# Study Programmes and Branches of Master Studies

## for the Academic Year 2020/2021

- Study Programme Computational Mathematics
- Study Programme Computer Science - Artificial Intelligence
- Study Programme Computer Science - Discrete Models and Algorithms
- Study Programme Computer Science - Language Technologies and Computational Linguistics
- Study Programme Computer Science - Software and Data Engineering
- Study Programme Computer Science - Software Systems
- Study Programme Computer Science - Theoretical Computer Science
- Study Programme Computer Science - Visual Computing and Game Development
- Study Programme Financial and Insurance Mathematics
- Study Programme Mathematical Analysis
- Study Programme Mathematical Modelling in Physics and Technology
- Study Programme Mathematical Structures
- Study Programme Mathematics for Information Technologies
- Study Programme Probability, Mathematical Statistics and Econometrics

# Study Programme
*Computational Mathematics*

**Computational
Mathematics**

*Form of study:* full-time

*Outline of study:* The programme
Computational Mathematics is devoted to the development, 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 the creative use of
information technology and production of programming applications. An integral
part of the programme is the verification of employed methods. The study is a natural continuation of the bachelor's programme General Mathematics, branch
Numerical Analysis and Mathematical Modelling at the Faculty of Mathematics and
Physics of the Charles University. The programme Computational Mathematics is
designed in such a way that it enables to admit also students who finished a bachelor's study of Mathematics of another branch or at another university,
requiring that they complete the missing knowledge.The students will first
obtain knowledge of the modern theory of partial differential equations, linear
and nonlinear functional analysis, finite element method, basics of numerical
software, and methods for matrix calculations. Later the students will choose
elective courses, in particular according to the topic of their master’s
thesis.

*Prospects for graduates:* The graduate of
the master's programme Computational Mathematics has obtained a knowledge in
basic fields of numerical mathematics and computational techniques as well as of
the theory of partial differential equations and he/she is able to apply them to
the numerical solution of problems in applications, including an efficient
computer implementation. For a given problem, he/she is able to design or choose
a suitable numerical method, carry out its numerical analysis, implement the
computer realization including the analysis of computational error and assess
how much the computational results approach the reality. He/she has a sufficient
qualification for both a doctoral study at a Czech or foreign university and a career in the practice, in particular, in industry, basic and applied research
or in public administration.

*Details of study:*

# Study
Programme *Computer Science - Artificial Intelligence*

**Computer Science -
Artificial Intelligence**

*Form of study:* full-time

*Outline of study:* The study program
Computer Science - Artificial Intelligence provides 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.

*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:*

# Study
Programme *Computer Science - Discrete Models and Algorithms*

**Computer
Science - Discrete Models and Algorithms**

*Form of study:* full-time

*Outline of study:* The study branch
Discrete models and algorithms offers wide education in theoretical and
mathematical fundaments of computer science. Student obtains knowledge in the
area of discrete models and related algorithmic and data techniques and various
mathematical methods for their design. The study familiarizes the student both
with the last results on discrete models, algorithms and optimization, and with
possibilities and limitations in solving related algorithmic questions. The
student acquires thorough mathematical knowledge necessary for analysis and
design of discrete models and algorithms. The student can apply his or hes
skills in practice or can continue in the Ph.D. study of computer science or
related areas.

*Prospects for graduates:* The graduate is
familiar with discrete approaches and techniques and discrete structures in
computer science and in algorithmic modelling of practical phenomena. Depending
on profilation, he or she has good knowledge in several of the areas:
combinatoric (graph theory), probabilistic techniques and methods, discrete and
computational geometry, algebraic and topological methods, number theory, linear
and nonlinear programming, discrete optimization. He or she is prepared for
Ph.D. study and is in contact with the last results in the area and, ideally,
make his or her own contribution. The graduate can work in academia or in
practical areas applying algorithms and discrete modelling.

