Title	Matroid theory
Code	ÚMV/TMT/04	Teacher	Horňák Mirko
ECTS credits	5	Hrs/week	3/-
Assessment	Examination	Semester	3
T/L method	Lecture
Objective	To acquaint students with basic notions of matroid theory and possibilities of using matroids in various disciplines of discrete mathematics.
Content	Independent sets and bases. Properties of rank function. Closure operator. Circuits. Duality in matroids. Hyperplanes. Submatroids. Restriction, contraction, minor of a matroid. Transversals. Radó-Hall's Theorem and its generalisations. Greedy algorithm versus matroids.
Recommended reading	D. J. A. Welsh, Matroid Theory, Academic Press, 1976

Title	Selected Topics in Probability
Code	ÚMV/VKP1/04	Teacher	Žežula Ivan
ECTS credits	5	Hrs/week	3/-
Assessment	Examination	Semester	3
T/L method	Lecture
Objective	To present the perspective of probability from the standpoint of measure theory and to have students understand the most important results of probability theory.
Content	General definition of probability. Distribution function and its properties. Basic types of multivariate distributions. Conditional distributions and means. Convolutions. Types of convergence of random variables. Strong law of large numbers. Central limit theorems.
Alternate courses	ÚMV/VKP1/99
Recommended reading	Loeve: Probability theory, Van Nostrand, 1960 Rényi: Foundations of Probability, Holden-Day, 1970

Title	Differential and Integral Equations
Code	ÚMV/DIR/06	Teacher	Mihalíková Božena
ECTS credits	6	Hrs/week	3/1
Assessment	Examination	Semester	3
T/L method	Lecture, Practical
Content	Boundary value problems. Asymptotic properties and the stability of linear differential systems. Fredholm's integral equations with degenerate and nondegenerate kernel. Integral equations with symmetric kernel.
Prerequisite courses	ÚMV/FAN/06 orÚMV/FAN/04
Recommended reading	P. Hartman, Ordinary differential equations, New York, 1964 G.F.Trikomi, Integral equations, New York, 1967

Title	Combinatorial Optimisation
Code	ÚMV/KOO/04	Teacher	Jendroľ Stanislav, Lacko Vladimír
ECTS credits	6	Hrs/week	3/1
Assessment	Examination	Semester	4
T/L method	Lecture, Practical
Objective	To teach students basic knowledge about the  methods of modelling and controlling and how to apply them to typical problems using methods of discrete mathematics.
Content	Complexity of combinatorial algorithms. Sorting problems. Searching  algorithms. Greedy algorithm. Trees and spanning trees: rooted trees. Minimal spanning tree problem. Optimal path problems. Introduction to network analysis. Distribution problems. Flows. Assignment problem. The Chinese Postman problem. The Travelling Salesman problem. Transportation problems.
Exclusive courses	ÚMV/KOA1/04
Recommended reading	N. Christofides: Graph Theory - An Algorithmic approach, Academic Press, New York 1975 (ruský preklad z r. 1978). J. Plesník: Grafové algoritmy, Veda Bratislava 1983. G. Chartrand, O.R. Vellermann: Applied and Algorithmic Graph Theory, McGraw-Hill, Inc. New York 1993.

Title	Functional Analysis
Code	ÚMV/FAN/06	Teacher	Doboš Jozef
ECTS credits	6	Hrs/week	3/1
Assessment	Examination	Semester	2
T/L method	Lecture, Practical
Content	Metric spaces and their fundamental properties. Complete metric space and the contrary mapping principle. Normed linear spaces. Hilbert's space. Linear operators. The spectrum of the operator.
Recommended reading	N. Dunford, J.T. Schwartz, Linear operators, Part I, Generaly theory, New York, 1963 N. Dunford, J.T. Schwartz, Linear operators, Part II, Spectral theory, New York, 1963

Compulsory elective courses

Title	Mathematical Foundations of Cryptography
Code	ÚINF/MZK/06	Teacher	Geffert Viliam, Lacko Vladimír
ECTS credits	6	Hrs/week	3/2
Assessment	Examination	Semester	1
T/L method	Lecture, Practical
Content	Classical cryptography. Steganography. Conventional symmetric cryptography. Feistel networks. Encryption modes: ECB, CBC, CFB, OFB. Security definitions. Models of an adversary. Cryptoanalysis. Asymmetric cryptosystems. One-way functions with trapdoors. RSA cryptosystem. El-Gamal cryptosystem. Generating large prime numbers. Elliptic curves cryptography. Keyed Hash functions. Collision resistant functions. Birthday paradox. SHA-1. Message authentication codes. Password security. Digital signatures. Blind signatures. Key management. X509. Certificates. Certification authorities. Electronic payments. Electronic cash.
Exclusive courses	ÚINF/UKR1/03

