mathematics mathematics, undergraduate - up famnit

University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies

MATHEMATICSMATHEMATICSMATHEMATICSMATHEMATICS, undergraduate , undergraduate , undergraduate , undergraduate –––– course descriptioncourse descriptioncourse descriptioncourse descriptionssss

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CCCCOMPULSORY COURSESOMPULSORY COURSESOMPULSORY COURSESOMPULSORY COURSES

Course name: ALGEBRA I ALGEBRA I ALGEBRA I ALGEBRA I ---- MATRIX CALCULUSMATRIX CALCULUSMATRIX CALCULUSMATRIX CALCULUS

Number of ECTS credits: 6666

Content:Content:Content:Content:

- Vectors, analytic geometry in space.

- Matrices. Types of matrices and basic operations with matrices. Rank of a matrix. Inverse.

Systems of linear equations. Matrix interpretation and theorem of solvability. Elementary

matrices, Gauss method. Determinants. Cramer's rule.

Course name: ALGEBRA II ALGEBRA II ALGEBRA II ALGEBRA II ---- LINEAR ALGEBRALINEAR ALGEBRALINEAR ALGEBRALINEAR ALGEBRA


Content: Content: Content: Content:

- Groups, rings, fields. Ring of polynomials.

- Vector space. Subspaces, linear operators. Linear independence. Basis and dimension of

- vector space.

- Eigenvalues. The characteristic and minimal polynomial.

- Inner product. Orthogonal systems. Gramm-Schmidt process of ortogonalization. Norm. Norm of

the matrix and the operator. Normal and related operators.

- Convexity in the vector space.

- Normalized vector spaces as metric spaces. Isometries of R2 and R3.

Course name: ANALYSIS I ANALYSIS I ANALYSIS I ANALYSIS I ---- THE FOUNDATHE FOUNDATHE FOUNDATHE FOUNDATIONS OF ANALYSISTIONS OF ANALYSISTIONS OF ANALYSISTIONS OF ANALYSIS


Content:Content:Content:Content:

- The natural numbers. Rational numbers. Real numbers. Complex numbers.

- The sequence of real numbers. Limits and accumulation points. Cauchy condition. Upper and

lower limit. Monotone sequences. Bolzano-Weierstrass theorem.

- Series. The convergence criteria. Absolutely and conditionally convergent series.

- Functions of real variables, even and odd functions, periodicity. Limits of functions, left and right

limits. Continuity. Continuous functions on closed intervals limited. Bisection method for finding

zeros.

- The elementary functions. Cyclometric functions.

Course name: ANALYSIS II ANALYSIS II ANALYSIS II ANALYSIS II ---- CALCULUSCALCULUSCALCULUSCALCULUS




ContentContentContentContent: : : :

- Derivative. Mean value theorems. Differentiation of monotone functions. L'Hopital's rule. Higher

derivatives. Taylor's formula. Local extrema. Convex and concave functions. Inflection points.

Tangent method of finding the zeros.

- The indefinite integral. Definite Integrals. Darboux and Riemann sums. Leibniz-Newton formula.

Mean value theorems. Integration methods. Applications of the definite integral in geometry.

Improper integral. Numerical integration.

- The logarithm, the number e, and the definition of exponentiation with the real exponent.

- Drawing planar curves.

- Sequences and function series. Power series. Taylor series. Elementary

- complex functions.

Course name: DISCRETE MATHEMATICSDISCRETE MATHEMATICSDISCRETE MATHEMATICSDISCRETE MATHEMATICS II II II II ---- COMBINATORICSCOMBINATORICSCOMBINATORICSCOMBINATORICS



- The principle of the sum, product. Counting pairs. Elementary combinatorics. Assignment.

Assignment within the set. The existence of a 1-factor. Assignment between two sets, Hall’s

theorem. König’s theorem, applications. Recursion. Generating functions. Linear recursion with

constant coefficients. Applications of combinatorics. Inclusion-exclusion principle. Rook

polynomial. Möbius inversion. Partially ordered sets and the Möbius function. Theorem on the

inversion. Designs. Finite projective planes. Correction code. Steiner systems. Kirkman schoolgirl

problem. Ramsey theorem, proof and application. Polya Theory. Burnside’s lemma. Polya’s

theorem.

