Study Programmes and Branches of Doctoral Studies

Academic Year 2024/2025

Algebra, number theory, and mathematical logic
Atmospheric physics, meteorology and climatology
Bioinformatics and computational biology
Biophysics, Chemical and Macromolecular Physics
Computational linguistics
Computational mathematics
Computer Science – Software Systems
Computer Science – Theory of Computing, Discrete Models and Optimization
Computer Science – Visual computing and computer games
General Questions of Mathematics and Computer Science
Geometry, topology, and global analysis
Mathematical analysis
Mathematical and computer modeling
Particle and Nuclear Physics
Physics Education and General Problems of Physics
Physics of Condensed Matter and Materials Research
Physics of nanostructures and nanomaterials
Physics of Plasmas and Ionized Media
Physics of Surfaces and Interfaces
Physics of the Earth and Planets
Probability and statistics, econometrics and financial mathematics
Quantum Optics and Optoelectronics
Theoretical Computer Science and Artificial Intelligence
Theoretical Physics, Astronomy and Astrophysics

Study Programme Algebra, number theory, and mathematical logic

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study program Algebra, number theory and mathematical logic offers students an advanced education in a selected area. The education allows the program graduates to follow contemporary research. It teaches them basics of independent scientific work and how to approach various abstract problems.

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Study Programme Atmospheric physics, meteorology and climatology

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: Studijní program je zaměřen na rozsáhlý komplex atmosférických jevů a procesů, které mají fyzikální charakter, uplatňují se však také v interdisciplinárních vazbách např. k atmosférické chemii, oceánologii, fyzické geografii, environmentálním vědám apod. V rámci Univerzity Karlovy jde o jedinečný program z hlediska komplexního pohledu na dynamický systém zemské atmosféry v širokých interdisciplinárních vazbách. I v rámci ČR se jedná o jediný program poskytující vzdělání v oblasti fyziky atmosféry, meteorologie a klimatologie. Z metodologického hlediska se interaktivně a komplementárně uplatňuje rozsáhlé spektrum aplikací z oblasti teoretické, experimentální i počítačové fyziky.

Prospects for graduates: Absolventi získávájí komplexní vědeckou erudici pro studium atmosférických procesů v širším kontextu s dalšími procesy probíhajícími v klimatickém systému i přilehlé části vnějšího meziplanetárního prostoru. Oblast znalostí absolventů je charakterizována zejména tématy fyzika atmosféry, dynamická a synoptická meteorologie, modelování atmosférických procesů, klimatologie a změny klimatu, děje v mezní vrstvě atmosféry, turbulence a modelování proudění, chemismus atmosféry a kvalita ovzduší anebo charakteristiky vyšších vrstev atmosféry. Absolventi jsou připraveni tvůrčím způsobem uplatňovat nabyté vědomosti na akademických pracovištích, v resortním výzkumu i v různých aplikovaných odvětvích komerční sféry.Absolventi mají širokou perspektivu uplatnění například ve výzkumných ústavech a na pracovištích vysokých škol, v průmyslových vývojových centrech zaměřených na studium proudění, v business prostředí v souvislosti s expertními znalostmi postupů statistického modelování, v oblasti krizového managementu v souvislosti s extrémními meteorologickými jevy anebo v řadě hospodářských odvětví ovlivňovaných atmosférickými ději jako je třeba energetika.

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Study Programme Bioinformatics and computational biology

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: Bioinformatics and computational biology are multidisciplinary disciplines on the interface of computer science (especially algorithms and software development, data engineering), mathematics (especially probability, statistics, and mathematical modeling), and biology (especially molecular and evolutionary) aimed at efficient processing, analysis, and modeling of biological data and processes at the molecular and cellular level. The common denominator of bioinformatics and computational biology, which also includes areas such as systems biology, neuroinformatics, bioimaging, and computational drug design, is the development of analytical procedures and software tools for processing and analyzing large, domain-specific, and heterogeneous data to understand cellular processes at the molecular level, to learn from the evolution of given processes and subsequently apply this knowledge, especially in medicine and biotechnology.

Prospects for graduates: The graduate understands key areas of informatics, such as algorithms and software systems development. She/he is also well acquainted with the most important methods and new discoveries in the field of natural sciences related to her dissertation topic. The graduate can define problems, come up with their solutions, implement these and present and defend the results of her work in the domestic and international environment. The graduate will find employment mainly in research and development, both in academic and commercial settings, whether it is a position requiring processing and analysis of biomolecular data (e.g., in hospitals) or research positions in the pharmaceutical industry or biotechnology companies. However, the interdisciplinarity of the field requires the graduate to be able to integrate knowledge and data from different domains, making her also prepared for data-oriented positions outside the field of natural sciences.