Title	Real Functions Theory
Code	ÚMV/TRF/07	Teacher	Doboš Jozef
ECTS credits	5	Hrs/week	2/1
Assessment	Examination	Semester	1
T/L method	Lecture, Practical
Content	Continuity properties of real functions, generalisations of continuity, quasi-uniform convergence, sets of discontinuity points, stationary sets, determining sets, metric preserving functions.

Title	Geometric Transformations
Code	ÚMV/GZ/04	Teacher	Ivančo Jaroslav
ECTS credits	5	Hrs/week	2/1
Assessment	Examination	Semester	1, 3
T/L method	Lecture, Practical
Objective	To provide deeper knowledge of projective spaces and transformation groups.
Content	Projective spaces, Projective transformations, collineations. Fixed elements of a collineation. A clasification of collineations.
Recommended reading	S. V. Duzhin, B. D. Chebotarevsky: Transformation Groups for Beginers, AMS  2004

Title	Probability and Statistics
Code	ÚMV/PST1b/04	Teacher	Skřivánková Valéria, Ohriska Ján
ECTS credits	6	Hrs/week	2/2
Assessment	Examination	Semester	1, 3
T/L method	Lecture, Practical
Content	Random vectors, their distributions and characteristics. Correlation and regression. Random sample, sampling distributions and characteristics. Point estimates and their properties. Maximum likelihood method. Interval estimates; confidence interval construction. Testing of statistical hypothesis; critical region and level of significance. Parametric and nonparametric tests.
Recommended reading	Mandenhall W.: Introduction to probability and statistics, PWS Publishers, Boston, 1987 Sincich T.: Statistics by example, Dellen Publishing Company, New Jersey, 1990

Title	Game Theory
Code	ÚMV/TH1/04	Teacher	Cechlárová Katarína, Hajduková Jana
ECTS credits	6	Hrs/week	3/1
Assessment	Examination	Semester	1, 3
T/L method	Lecture, Practical
Objective	To teach the basic methods of game theory and to have students model situations from everyday life as simple games.
Content	Examples of games. Extensive form of a game, value of the game. Von Neumann Morgenstern theory of utility. Matrix games and their solution. Bimatrix games.Theory of negotiations. n-person games: core, Shapley value. Economic applications of game theory.
Alternate courses	ÚMV/TH1/99
Recommended reading	1. K. Binmore, Fun and games, D.C. Heath, 1992. 2.  G. Owen,  Game Theory, Academic Press. 3. L.C. Thomas,  Games, Theory and Applications,  Wiley, New York. 4. H.S. Bierman, L.Fernandez, Game Theory with Economic Applications, Addison-Wesley, 1998.

Title	Theory of Codes
Code	ÚMV/TKO1/04	Teacher	Horňák Mirko
ECTS credits	6	Hrs/week	4/-
Assessment	Examination	Semester	1, 3
T/L method	Lecture
Objective	To acquaint students with the basic principles and theoretical bases of text coding and possibilities for their application.
Content	Monoids. Basic notions of theory of codes. Examples of codes. Important classes of codes. Maximal codes. Submonoids generated by codes. Stable submonoids. Group codes. Free hull of a set of words. Test for recognising codes. Measure of a code. Bernoulli distribution. Dyck code. Complete sets in monoids. Thin codes. Composition of codes. Indecomposable codes.
Recommended reading	J. Berstel and D. Perrin, Theory of Codes, Academic Press 1985

