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## The Faculty of Mathematics and Physics Today

The Faculty of Mathematics and Physics offers undergraduate and postgraduates courses in Computer Science, Mathematics and Physics. It also offers an undergraduate program for would-be teachers of Computer Science, Mathematics and Physics. The Faculty has nearly 1750 postgraduate and undergraduate full-time and more than 500 part-time registered students the current academic year (1997/98).

A characteristic feature of the Faculty is the close interconnection of teaching activities and research work. At this Faculty students benefit from being taught by those at the forefront of scholarship and research in their fields. A part of the research has an applied aspect (in 1997, for example, there have been 18 major projects undertaken with significant importance for industry and research institutions). Teaching is provided by 343 teachers (including 30 full- and 92 associate-professors) in thirty departments and Faculty Institutes (representing three sections: the School of Computer Science, the School of Mathematics and the School of Physics). The scientific reputation of the Faculty is reflected in the high success rate of domestic and international grant proposals: in 1997 experts of the Faculty have participated in 239 projects of Czech grant agencies and 67 international projects. The total of all grant funds in 1997 was 57,900,000 Kã (an equivalent of 1,790,000 US$). The same year the staff of the Faculty published 8 monographs, 23 textbooks and 1 051 papers – 712 of which are original works. Together with research workers from the Academy of Sciences of the Czech Republic, the committed staff of the Faculty supervised 549 postgraduate students in 29 fields of study and 52 PhD theses were successfully defended along with 2 CSc. and 6 DrSc.

An integral part of the pedagogic and research activity are international contacts. The 726 trips to 40 countries took place in 1997, totalling more than 13,500 days. We have welcomed 322 colleagues from 33 countries in addition to the many participants at meetings and conferences. The Faculty was the main organizer of 24 conferences with more than 2,500 participants, and co-organizer of 14 international symposia. Several Faculty members were key speakers at conferences abroad. This confirms the high quality of the research carried out at the Faculty.

The success of the staff is important not only for the good name of the Faculty and that of Charles University, but also stimulates interest among the young to study natural sciences. Last but not least it provides an important and necessary financial contribution to the budget.

First of all, we would like to present you with the scientific profile of our Faculty departments, grouped into three sections – The School of Computer Science, School of Mathematics and School of Physics.

### School of Computer Science

The School of Computer Science provides students with a full grounding in computer science. It is one of the faculty’s strongest academic body, and its education programs are highly regarded. It offers a comprehensive curriculum from introductory-level courses to graduate seminars focusing on critical research areas. Students find a unique set of opportunities available to study for the Bachelor’ degree, the Master’s degree or the Doctoral degree. The MSc program thoroughly prepares and qualifies students for advanced careers within the computer industry, and the PhD program directly involves students in some of the most exciting and significant research being conducted anywhere in Czech Republic.

The School of Computer Science has developed an outstanding research program supported by national as well as EC grants.

#### Department of Software Engineering

The department is responsible for education in data engineering, software engineering, and computer systems administration. Its other research and educational activities include neural networks and distributed computing. Research in databases and object-orientation was supported by large international projects in the middle of the 90s. The department co-organizes the international conferences ADBIS (Advances in Databases and Information Systems) and the national database-oriented conference DATASEM every year.

#### Department of Theoretical Computer Science

The department is responsible for teaching the theory of automata and languages, complexity theory, logic, and logic programming. The research activities of the members of the department include logic, logic programming, theory of automata, parallelism, and complexity theory. The department guarantees the education and research activities of postgraduate students in Theoretical Computer Science. Members of department organize the international conferences Mathematical Foundation of Computer Science and Logic Colloquium.

#### Network and Labs Management Centre

This center is responsible for the managing of the School of Computer Science computer network, the computer labs in the building at Malostranské square and the computer network and lab in the student residence. Besides these service tasks, members of the Centre teach topics closely related to their professional branches, like programming, networking, UNIX etc.

#### Institute of Formal and Applied Linguistics

The Institute was established in 1990 after the political changes, as a continuation of the research work and teaching carried out by the former Laboratory of Algebraic Linguistics since the early 60’s at the Faculty of Philosophy and later at the Faculty of Mathematics and Physics. The Institute aims to develop educational programmes and carries out research in the domain of theoretical and computational linguistics, both on the general level and with special regard to automatic processing of Czech and developing methods and tools for processing large scale Czech corpora. The Institute actively and fruitfully co-operates with many European and US institutions, and also participates in several international collaborative research projects.