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Study Programme Biophysics, Chemical and Macromolecular Physics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Prospects for graduates: Absolvent tohoto doktorského programu je odborník připravený pro samostatnou vědeckou práci v základním i aplikovaném výzkumu v oblasti přírodních věd v interdisciplinárních oblastech mezi fyzikou, chemií a biologií. Má hluboké znalosti odpovídajících experimentálních i teoretických metod i znalosti v oblastech chemie (biologie) potřebné pro zapojení do vědeckých týmů s chemickým či biologickým zaměřením. Velmi dobře se uplatňuje v oborech biofyzika, biochemie, fyzikální chemie a chemická fyzika, makromolekulární fyzika a chemie, mikrobiologie i v biologických směrech lékařského výzkumu na výzkumných akademických nebo vývojových pracovištích stejně jako vedoucí odborník v laboratořích zaměřených na fyzikálně-chemické či biologicko-fyzikální analýzy.

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Study Programme Computational linguistics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: Computational linguistics is an interdisciplinary scientific field involving mathematics (including topics such as discrete mathematics, statistics and probability), computer science (e.g. algorithmization, machine learning, artificial intelligence) and classical linguistics (e.g. morphology, syntax, language typology). Computational linguistics investigates language from a formal point of view, and it aims at developing methods that could be used in software applications in the field of Natural Language Processing, in which languages in their spoken or written form are handled.

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Study Programme Computational mathematics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study programme provides advanced theoretical and practical knowledge of the computational mathematics, which deals with solution of mathematical problems describing phenomena in natural, technical and social sciences. The study is focused on the understanding of problems in a wider context. The study includes the theoretical aspects of the methods of the computational mathematics as well as a computer solution of the mathematical tasks motivated by practical problems. The students are prepared for development of the field itself as well as to employ the achieved knowledge in solving mathematical problems in natural and applied sciences.

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Study Programme Computer Science – Software Systems

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program addresses open topics in software system analysis, development and application. In both theoretical and practical terms, it has foundations in the research of software architectures, programming languages and notations, together with tools and methods for software analysis and construction. These are studied both in general terms and in the context of important software system classes such as the information systems, or the distributed or parallel systems. On the creative side, the program combines projects of basic and applied research, often with strong experimental aspects, with outputs including research prototypes alongside traditional publications.

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Study Programme Computer Science – Theory of Computing, Discrete Models and Optimization

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program aims at providing the graduate with knowledge and research experience in a wide range of fields in discrete mathematics and theoretical computer science, based both on contemporary theoretical trends and on applications in physics, biology and other branches of science. The graduate gains knowledge and experience necessary to contribute to the research and development on international level and is ready to take a leading role in shaping the trends in these fields.

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Study Programme Computer Science – Visual computing and computer games

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program focuses on the education of graduates prepared to solve research problems in the sub-area of computer science related to the generation and processing of visual information (computer graphics, image analysis, machine vision) and/or computer games development. The primary means of education is independent research, publication and presentation of research results, as well as their eventual transfer to the industry through student internships. The creative activity within the program focuses on developing new or improving existing mathematical methods, algorithms and technologies dealing with computer processing of visual information and with computer games. The program reflects the growing demand for advanced technologies and builds on the exceptional expertise of MFF UK and UTIA ASCR in these research areas. Graduates can be employed in academia, public research institutions, and private companies.

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Study Programme General Questions of Mathematics and Computer Science

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

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Study Programme Geometry, topology, and global analysis

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program Geometry, topology, and global analysis offers to students a broad and deep knowledge in the selected areas. The aim is to train the students to be able to learn and use new scientific achievements, mathematical methods and theories, independently develop and apply them, and present the results at international conferences and meetings. The program prepares students to pursue an academic career at universities, scientific institutes, and also in companies and firms having applied research and development branches.

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Study Programme Mathematical analysis

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study field of mathematical analysis is focused on the studium of basic and advanced parts of mathematical analysis. It is a subdiscipline of mathematics whose primary goal is the description of natural or social processes which involve certain form of a dynamic progress, mostly a motion or a change. The basic priciples of mathematical analysis consist of all forms of limiting processes. The top education in mathematical analysis consists of the ability to solve differential equations of all types.