Title	Theory of Categories
Code	ÚMV/TK/07	Teacher	Ploščica Miroslav
ECTS credits	5	Hrs/week	2/1
Assessment	Examination	Semester	2
T/L method	Lecture, Practical
Objective	To teach students a categorical approach to various mathematical objects and constructions. To provide basic knowledge about categories, functors and natural transformations.
Content	Abstract and concrete categories. Morphisms, monomorphisms, epimorphisms and isomorphisms. Subobjects, quotient objects, free objects. Products and copoducts. Limits and colimits, completeness. Functors. Natural transformations. Adjoint functors.
Recommended reading	Adámek J. : Theory of Mathematical Structures, Reidel Publications, Dordrecht-Boston 1983 Mac Lane S., Birkhoff G.: Algebra, The Macmillan Company, 1967 Lawvere F. W., Schanuel S. H.: Conceptual Mathematics (A first introduction to categories), Cambridge University Press 1997 Adámek J., Herrlich H., Strecker G.: Abstract and concrete categories: The joy of cats, John Wiley and Sons, New York 1990

Title	Applied Linear Algebra
Code	ÚMV/ALA1/04	Teacher	Studenovská Danica
ECTS credits	5	Hrs/week	2/1
Assessment	Examination	Semester	2, 4
T/L method	Lecture, Practical
Objective	To teach students basic knowledge about linear algebra; to make students able to apply the theory in concrete excercises.
Content	Matrices over Euclidean rings, canonical forms. Polynomial matrices. Similar matrices. Jordan normal form. Functions of matrices, sequences, series. Inversion of singular matrices, pseudoinverse matrices and their application.
Alternate courses	ÚMV/ALA1/99
Recommended reading	H.E.Rose: Linear algebra, A pure mathematical approach, Birkhäuser   Verlag, 2002 D.Serre: Matrices, Theory and applications, Springer Verlag, 2002. http://www.cs.ut.ee/~toomas_l/linalg/

Title	Fractal Geometry
Code	ÚMV/FRG1/03	Teacher	Bukovský Lev
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	2
T/L method	Lecture
Objective	To introduce students to the mathematical approach to analysing the concept of a fractal with the possibility of using the results for the construction of fractals.
Content	Concept of a fractal. Basic topology of metric spaces. Self-similarity of a fractal. Fractal as fixpoint of a mapping. Construction of a fractal by iteration. Topological dimension and basic properties. Hausdorff measure and Hausdorff dimension. Topological and Hausdorff dimension of particular fractals. Some methods of construction of a fractal (topological dynamics).
Recommended reading	G. A. Edgar: Measure, Topology and Fractal Geometry, Springer 1990. K. Falconer, Fractal Geometry, John Willey 1992 H. O. Peitgen, H. Jurgens and D. Saupe, Fractals for Classroom, I, II, Springer Verlag, Berlin 1991

Title	Number Theory
Code	ÚMV/TCI/04	Teacher	Harminc Matúš
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	2
T/L method	Lecture
Objective	To familiarise students with the divisibility and congruences of integers, linear and quadratic congruences and arithmetic functions.
Content	Euclidean algorithm. Fundamental theorem of arithmetic. Primes, composites, canonical form and its applications. Congruences, criteria of divisibility. Arithmetic functions. Euler’s theorem. Fermat’s theorem. Wilson’s theorem. Linear and quadratic congruences.
Recommended reading	M. B. Nathanson: Elementary Methods in Number Theory. Springer, 2000 H. E. Rose: A Course in Number Theory. Clarendon Press, Oxford, 1994

Elective courses

Title	Foundations of Knowledge Systems
Code	ÚINF/ZNA1/06	Teacher	Vojtáš Peter
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	3
T/L method	Lecture
Content	Relations of formal models: DBMS, SQL, and logic programming. Summary of different formal models of computational processes, connections among them and translations. Gentzenov systems, semantics and verification of programs. Formal specifications, temporal logics: formulas, models, tableaux.
Recommended reading	M. Ben-Ari. Mathematical logic for Computer Science 2ed. Springer Verlag London 2001 J. Ullman. Principles of database and knowledge based systems. Comp. Sci. Press 1988 J. W. Lloyd. Foundations of logic programming. Springer Berlin 1987

Title	Theory of Information
Code	ÚMV/TIN1/03	Teacher	Bukovský Lev
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	1, 3
T/L method	Lecture
Objective	To introduce students to mathematical attempts at solving selected problems of computer science.
Content	Measurement of information. Entropy and its properties. Shanon’s theorems. Coding and basic types of codes. Using of algebraic structures in construction of codes. Kolmogorov complexity. Basic properties and relation to the notion of entropy. Complexity and randomness.
Recommended reading	J. H. van Lint, Introduction to Coding Theory, Springer 1992 M. Li and P. Vitanyi, Kolmogorov Complexity and its Applications, Handbook of Theoretical Computer Science, Elsevier, 1990, p. 188-252