#### Department of Applied Mathematics

The department is responsible for teaching of discrete mathematics (including combinatorics, graph theory and algorithms), optimization and operations research both at undergraduate and graduate levels. Members of the department conduct active research in all of these areas. The international activities of the department are organized mainly through the DIMATIA center, which offers postdoctoral positions for young foreign researchers, annually organizes international conferences and workshops and cooperates with several European and US institutions. The large scientific output of the department is reflected by the KAM-DIMATIA Preprint Series which are exchanged with leading institutions internationally.

#### Department of Software and Computer Science Education

The department is responsible for programming courses not only for students of Computer Science, but also for students of Mathematics and Physics, teaching Computer Graphics, as well as for the Computer Science branch of the curricula of future high school teachers. Major attention is devoted to active work with students on their various types of software projects. The department takes care of the Computer lab Carolina for blind students. The research interests of members range from computer graphics, programming languages to the didactic aspect of Computer Science.

#### Department of Mathematical Logic and Philosophy of Mathematics

The department ensures the provision of basic courses in the foundations of mathematics. These includes set theory, mathematical logic, and general topology. The research, advanced courses and courses for postgraduate study, led by members of this department, cover alternative set theory, the history and philosophy of mathematics, topological dynamics, and advanced mathematical logic. The department is responsible for publishing the journals Acta Universitatis Carolinae – Mathematica et Physica and Scientia et Philosophia.

### School of Mathematics

Teaching mathematics connected with research has a long tradition at Charles University. Probably its most famous mathematician was Bernard Bolzano, and from this century it is Eduard Čech, the famous topologist and geometer.

There are about 90 academicians and 10 additional staff members employed by the mathematical part of the faculty. They provide mathematical classes both for its own students and students of other faculties of Charles University (e.g. Natural Sciences, Education, Social Sciences). The School consists of five departments and a Mathematical Institute.

#### Department of Algebra

The department is active in several branches of abstract algebra, with an emphasis on module theory, representation theory, Abelian groups, lattices, universal algebra, quasigroups and self distributive systems. In recent years, important findings have been achieved both by the long-term staff and by post-graduate students. Every second year, an international conference Some trends in algebra as well as the Budapest-Chemnitz-Praha-Torun Algebra Seminar, is (co)organized by the department.

#### Department of Didactics of Mathematics

The department provides the education for future teachers of mathematics at high and primary schools. The department prepares (or helps with the preparation of) textbooks for mathematics teaching at high schools, and organizes seminars for high-school teachers, to keep them in touch with progress in didactics and mathematics. It also organizes competitions in mathematics for high-school students.

#### Department of Mathematical Analysis

The research activity of the department members covers all of important branches of modern analysis: theory of the functions of real and complex variables, theory and applications of partial differential equations, functional analysis and topology, potential theory and some special topics of mathematical physics. The department successfully (co)organizes many mathematical events from workshops and schools (Spring Schools in Functional Analysis, EVEQ) to major conferences (Topological Symposia, EQUADIFF, Conferences on Potential Theory).

#### Department of Numerical Analysis

The members of the department are active in a number of areas of numerical and applied mathematics, as well as in some other fields which have a close relation to numerical and applied mathematics. The fundamental research of the department is oriented to numerical algebra, numerical analysis, the solution of non-linear problems and modern methods of solving of partial differential equations. The main applications are concerned with mathematical modelling in fluid dynamics, CFD, solid mechanics, ecological problems and industrial modelling. An emphasis is also put on the development of numerical software. The department regularly organizes international conferences and workshops (e.g. Numerical Modelling in Continuum Mechanics, Software and Algorithms of Numerical Mathematics).

#### Department of Probability and Mathematical Statistics

The department consists of three groups: Econometrics, Mathematical Statistics, and Finance and Insurance Mathematics.

The research activity covers most of the important areas of Stochastics. Internationally recognized results have been achieved in a number of areas, for example, nonparametric and robust statistics, time series, resampling methods, computational statistics, stochastic optimization and in insurance mathematics. The development of the department was strongly influenced by the famous statistician J. Hájek. Presently, half of the students of mathematics study a branch of stochastics as their main field of interest. Every fifth year the department organizes the international conference Asymptotic Statistics and every second year it organizes ROBUST.

#### Mathematical Institute

The Mathematical Institute was founded by Eduard âech. Nowadays, its members contribute to three fields of research – differential geometry and topology, potential theory and mathematical modelling in physics. A small group is also very active in the study of the history of mathematics. Members of the Institute regularly (co)organize several traditional conferences and schools (Topological Symposia, EQUADIFF, Conferences on Potential Theory, Winter Schools "Geometry and Physics", and "Mathematics of mechanics of fluids").