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Study Programme Mathematical and computer modeling

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: It is an interdisciplinary study branch which connects classical physics (particularly continuum mechanics and thermodynamics) with mathematical analysis and numerical mathematics. The student should go through the construction or understanding of the physical model, its mathematical analysis up to its numerical solution. Due to the complexity of problems studied both in the research and in the praxis a closed colaboration among specialist from different areas is needed. Typically, the physicists and engineers contruct the models and mathematicians study the mathematical properties of the models and solve the models numerically. These specialists often use different languages to describe the same problem. The graduates of this programme should be able to communicate with all of them and are therefore prepared to lead such groups. Moreover, they should also be prepared to solve simpler problems by themselves: from the construction of the model through its analysis up to its numerical solution.

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Study Programme Particle and Nuclear Physics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program has two specializations: particle physics and nuclear physics. Study within this programme is based on teaching the theoretical and experimental aspects of nuclear or particle physics, supported by detailed understanding of quantum mechanics, quantum field theory and phenomenology of nuclear and subnuclear processes. Particular emphasis is placed on mastering relevant theoretical computational methods and familiarization of the data acquisition and analysis, including effective control of information technology. Students should employ and develop these skills in their own scientific work, which is an important part of the doctoral programme.

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Study Programme Physics Education and General Problems of Physics

Form of study: full-time, full-time

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study program is focused on the problematic of didactics of physics and general problems of physics. It stems from scientific disciplines such as physics, didactics of physics, pedagogy and psychology. The main goal is to provide students with a complex overview of didactics of physics, teach them independent scientific practice in this field and allow for a deeper understanding of some parts of physics. This programme naturally follows the master’s programme Physics Education for Secondary Schools which, out of the whole Charles University, can be studied solely at the Faculty of Mathematics and Physics. It is therefore natural that this faculty also has a doctorate program focused on didactics of physics and general problems of physics. This study programme is unique by being the only one at our university to offer doctorate level studies in the field of didactics of physics.

Prospects for graduates: The graduate has deeper knowledge in physics, physics education, pedagogical-psychological disciplines or philosophy and history of physics and is prepared for independent research work in various branches of physics education or philosophy and history of physic. Graduate specialized in physics education is able to solve problems connected with physic education on secondary school level and to plan, conduct and evaluate research in the field of physics education. The graduates will find employment at university departments providing pre-service physics teacher training, in scientific and pedagogical institutions, in management positions in school system and as a highly qualified teacher at junior and senior secondary schools and at colleges.

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Study Programme Physics of Condensed Matter and Materials Research

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: Cílem studia tohoto programu je poskytnout studentům pokročilé experimentální a teoretické znalosti a dovednosti pokrývající v plné šíři fyziku kondenzovaných látek a materiálový výzkum a připravit je pro aktivní a tvůrčí uplatnění nabytých znalostí v moderních směrech základního výzkumu i relevantních aplikacích.

Prospects for graduates: Absolvent dosahuje širokého vzdělání v teoretických a experimentálních disciplínách vázaných na fyziku kondenzovaných látek a materiálový výzkum v jejich moderní podobě a disponuje potřebnými znalostmi matematických metod a IT. Je odborník připravený pro samostatnou vědeckou práci v základním i aplikovaném výzkumu v oblastech studia fyzikálních vlastností kondenzovaných látek a materiálů. Má hluboké znalosti odpovídajících teoretických přístupů (kvantová teorie, termodynamická a statistická fyzika) a jejich aplikací v teoretické a experimentální fyzice kondenzovaných soustav a je seznámen s moderními experimentálními metodami oboru a technologickými postupy. Velmi dobře se uplatňuje jako tvůrčí pracovník v ústavech základního fyzikálního, materiálového, chemického a biomedicínského výzkumu a na vysokých školách uvedeného zaměření, ale i jako vedoucí odborník v laboratořích aplikovaného materiálového výzkumu a vývoje nebo průmyslových zkušebních laboratořích.