Title	Control Theory
Code	ÚMV/TS1/04	Teacher	Cechlárová Katarína
ECTS credits	6	Hrs/week	3/1
Assessment	Examination	Semester	1, 3
T/L method	Lecture, Practical
Objective	To teach students the basic concepts of controllable systems.
Content	Controllable systems. Pontrjagin maximum principle. Linear systems, bang-bang controls,  singular controls.. Discrete systems, dynamic programming, Bellmann’s optimality principle. Practical applications of theoretical results.
Alternate courses	ÚMV/TS1/99 orÚMV/TS1/00
Recommended reading	K. Macki, A. Strauss: Introduction to Optimal Control Theory, Springer, 1980 G. Feichtinger, R.F. Hartl: Optimale Kontrolle okonomischer Prozesse, Berlin, 1986

Title	Computational Complexity
Code	ÚINF/VYZ1/04	Teacher	Geffert Viliam
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	1, 3
T/L method	Lecture
Objective	To give students background in the computational complexity and theory of NP-completeness.
Content	Deterministic and nondeterministic algorithms with polynomial time; NP-completeness. Deterministic simulation of a nondeterministic Turing machine. Satisfiability of Boolean formulae. Other NP-complete problems: satisfiability of a formula in a conjunctive normal form, 3-satisfiability, 3-colorability of a graph, 3-colorability of a planar graph, knapsack problem, balancing, etc. Space bounded computations, classes LOG-space and P-space. Deterministic simulation: Savitch’s theorem. Closure under complement. Classification of computational complexity of problems.
Alternate courses	ÚINF/VYZ1/03 orÚINF/VYZ1/00
Recommended reading	A.V.Aho and J.D.Ullman. The design and analysis of computer algorithms. Addison-Wesley, 1974 P.van Emde Boas. Machine models and simulations. In J.van Leeuwen (ed.): Handbook of theoretical computer science. North-Holland, 1990 Ch.K.Yap. Introduction to the theory of complexity classes. To be published by Oxford Univ. Press. (Electronic version available via anonymous ftp://cs.nyu.edu/pub/local/yap/complexity-bk).

Title	Algorithmically Unsolvable Problems
Code	ÚMV/ANP/03	Teacher	Bukovský Lev
ECTS credits	4	Hrs/week	2/-
Assessment	Examination	Semester	2
T/L method	Lecture
Objective	To introduce students to the most important results about the non-existence of an algorithm for solving a given problem.
Content	Axiomatic theories of natural numbers. Definability of recursive functions. Tarski’s theorem on undefinability of truth in formalised arithmethic. Godel incompleteness theorem. Algorithmic unsolvability of particular mathematical problems. Non-existence of an algorithm for finding a solution to Diophantine equations. Reduction of problems and degrees of unsolvability.
Recommended reading	J. Barwise ed., Handbook of Mathematical Logic, North Holland 1977S. C. Kleene, Introduction to the Metamathematics, Van Nostrand 1952, ruský preklad Moskva 1957. E. Mendelson, Introduction to Mathematical Logic, Van Nostrand 1963. M. Davis, Hilbert's Tenth Problem is Unsolvable, Amer. Math. Monthly, 1973, 233--269.

PHYSICS

Study programme   Biophysics

(Full-time master)

  Code   Title   ECTS Credit   Hours/week   Assessment     Recommended Year/Semester

Compulsory courses

ÚFV/CHV1/03	Molecular Structure and Chemical Bonding	6	2/2	Examination	1/1
ÚFV/SP1/04	Semester Project	4	-/4	Assessment	1/1
ÚCHV/STA1/03	Structure Analysis	6	2/2	Examination	1/1
ÚFV/FCH1/02	Physical Chemistry for Biological Sciences	6	3/2	Examination	1/1
ÚCHV/BCH1a/03	Biochemistry I	3	2/-	Examination	1/1
KFaDF/DF2p/07	History of Philosophy	4	2/1	Examination	1/1
ÚFV/BME1/00	Introduction to Physics of Biological Membranes	3	2/-	Examination	1/2
ÚFV/EMB1b/04	Optical Spectroscopy	6	4/-	Examination	1/2
ÚCHV/BCH1b/03	Biochemistry II	5	3/-	Examination	1/2
ÚFV/EMB1d/04	Nuclear Magnetic Resonance	5	3/-	Examination	1/1
ÚFV/RP1/04	Annual Project	6	-/6	Assessment	1/2
ÚFV/SP2/04	Semester Project	6	-/6	Assessment	2/3