*Details of study:*

# Study
Programme *Computer Science - Language Technologies and Computational
Linguistics*

**Computer
Science - Language Technologies and Computational Linguistics**

*Form of study:* full-time

*Outline of study:* The aim of the study
programme “Computer Science – Language Technologies and Computational
Linguistics” is to get the graduates 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, information extraction and summarization, machine translation, text
analytics, grammar checking, automatic speech recognition, spoken dialogue
systems, and speech synthesis. The emphasis is put on deep understanding of
formal mathematical and algorithmic foundations and their practical
applicability in natural language processing tasks. Students of the programme
have the possibility to focus either on theoretical aspects of formal
description of natural languages or on the technology-oriented side
(state-of-the-art methods in statistics, machine learning and deep learning) for
language data processing.

*Prospects for graduates:* The graduate is
familiar with mathematical and algorithmic foundations of automatic natural
language processing, with theoretical foundations of formal description of
natural languages, as well as with state-of-the-art machine learning techniques.
Graduates have the ability to apply the knowledge acquired during their studies
in the design and development of systems automatically processing natural
language and large quantities of both structured and unstructured data, such as
information retrieval, question answering, summarization and information
extraction, machine translation and speech processing. They are equipped with
good knowledge, skills, and experience in software development and teamwork
applicable in all areas involving the development of applications aiding
human-computer interaction and/or machine learning.

*Details of study:*

# Study
Programme *Computer Science - Software and Data Engineering*

**Computer
Science - Software and Data Engineering**

*Form of study:* full-time

*Outline of study:* The study program
Computer science - 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:*

# Study Programme
*Computer Science - Software Systems*

**Computer Science -
Software Systems**

*Form of study:* full-time

*Outline of study:* The study program puts
emphasis on system-oriented programming in one of three focus domains. The
System Programming domain focuses on designing and 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:* The graduate
possesses robust programming skills in the given focus domain: System
Programming for modern operating systems and system-related technologies
(middleware, virtual machines), Dependable Systems for dealing with the
systematic construction of systems with guaranteed reliability, and High
Performance Computing for software development on modern parallel and
distributed systems. The graduate has absorbed both the necessary theoretical
foundations and the skills required for solving practical programming tasks. He
can use modern programming languages and tools. He can adapt to the fast-moving
technologies of today and use these technologies in team software projects. He
can solve problems individually and systematically, and apply deep system
knowledge in delivering outside-the-box solutions.

*Details of study:*

# Study
Programme *Computer Science - Theoretical Computer Science*

**Computer
Science - Theoretical Computer Science**

*Form of study:* full-time

*Outline of study:* The study program is
intended as research oriented study. Students are expected to have strong
mathematical background which is further developed during the study with focus
on exact thinking. Students gain overview and understanding in many areas of
contemporary theoretical computer science - from cryptography and limits of
computational systems to state-of-the-art techniques in the design of efficient
algorithms and data structures. They will learn about frontiers of current
knowledge in areas of their interest. Study may include working in international
environment under guidance of recognized experts while writing a master thesis.
Graduates are sought after by companies developing future technologies based on
current research. At the same time, the study program excellently prepares for
doctoral study at any university worldwide.

*Prospects for graduates:* The graduate
has a broad overview of theoretical computer science, thoroughly understands the
limits and possibilities of computational systems, understands the foundations
of cryptography and computer security, knows advanced algorithmic techniques,
and is able to apply these techniques to new problems. He also has skills
necessary to convey abstract ideas with precision and clarity. The graduate can
apply his skills in the design and analysis of complex systems and in the
development of innovative solutions and transformative technologies. The
graduate is also well prepared for doctoral studies in theoretical computer
science and related areas.