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Study Programme Physics of nanostructures and nanomaterials

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The goal of the doctoral study program (DSP) is to educate excellent experts in the physics of nanostructures and nanomaterials suited for future carrier in basic and applied research in nanotechnologies. The main pillars of the DSP are the theoretical and experimental condensed matter physics and physics of surfaces, advanced experimental and theoretical methods for studying the nanostructures, and smart technologies for preparation of nanostructures and nanomaterials. The DSP is of highly interdisciplinary nature and fits to the cutting-edge topics of current physical and material sciences like spintronics, nanoelectronics, nanomedicine and quantum computing. It is the only DSP in the Faculty of mathematics and physics, which integrates various areas of physics and materials research with outreach to chemistry, biology and medicine. In coherence with the tradition of the education in the Faculty of mathematics and physics, the ultimate goal of the education in the DSP is to provide deep theoretical background for understanding the key physical principles and phenomena underlying the unique properties of nanostructures and nanomaterials.

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Study Programme Physics of Plasmas and Ionized Media

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study program covers all aspects of plasma physics and with extensions to theoretical physics (elementary processes) and to some topics of astrophysics (interplanetary space plasma, dust / ice cloud problems in the solar system) and nuclear fusion. Studies include also borderline disciplines such as plasma chemistry, plasma interaction with solid surface and complex plasma. The program prepares professionals with a broad foundation in mathematics, physics, and computer modeling of physical processes and with deep knowledge of plasma physics.

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Study Programme Physics of Surfaces and Interfaces

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study program provides advanced teoretical and practical knowledges in the area of surface science, physics of interfaces and thin film physics, areas supporting contemporary nanotechnology. It includes study of surface processess and structures at atomic scale using a number of various experimental techniques for surface imaging and analysis. The study covers also borderline disciplines related to surface chemistry (surface catalysis,electrochemistry, on-surface synthesis). The program prepares professionals with a broad foundation in mathematics and physics and with a deep knowledge in the area of surface science and physics of thin films.

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Study Programme Physics of the Earth and Planets

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program provides advanced theoretical knowledge of the physics of the Earth and planetary bodies and trains students in theoretical and numerical solutions of the forward and inverse problems. The graduate is able to carry out independent scientific research focused on the physical processes in the Earth, planets and satelites. He/she can pursue career in the research institutions focused on Earth and planetary evolution, but also in the industrial research focused on the issue of continuum mechanics.

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Study Programme Probability and statistics, econometrics and financial mathematics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The study branch is based on mathematical background, which involves probability theory, stochastic processes, mathematical and computational statistics, optimization, econometrics, operational research, financial and insurance mathematics. The connected creative work is represented especially by the basic mathematical research, and partly by applications, e.g. in finance and insurance. The doctoral students enhance their knowledge in advanced courses and seminars, according to their individual study plans. Under the supervision of their advisor they provide research work in a given topic and publish their results and presents them at scientific conferences. The study branch will prepare experts who can become successors of faculty professors, others will profit from their mathematical thought in practice.

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Study Programme Quantum Optics and Optoelectronics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The students of the branch of study will have acquired comprehensive knowledge and skills required for conducting independent research and other scientific activities in quantum optics and optoelectronics. In accord with individual study plans students concentrate on the topic of their thesis. They can find employment in both fundamental and applied research at universities, research institutes, and in industry. The progress in application of optics in numerous research areas (physics, biology, chemistry, medicine, communications, and robotics) leads to an increase in the range of employment possibilities.

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Study Programme Theoretical Computer Science and Artificial Intelligence

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The program prepares experts for research and development in the areas of Theoretical Computer Science and Artificial Intelligence. Education is implemented by doing independent research under the supervision of senior experts. In addition to obtaining foundations in Computer Science, the students acquire deep knowledge in a chosen specialization area such as: algorithms and data structures and their analysis, knowledge representation and reasoning, cognitive sciences and their applications, machine learning, multi-agent systems, problem modeling (e.g., in automated planning or decision making) and problem solving using logical, probabilistic, and nature-inspired methods. Students learn how to formulate research goals, prepare a project proposal to achieve the set goals, and present the results in the international environment. Further, they gain experience teaching and mentoring students including thesis supervision.

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Study Programme Theoretical Physics, Astronomy and Astrophysics

Form of study: full-time, combined, full-time, combined

Possible acceptance without taking the entrance examination, for requirements see Admission procedure.

Outline of study: The programme offers a training in theoretical physics, astronomy and astrophysics. The graduate acquires a wide range of theoretical knowledge and practical experience in solving difficult physical problems. A graduate of astronomy gains also experimental skills, all graduates manage a variety of numerical and computer methods. In addition to mathematical methods, graduates also get a physical intuition that is extremely important in scientific research and for the solution of unexpected technical obstacles and problems.

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