Compulsory elective courses

ÚFV/NOT1a/03	Nontraditional Optimisation Techniques I	5	2/2	Examination
ÚFV/ZSY1/03	Complex Systems	5	2/2	Examination
ÚFV/MBB1/03	Fundamentals of Cellular and Molecular Biology	5	3/-	Examination
ÚFV/EMB1c/04	Modern Trends in Biophysical Methods	5	3/-	Examination
ÚFV/SBFc/03	Biophysical Seminar	1	-/1	Assessment
ÚFV/SBFe/03	Biophysical Seminar	1	-/1	Assessment
ÚCHV/ENZ/04	Enzymology	5	3/-	Examination
ÚFV/BSIM1/03	Biomolecular Simulations	6	2/2	Examination
ÚFV/BIOE1/02	Bioenergetics	3	2/-	Examination
ÚFV/PRb/04	Laboratory Training II: Optical Spectroscopy Methods	3	-/3	Assessment
ÚFV/PRd/04	Laboratory Training III: NMR	3	-/3	Zápočet
ÚFV/SBFd/03	Biophysical Seminar	1	-/1	Assessment
ÚFV/NOT1b/03	Nontraditional Optimisation Techniques II	5	2/2	Examination
ÚFV/NANO1/02	Nanotechnologies	3	2/-	Examination
ÚFV/MSA1/03	Methods of Structural Analysis	7	3/2	Examination
ÚFV/SBFf/03	Biophysical Seminar	1	-/1	Assessment
ÚFV/BMM1/05	Introduction to Physics of Biomacromolecules	3	2/-	Examination
ÚFV/ZBF1/05	Fundamentals of Biophotonics	3	2/-	Examination

Course units

Compulsory courses

Title	Molecular Structure and Chemical Bonding
Code	ÚFV/CHV1/03	Teacher	Uličný Jozef
ECTS credits	6	Hrs/week	2/2
Assessment	Examination	Semester	1
T/L method	Lecture, Practical
Objective	To teach actual methods used for computer simulations of molecules and to give students hands-on experience with standard methods.
Content	Born-Oppenheimer approximation. Methods and approaches of classical molecular mechanics. Force fields and force constants for polyatomic simulations. Force fields for biomolecular simulations (CHARMM, AMBER, MM2-4, MMFF, CVFF, etc.). Independent electron approximation. Hartree-Fock self-consistent field method. Post Hartee-Fock methods. Density functional theory (DFT): basic principles and implementation. LSDA approximation and gradient corrected methods. Hybrid methods. Wavefunction and electron density analysis. Limits and perspectives of classical and quantum molecular mechanics. Alternative methods. Ab initio computations and experimental observables. Experimental and computational observables. Molecular  dynamic and stochastic methods. Integration algorithms. Car-Parinello dynamics.
Recommended reading	Leech: Molecular Modelling: Principles and Applications, Longmann, 1996 M.P. Allen, D.J. Tildesley: Computer Simulation of Liquids, Oxford, University Press, 1989 P. W. Atkins, R. S. Friedman: Molecular Quantum Mechanics.Oxford University Press, 1997 (3. edition)

Title	Semester Project
Code	ÚFV/SP1/04	Teacher	Miškovský Pavol
ECTS credits	4	Hrs/week	-/4
Assessment	Assessment	Semester	1
T/L method	Practical
Objective	To realise experimental and/or theoretical works within the frame of a chosen theme and to present the results of this work in a consistent way.
Content	Work on a chosen theme for the semester project in the Department of Biophysics.
Recommended reading	The literature will be recommended by supervisors of individual works.