*Details of study:*

# Study
Programme *Computer Science - Visual Computing and Game Development*

**Computer
Science - Visual Computing and Game Development**

*Form of study:* full-time

*Outline of study:* The program consists
of two closely related study tracks, Visual Computing and Computer Game
Development. Within the scope of Visual Computing, the program 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 focuses - apart from computer graphics techniques
- on artificial intelligence and intelligent agent systems as well as on
software engineering skills necessary for the development of large-scale gaming
projects. Both study tracks 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 focus, 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:*

# Study Programme
*Financial and Insurance Mathematics*

**Financial and Insurance
Mathematics**

*Form of study:* full-time

*Outline of study:* Study program
Financial and insurance mathematics provides education concerning the
theoretical and practical knowledge of financial and insurance mathematics. On
the solid mathematical background one develops mathematical modeling in
insurance, banking and other financial institutions. The graduate is capable to
construct financial and insurance products and analyze them from the point of
view of profit and risk. The graduates of Financial and Insurance Mathematics
have education which is necessary to obtain certificate of competence to execute
the actuarial practice in the international context.

*Prospects for graduates:* The graduate of
study program Financial and Insurance Mathematics has a deep knowledge of basic
mathematical disciplines and a special knowledge of probability and mathematical
statistics, stochastic processes, mathematical methods in finance, life and
nonlife insurance, advanced parts of financial management, risk theory,
accounting (including accounting of insurance companies) and modeling of
progressive software systems. The graduate is capable to model financial and
insurance products and perform their analysis from the point of view of profit
and other characteristics which are necessary for effective financial
management. The graduates of Financial and Insurance Mathematics have education
which is necessary to obtain certificate of competence to execute the actuarial
practice in the international context.

*Details of study:*

# Study Programme
*Mathematical Analysis*

**Mathematical Analysis**

*Form of study:* full-time

*Outline of study:* The study program
Mathematical analysis provides to the students advanced knowledge in several
branches of mathematics which are traditionally considered to belong to
mathematical analysis (theory of real functions, complex analysis, functional
analysis, theory of both ordinary and partial differential equations). It is
characterized by a deep insight to these branches and focus on their mutual
connections. Advanced level of basic knowledge in these branches is reached by
attending mandatory courses. In elective courses students deepen their knowledge
in more narrow areas, chosen namely with respect to the topic of their master
thesis. Thanks to the seminars the students may be in touch with current
problems of mathematical research. Mathematical analysis is a wide
well-established area with narrow connections to other parts of mathematics.
Methods of mathematical analysis are used, among others, in the probability
theory, in numerial mathematics and for creating and examining mathematical
models (in physics or other sciences). Students may encounter these connections
in some of the elective courses. Aims of the program include preparation for a PhD study of matematical analysis or related areas at the Charles university or
at another university. Students encounter applications of mathematical theories,
theorems and methods for solving concrete problems. Therefore their future
employment is not limited to academic positions.

*Prospects for graduates:* A graduate of
the study program Mathematical analysis has advaced knowledge in basic areas of
mathematical analysis (theory of real functions, complex analysis, functional
analysis, theory of ordinary and partial differential equations) and understands
their mutual connections, including connections to other areas of mathematics.
He or she is able to apply advanced theoretical methods to solving concrete
problems. He or she is prepared for a PhD study, but the acquired knowledge and
ability can be succesfully used in other areas (economics, technics, finance,
natural sciences) as well.

*Details of study:*

# Study
Programme *Mathematical Modelling in Physics and Technology*

**Mathematical
Modelling in Physics and Technology**

*Form of study:* full-time

*Outline of study:* Mathematical modeling
is an interdisciplinary study programme that combines mathematical analysis,
numerical mathematics and physics. The programme is designed in such a way that
the students acquire specialised as well as general knowledge in all mentioned
fields, and they are ready, if required by the problem they are studying, to
deepen their knowledge by studying highly specialized scientific works. All
students are required to attend lectures on continuum mechanics, mathematical
analysis of partial differential equations and numerical mathematics with the
objective to acquire the ability to design mathematical models of natural
phenomena (especially in the field of mechanics and continuum thermodynamics),
and analyze and implement numerical methods for computer simulations of the
given phenomenon. After completing the compulsory courses the students focus
more closely on either the physical aspects of mathematical modeling (design of
mathematical models), the mathematical analysis of partial differential
equations, or methods for numerical solution of these equations. Extensive
experience with all aspects of mathematical modeling (model design, analysis,
simulation) enables students to use the state-of-the-art knowledge from all
aforementioned fields in solving complex problems in physics, technology,
biology and medicine that are beyond the scope of particular specialised fields.
Graduates of the study programme are ready to work in the academic as well as
commercial institutions that rely on mathematical modelling and simulations in
their study of natural phenomena.