A special subgroup in the Institute ensures the operation of the computer network School of Mathematics and maintain the student computer laboratory (with about 40 computers). Members of the Institute also participate in the publishing activities: One group is responsible for the traditional mathematical journal Commentationes Mathematicae Universitatis Carolinae (CMUC) founded by E.âech in 1960 which seems to have found a place among the more highly-ranked mathematical journals. Another teams prepare the column Brief Reviews of the Newsletter of European Mathematical Society.

There are also research groups spanning several departments. For instance, mathematical modelling in physics (mainly liquid flow) is researched by members of at least three departments. Similarly, the group interested in general topology come from three departments, one of them computer science.

The research is supported by many grants and international projects. All of the departments have sound and fruitful research contacts (some of them based on official agreements) with many other universities all over the world; a full list would be very long. Naturally, the closest co-operating mathematical institute (both in research and teaching) is that of the Czech Academy of Sciences.

### School of Physics

The scientific activity of the School of Physics covers (and is the only school in the Czech Republic to cover) the full range of modern physics. Disciplines with a long tradition, such as physical electronics and vacuum physics, astronomy, meteorology and geophysics are cultivated. On the base of a small group studying "atomic physics" in the thirties new departments were established engaged in solid state physics, chemical physics, nuclear and subnuclear physics. The scientific community of the School responds vividly to the modern trends in physics (for example low temperature physics, quantum optics, physics of molecular and biological structures, cosmic physics, surface physics). The experimental activities are supported by applied physics research, by well equipped laboratories (cryogenic laboratory, optical methods laboratory, surface physics laboratory, solid state laboratory, high vacuum and plasma laboratory, low energy accelerator laboratory) and by the School’s development and production base (glass and optics workshop, Association Vacuum/MFF Praha). Applied research has been an integral part of the School of Physics’ output and covers a wide spectrum of problems – from modelling the influence of pollution on the quality of the environment to the construction of the hygrometer or radon concentration meter.

Modern physics is developing broad collaborations on joint projects with other Czech universities as well as with the Academy of Sciences Institutes. Two-sided agreements are the main form of collaboration with colleagues from universities and research institutions around the world (we are participating at 57 from 119 University agreements to date). The top quality collaboration represents the active participation in the Europe-wide projects such as the LHC accelerator at CERN.

Research and teaching activities are provided by different departments. Besides that the parts of the School are the Department of Didactics of Physics and the Laboratory of General Physics Education.

#### Institute of Astronomy

was founded in 1887. Its research concentrates on the dynamics of asteroids and comets, interplanetary matter, variable stars and on the processes in the nuclei of active galaxies and in the early stages of Universe evolution.

#### Institute of Physics

The research activities fall into two broad groups, dealing with experimental and theoretical studies of electronic energy structure of semiconductors and of biologically important molecules, membranes and cell structures.

In the case of work on semiconductors, the material research is focused on the technological problems of radiation detectors, electrical and optical properties and magnetooptics of AIIBVI compounds, nanostructures and of magnetic thin layers for optoelectronic devices. The structures and functions of biologically active molecules important for biology and medicine (nucleic acids constituent analogs, porphyrins) are examined by advanced methods of Raman spectroscopy. Membrane and cellular structures (liposoms, biological membranes, Saccharomyces cerevisiae) are studied by methods of emission spectroscopy, laser pulsed fluorometry and microfluorometry.

There is an active theoretical programme providing both groups with theoretical support in transport and optical properties in condensed matter, energy transfer and relaxation processes in molecular systems.

#### Department of Electronics and Vacuum Physics

The main problems studied are those connected with the movement of neutral and charged particles in vacuum, gases, and condensed matter. The basic research field is the interaction between particles and the particle interaction with gases, solid structures and surfaces. In particular, the research concerns vacuum physics, physics of thin films and surfaces, plasma physics and space physics together with their applications in diagnostics and modern technologies in material science.

#### Department of Metal Physics

The main direction of the research lies in studies of the structure, mechanical and magnetic properties of metals, intermetallic compounds and composite materials (from pure metals to 4f and 5f elements and modern light compounds). A large effort is targeted on complex investigation of physical aspects of plastic deformation, magnetic state as well as phase transitions in metallic materials. Industrial applications are a very important feature of departmental activities.