Title	Structure Analysis
Code	ÚCHV/STA1/03	Teacher	Černák Juraj
ECTS credits	6	Hrs/week	2/2
Assessment	Examination	Semester	1
T/L method	Lecture, Practical
Objective	To teach students about symmetry at the micro- and macrostructural level,  about diffraction methods used for crystal structure determination and how to use the results of the crystal structure analysis in their own work.
Content	Historical introduction: importance of diffraction methods. Origin and properties of x-rays. Elements of symmetry; space groups. Crystallographic systems; Bravais unit cells. Miller indices. Theory of diffraction; Laue and Bragg equations. Reciprocal space; Ewald construction. Single crystal diffraction methods; automatic diffractometers. Powder diffraction: Debye-Scherrer and diffractometric methods, their theory and use. Atomic factor, structure factor, electronic density and their relationship. The phase problem: overview of the methods for solving the phase problems. Refinement of the structure; geometric parameters. Crystallisation processes; methods of preparation of single crystals. Density. Basic inorganic structure types.
Recommended reading	Clegg W.: Crystal Structure Determination, Oxford University Press, 1998 Luger, P.: Modern X-ray Analysis on Single Crystals. Walter de Gruyter, Berlin, 1980

Title	Physical Chemistry for Biological Sciences
Code	ÚFV/FCH1/02	Teacher	Jancura Daniel, Miškovský Pavol
ECTS credits	6	Hrs/week	3/2
Assessment	Examination	Semester	1
T/L method	Lecture, Practical
Objective	To introduce students to fundamental knowledge of physical chemistry emphasizing the physico-chemical properties of biomacromolecules and biological systems.
Content	Description of macroscopic systems, energy and 1st law of thermodynamics, entropy and 2nd law of thermodynamics, Gibbs energy and equilibrium state, chemical potential, binding constants of ligand-macromolecule interactions, biophysical applications of the thermodynamics. Solutions, electrolytic solutions, electrochemical equilibrium, electrodes, electrochemical potential. Statistical thermodynamics: the interpretation of energy, heat, entropy and information; the partition functions, biological applications of statistical thermodynamics, the conformational transitions in proteins and nucleic acids. Chemical reactions, chemical and biochemical kinetics, dynamics of the chemical reactions, kinetics of enzymatic reactions, inhibition of enzymes. Transport processes, molecular diffusion, membrane transport and its significance for biological organisms.
Recommended reading	P. Atkins and J. de Paula: Physical chemistry (7th Edition), Oxford University Press, 2002 D. Eisenberg and D. Crothers: Physical chemistry with applications  to the life sciences, Benjamin/Cummings, 1979 K. van Holde, W. Johnson and P. Ho, Principles of physical  biochemistry, Prentice Hall, 1988

Title	Biochemistry I
Code	ÚCHV/BCH1a/03	Teacher	Potočňák Ivan, Podhradský Dušan
ECTS credits	3	Hrs/week	2/-
Assessment	Examination	Semester	1
T/L method	Lecture
Objective	To provide understanding of life’s processes in molecular terms.
Content	Basic structures of biomolecules. Structures and functions of saccharides and lipids. Amino Acids and nucleic acids. Techniques of protein and nucleic acid purification. Three-dimensional structures of proteins. Protein folding, Dynamics and structural evolution. Hemoglobin: protein function in a microcosm. Flow of genetic information. Proteosynthesis. Biosynthesis of nucleic acids, replication, transcription and translation. Enzymes: structure and function. Rates of enzymatic reactions Mechanisms of enzyme action and control of enzymatic activity.
Recommended reading	Lubert Stryer and col.: Biochemistry 5th edition, W.H.Freeman and Company, New York, 2003 Voet, Voet: Biochemistry 3rd edition, John Wiley & sons, England, 2004

Title	Introduction to Physics of Biological Membranes
Code	ÚFV/BME1/00	Teacher	Fabriciová Gabriela, Miškovský Pavol
ECTS credits	3	Hrs/week	2/-
Assessment	Examination	Semester	2
T/L method	Lecture
Objective	To teach the fundamental processes that occur in biological membranes.
Content	Structure and models of membranes. Physico-chemical properties of biological membranes. Functions of membranes. Propagation of nerve impulse and the process of vision. Physical methods for the study of membranes.
Recommended reading	C.Hidalgo: Physical Properties of Biological Membranes,Plenum Press, New York 1988 van Winkle I. J.: Biomembrane transport, Academic Press, San Diego 1999 Stein W. D.: Channels, carriers, and pumps, Academic Press, San Diego 1990 Glaser R.: Biophysics, Springer-Verlag, Heidelberg 1999 Pollard T. D., Earnshaw W. C.: Cell biology, Saunders, Philadelphia 2004 Alberts: Molecular biology of the cell, Garland Science, New York 2002