Outline of study: The ‘Atmospheric Physics, Meteorology and Climatology’ program leads students to acquire knowledge and skills in the field of atmospheric properties and the related processes. Within the framework of Charles University, this program is unique in its comprehensive view of the Earth's atmosphere as a dynamical system of in a broad interdisciplinary context. Even within the Czech Republic this is the only program providing full-scale education in the field of atmospheric physics, meteorology and climatology. The program follows from the bachelor's study of physics, in which students acquire necessary knowledge of basic physical principles (mechanics, thermodynamics, electricity and magnetism, optics and others) as well as of proficiency in related mathematical methods. The elements of the study program are primarily focused on acquiring theoretical knowledge in the field of atmospheric physics (hydrodynamics and atmospheric thermodynamics), thus extending previously acquired expertise in this field. Furthermore, skills necessary for practical as well as scientific activities in the field of atmospheric physics are acquired during the study, especially in the field of numerical mathematics, mathematical statistics, data processing and visualization. Part of the course aims to prepare graduates for basic applications of the atmospheric physics, such as weather forecasting, air pollution analysis and climate research (including modelling and research of higher atmospheric layers). Other subjects of the program serve to deepen the student's focus in particular specialized topics or to expand knowledge in areas close to other physical disciplines (e.g., electrical, optical and acoustic phenomena in the atmosphere or the oceans). As a part of the study, a master-level diploma thesis is prepared and submitted, in which the application of competences acquired during the study is demonstrated, as well as ability to cooperate in solving the assigned scientific problem.

Prospects for graduates: Graduates have broad knowledge of physics, especially with regard to atmospheric processes, and related mathematical methods. They are ready to engage in the tasks of basic and applied research as well as able to use their knowledge in practice. Content is is focused mainly on atmospheric dynamics, thermodynamics, energy and air circulation, with possible applications in the field of numerical diagnostic and prognostic models and in the hydrometeorological services. It also involves knowledge of transport, transformation and modelling of pollutants in the atmosphere as well as the climatology, including the structure and dynamics of the climate system, climate modelling, anthropogenic effects on climate, or climate changes in general. 

Outline of study: The focus of this field lies at the interface between physics, biology, and chemistry. The course builds on the basic physics education that deepens in the fields of theoretical and experimental physics important for the description and investigation of molecules, biopolymers, supramolecular systems, and biological objects. The graduate gains knowledge of quantum theory and statistical physics of molecules and molecular systems, experimental methods of biophysics and chemical physics, especially optical and other spectroscopic methods, structural analysis, and imaging techniques. Students choose one of two specializations: theoretical or experimental biophysics and chemical physics. In the theoretical specialization they will gain deeper knowledge in the field of quantum chemistry, molecular dynamics, or advanced theoretical spectroscopy; in the experimental specialization they will acquire knowledge in the field of biochemistry and molecular biology, biophysics of photosynthesis, or structural methods. Through regular seminars, diploma theses, and thematic lectures students get an idea of the current problems solved in individual fields and methods of scientific work. Thanks to a wide range of knowledge, graduates have the opportunity to apply in research and applied disciplines related to physics, biology, chemistry, medicine, material research, bio- and nano-technologies or pharmacy.

Prospects for graduates: The graduate has knowledge of quantum theory and statistical physics of molecules and molecular systems, experimental methods of biophysics and chemical physics, especially optical and other spectroscopic methods, structural analysis, and imaging techniques. Graduates of theoretical specialization gain a deeper knowledge in the field of quantum chemistry, molecular dynamics, or advanced theoretical spectroscopy. Graduates of experimental specialization acquire a deeper knowledge in the field of biochemistry and molecular biology, biophysics of photosynthesis, or structural methods. Through regular seminars the students will get an idea of the current problems solved in individual fields and methods of scientific work. They are proficient in communicating expertise in the form of presentations or written texts, also in English. Many graduates are expected to enter a career as a scientist. The acquired education offers graduates the opportunity to apply in interdisciplinary teams dealing with physics, biology, chemistry, medicine, material research, bio- and nano-technologies or pharmacy.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Outline of study: Particle physics (high-energy, subnuclear physics) investigates the structure of matter on the level of elementary particles and their fundamental interactions. Nuclear physics studies the structure of atomic nuclei and more generally the behaviour of finite quantum systems of mutually interacting particles. The study is based on comprehensive courses of theoretical and experimental particle and nuclear physics, based on extensive courses of quantum mechanics and quantum field theory. The emphasis is put on mastering the relevant computational techniques and managing the methods of acquisition and evaluation of experimental data, including an efficient use of computing and advanced software tools. With the aid of optional courses and the Master thesis project, the students gain deep knowledge in a selected area and choose orientation to theory or experiment.

