved
with 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 the students to use modern results from
all relevant fields to address problems in physics, technology, biology, and
medicine that surpass the scope of the individual fields. 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
analyze, 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 the 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 Procedure for Master
Studies**

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

*Prospects for graduates*: The graduate
has very advanced knowledge of algebra, geometry, combinatorics and logic.
He/she is in a 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 the ability to analyze, structure and
solve complex and difficult problems. The graduate can pursue an academic career
or realize himself in jobs that involve mastering of new knowledge and control
of complex systems.

*Details of study:*

**Mathematics for Information
Technologies**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

*Outline of study*: This Master Program
focuses on deeper knowledge of various mathematical disciplines and their
algorithmic aspects. The student can get specialized either in Mathematics for
Information Security or in Computer Geometry.

The direction Mathematics for Information Security is focused on deepening the 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.

The direction 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 specialized in Mathematics for |Information Security are well acquainted with both the 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 specialized in Computer Geometry have 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 academic career.

*Details of study:*

**Numerical and Computational Mathematics**

*Form of study*: full-time

**for
requirements, see Admission Procedure for Master
Studies**

*Outline of study*: This programme focuses
on design, analysis, algorithmization, and implementation of methods for
computer processing of mathematical models. It represents a transition from
theoretical mathematics to practically useful results. An emphasis is placed on
creative use of information technology and production of programming
applications. An integral part of the programme is verification of employed
methods. 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 the elective courses
according to the topic of their master’s thesis. They can specialize on
industrial mathematics, numerical analysis, or matrix calculations.

*Prospects for graduates*: The graduate
has attained knowledge needed for numerical solution of practical problems 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 the
numerical results and reality. He/she can conduct 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 Procedure for Master
Studies**

*Outline of study*: The programme is
targeted at students who want to obtain theoretical and practical knowledge
about 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 want to study more deeply. In seminars, they
learn to work independently as well as to collaborate on complex projects.
A big 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). The applications are inspired by real problems from economics,
medicine, technology, natural sciences, physics and informatics. The primary
objective of the programme is to prepare the students for successful careers in
academia as well as in finances, telecommunications, marketing, medicine and
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 towards 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 the theoretical knowledge to practical problems
in a creative way. The graduate’s ability to think logically, to analyze
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:*