*Prospects for graduates:* The graduate
has advanced theoretical knowledge of mathematical analytical and numerical
methods applicable in the mathematical modeling of natural phenomena. In
particular, he/she knows mathematical methods for the study of dynamical systems
described by ordinary or partial differential equations, and he/she knows how to
apply the methods in selected scientific disciplines. The graduate is able to
design mathematical models for given natural/technical/social phenomena, analyse
the basic mathematical properties of the proposed models, select the appropriate
numerical method for their computer processing, and evaluate the benefits and
limitations of the models in terms of their applicability in answering relevant
practical questions.

*Details of study:*

# Study Programme
*Mathematical Structures*

**Mathematical
Structures**

*Form of study:* full-time

*Outline of study:* The master level
program "Mathematical structures" is aimed at broadening student's general
mathematical background in algebra, geometry, combinatorics and mathematical
logic, and at acquiring a deeper knowledge in selected parts of these areas. The
aim is to offer a fairly general overview of modern structural mathematics as
well as leading the student towards an independent creative work. The emphasis
is on areas in which we have lecturers that are on top of their fields.

*Prospects for graduates:* A graduate of
the program has advanced knowledge of algebra, geometry, combinatorics and
mathematical logic. These enable him or her to understand and to contribute to
recent research. The abstract nature of the field, the depth and the difficulty
of the study, lead to a development of the graduate's ability to analyse,
structure and solve various problems of complex and abstract nature. Besides
academia the graduate will function well in various positions where it is
required to understand and to be able to use new advances and large
systems.

*Details of study:*

# Study
Programme *Mathematics for Information Technologies*

**Mathematics for
Information Technologies**

*Form of study:* full-time

*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 boolean functions, 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 relevant
applications numerical linear algebra.

*Prospects for graduates:* Graduates have
a broad knowledge of advanced algebra, geometry, logic, and their applications
in IT, and can use 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. 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:*

# Study
Programme *Probability, Mathematical Statistics and Econometrics*

**Probability,
Mathematical Statistics and Econometrics**

*Form of study:* full-time

*Outline of study:* The study program
Probability, Mathematical Statistics and Econometrics provides to the students
advanced knowledge in several branches of mathematics focused to random events
and their analysis (probability theory, mathematical statistics, econometrics,
optimization). It is characterized by a deep insight to these branches and focus
on their mutual connections. Advanced level of basic knowledge in these branches
is reached by attending mandatory courses. In elective courses students deepen
their knowledge in more narrow areas, chosen namely with respect to the topic of
their master thesis. Thanks to the seminars the students may be in touch with
current problems of mathematical research. Mathematical disciplines covered by
this study program are well-established with narrow connections to other parts
of mathematics. The theory is based mostly on mathematical analysis (measure
hteory) and linear algebra, many methods exploit numerical mathematics. On the
other hand these parts of mathematics are influenced and inspired also by
problems from probability and statistics. Mathematical methods for random
phenomena is one the most widely used parts of mathematics both in research and
in practice. Aims of the program include preparation for a PhD study of
probability, statistics or related areas at the Charles university or at another
university. Students encounter applications of mathematical theories, theorems
and methods for solving concrete problems. Their future employment is very
diverse in academia, industry, financial institutions, medical and biological
research or in humanities.

*Prospects for graduates:* A graduate of
the study program Probability, Mathematical Statistics and Econometrics has
advaced knowledge in basic areas of mathematics of chance (probability theory,
mathematical statistics, optimization) and understands their mutual connections,
including connections to other areas of mathematics. He or she is able to apply
advanced theoretical methods to solving particular problems. He or she is
prepared for a highly qualified work as a specialist in diverse areas
(economics, technics, finance, science and humanities) and also for a PhD study
as well.

*Details of study:*