Prospects for graduates: Graduates have a sound theoretical and experimental knowledge of classical and quantum optics and optoelectronics. They have mastered the mathematical modelling of physical processes in optics and optoelectronics. They can apply the knowledge and competences they have gained in research and scientific activities in optical disciplines as well as in a large number of fields where optics or optical spectroscopy are used (biology, chemistry, medicine). Their education in physics combined with a mastery of computer programming, information technologies and organization of scientific team collaboration enhances the chances of these graduates finding employment in research at universities and research institutes and in industry. Graduates are fully qualified to continue with their studies in postgraduate programmes.

Outline of study: Particle physics (high-energy, subnuclear physics) investigates the structure of matter on the level of elementary particles and their fundamental interactions. Nuclear physics studies the structure of atomic nuclei and more generally the behaviour of finite quantum systems of mutually interacting particles. The study is based on comprehensive courses of theoretical and experimental particle and nuclear physics, based on extensive courses of quantum mechanics and quantum field theory. The emphasis is put on mastering the relevant computational techniques and managing the methods of acquisition and evaluation of experimental data, including an efficient use of computing and advanced software tools. With the aid of optional courses and the Master thesis project, the students gain deep knowledge in a selected area and choose orientation to theory or experiment.

Prospects for graduates: The graduates have advanced knowledge of particle and nuclear physics, in both experimental and theoretical domains. They comprehend quantum theory, understand basic approaches to the description of microworld and manage experimental techniques of its study. They find employment mainly in fundamental experimental and theoretical research, but also in relevant applied research, e.g., in detector physics, nuclear medicine etc. The graduates are prepared to creatively develop the field of their scientific focus and to join international research teams. Experience in application of advanced software tools opens possibilities for employment e.g. in information technologies. 

Outline of study: The programme is devoted to experimental and theoretical study of properties of condensed systems, their microphysical interpretation and possible applications, in particular with respect to the current development of materials research. In addition to common study, the students can select one of the following specializations: Physics of atomic and electronic structures, Physics of macromolecular compounds, Physics of materials, Low temperature physics, Physics of surface modifications. Each of these blocks provides a general education in condensed matter physics at the contemporary level of knowledge and shapes the graduate in selected specialization.

Prospects for graduates: Graduates acquire a broad education in the fundamentals of quantum theory, thermodynamics and statistical physics of condensed systems and the corresponding computing methods. They are able to describe the structure of the systems in different forms, their mechanical, electrical, magnetic and optical properties. They have a general knowledge of experimental methods of characterizing the structure, composition and properties of condensed compounds through for example diffraction, spectroscopic and microscopic techniques, and they are able to apply them in practice. They are able to find suitable positions in institutions of basic physical, chemical and biomedical research, universities, applied research laboratories, testing laboratories, and in hygiene and ecology institutions.

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.

Outline of study: Surface and plasma physics is a master's degree program of interdisciplinary character that includes fundamental knowledge of interactions of neutral and charged particles in vacuum, gas and condensed phase and on the interfaces of these environments. The program provides expertise in surface physics and thin films, especially atomic and molecular nanostructures on solid surfaces with a significant link to physico-chemical and transport processes with applications in the field of catalysts, sensors or molecular electronics. The program in the field of laboratory and cosmic plasma physics covers the fields of plasma chemistry, hot and fusion plasma, and distinct topics in astrophysics. During the course of study, the use of modern diagnostic methods in material research, vacuum and plasma technologies and in the analysis of various kinds of space plasma or controlled thermonuclear fusion can be adopted. Individual disciplines can be oriented experimentally, theoretically, or solved by computer physics methods.

Prospects for graduates: Graduates have advanced knowledge in surface physics, plasma physics and related experimental methods and computer modeling practices with a solid foundation in general areas of physics and mathematics. The acquired knowledge and skills can apply both in basic and applied research at higher education institutions, academic institutions, scientific and technological centers, as well as in the industry and public administration.