#### Department of Semiconductor Physics

The main effort is concentrated on the study of the structure and properties of metallic magnetic multilayers, solar cells based on CdTe, organic semiconductors, low dimensional semiconductor structures A(III)B(V), research of intrinsic processes in bulk semiconductors and thin layers and quantum mechanical theory of electronic systems. The department also provides experimental services for other Faculty laboratories in structure analysis by X-ray diffraction methods.

#### Department of Macromolecular Physics

The research activities of the Department of Macromolecular Physics cover studies of homogeneous and heterogeneous polymers on the submolecular, molecular and supramolecular levels. In particular polymer networks, gels and recently also liquid crystal polymers are studied by mechanical, dielectric and other physical methods. Electronic structure of polymers and their photophysical properties are investigated by optical methods. Plasma polymerization and physical properties of plasma polymer layers are also studied.

#### Department of Low Temperatures Physics

The department staff can rely on up to date instrumentation, which allows the work in the field of nuclear magnetism, hyperfine interactions, radiospectroscopy (nuclear orientation, Mössbauer spectroscopy and nuclear magnetic resonance) and positron life time spectroscopy in solids. The department operates a modern helium liquefier, and liquid helium is supplied to almost all experimental departments.

#### Department of Geophysics

Seismology research is aimed at the seismic waves theory, the physics of earthquakes and applications (structural studies). In geodynamics and physical geodesy attention is paid to the study of the convective processes in the Earth’s crust and center and to the study of the Earth’s physical parameters with a close connection to gravimetry, geothermics and geomagnetism. Other topics are studied in collaboration with other organizations.

#### Department of Chemical Physics and Optics

Theoretical and experimental work is carried out at this department. It concentrates on molecular and biological complexes and their computer modelling development and use of modern spectroscopic methods together with laser technology. The depart-ment participates in environmental problem solving (atmospheric ozone problems).

#### Department of Nuclear Physics

The research activities cover the theoretical and experimental nuclear physics, namely the structure of complex nuclei and the mechanism of nuclear reactions. The theoretical investigations involve also topics beyond the nuclear physics (quantum chaos, general properties of finite fermionic systems, properties of metal clusters and quantum dots). The experimental activities are carried out in a broad international collaboration. The main subjects of interest are the rare processes in the beta-decay of nuclei and the investigation of collisions of hadrons at very high energies (CERN, ATLAS project). Research topics in applied nuclear physics cover physics of nuclear reactors, nuclear safety, nuclear technology and ecologically oriented radiational technology.

#### Department of Meteorology and Environmental Protection

The department primarily works on computerized meteorological forecasting, the movement of pollution in the Earth’s atmosphere, climatologic changes and climate modelling and the problems of strato-spheric and low level ozone. The department takes part in the following international programmes: the forecast system ALADIN development, the environmental problems of Central Europe.

#### Department of Theoretical Physics

The activities of the department include: relativistic physics, astrophysics and cosmology, theoretical atomic physics and other subjects of mathematical and computer physics. Recently developed subjects include the theory of gravitational physics and black holes, the theory of gravitational radiation and relativistic cosmology, electron-molecule resonance collisions, phase transitions theory and the phenomenological description of liquid structure.

#### Nuclear Center

There are two directions of research – theoretical and experimental. The theoretical department concentrates on several topics in subnuclear physics (deep inelastic scattering, electroweak interactions, chiral perturbation theory) and quantum field theory. The basic experimental tool is the Van de Graaff accelerator used for the polarization experiments, nuclear analytic methods and for particle detectors testing. The most important particle physics experimental activities are carried out in collaboration with the international centers DESY (H1 project), CERN (DELPHI and ATLAS experiments) and FERMILAB (D0 project). Research in cosmic ray physics is represented by experiments CAT and CELESTE.

#### Department of Didactics of Physics

The department offers study programs to instruct student-teachers of physics for all types of schools (lower secondary and upper secondary, general and technical schools), and courses for the further education of current physics teachers. It is an important center for research and development in physics education, oriented to new teaching methods, school experiments, physics curricula, teaching aids and the applications of computer and communication technologies in physics education. The department is involved in several international research projects, e.g. Third International Mathematics and Science Study (IEA), EU Project Socrates, Tempus, IRDIC.

An intensive co-operation with schools and with physics teachers, and raising their competence in physics education, is also an important part of the department’s activities.

#### Laboratory of General Physics Education

This laboratory developed and is taking care of all types of student laboratories (mechanics, electricity and magnetism, optics, atomic physics) for this and others Faculties of Charles University. The department is responsible of presenting the basic Physics course demonstration experiments.