- Graphs, examples of graphs. Trees. Basic properties, enumeration of trees. The cheapest tree.

Operations on graphs. Product of graphs. Deck graphs and voltage graphs. Graphs and groups.

Graph automorphism group. Cayley graphs and Frucht theorem. Symmetric graphs. Planarity

and duality. Criterion of planarity. Graph embeddings in other plots. Duality and Euler's theorem.

Graph coloring. Coloring vertices. Coloring edges. Chromatic polynomial. Directed graphs.

Eulerian digraphs. Tournaments. Markov chains. Connectivity. Menger’s and Hall’s theorem.

Different versions of Menger’s theorem and Ford-Fulkerson’s theorem. Matroid theory.

Definitions. Matroids and graphs. Examples of matroids and applications

Course name: MATHEMATICAL PRACTICMATHEMATICAL PRACTICMATHEMATICAL PRACTICMATHEMATICAL PRACTICUM IUM IUM IUM I



- Programs for presentations (eg PowerPoint), spreadsheet (eg Excel)

- Text editors (eg WinEdt, TextPad, Emacs, Auctech, Open Office, ...)

- Introduction to TeX and LaTeX-a (MikTeX, tetex, GSview, Acrobat Reader, ...)

- The basic tools to produce images (pdf, eps), working with the formats of images including

images in LaTeX

- Scanning and use of digital cameras.



Course name: DISCRETE MATHEMATICSDISCRETE MATHEMATICSDISCRETE MATHEMATICSDISCRETE MATHEMATICS I I I I –––– SET THEORYSET THEORYSET THEORYSET THEORY



- Introduction to mathematical theory, logic, truth tables, mathematical logic.

- Formal Languages.

- Basic concepts of mathematical logic.

- Methods of recording the sets. The basic relations between sets, the basic operations on sets or

families of sets. Power set. Relations. Graphs. Equivalence relations. Partial and linear ordering.

Latices and Boolean algebra. Well ordering. Function. Special types of functions. Category.

- Finite and infinite, countable and uncountable sets.

- Cardinal and ordinal numbers. Peano arithmetic, mathematical induction.

- The system of axioms of set theory NBG and ZFC. Axiom of choice. Zorn's lemma.

- Introduction to symbolic computation (Mathematica).

Course name: MATHEMATICAL MATHEMATICAL MATHEMATICAL MATHEMATICAL TOPICSTOPICSTOPICSTOPICS IN ENGLISH IIN ENGLISH IIN ENGLISH IIN ENGLISH I


CoCoCoContent: ntent: ntent: ntent:

Lectures are given on the most current research topics in the field of mathematics, which may

include the following topics

- History of the concept of number

- Number theory

- Algebra

- Analysis

- Famous planning tasks

- Overview of the history of computing

- History of Slovenian mathematics

- Historical development of mathematical concepts

Course name: ALGEBRA III ALGEBRA III ALGEBRA III ALGEBRA III ---- ABSTRACT ALGEBRAABSTRACT ALGEBRAABSTRACT ALGEBRAABSTRACT ALGEBRA



- Introduction to number theory, Euclidean algorithm, congruences.

- Polynomials o in single variable. Euclidean algorithm. Zeros of polynomials. Solving algebraic

equations. Polynomials in several variables. Symmetric polynomials. Fundamental theorem of

algebra.

- Grupoids, semigroups and groups. Homomorphisms of groups. Normal subgroups and factor

groups. Families of groups. Groups given by generators and relations. Sylow theorems.

Course name: ANALYSIS III ANALYSIS III ANALYSIS III ANALYSIS III ---- FUNCTIONS OF SEVERALFUNCTIONS OF SEVERALFUNCTIONS OF SEVERALFUNCTIONS OF SEVERAL VARIABLESVARIABLESVARIABLESVARIABLES



- Metric spaces. Cauchy-Schwarz inequality. Open and closed sets.

- Compactness and connectedness. Sequences in metric spaces. Cauchy sequences and complete

metric spaces. Continuity and uniform continuity. Properties of continuous mappings.



- Functions of several variables. Continuity, partial differentiability. Differential mapping from Rn

to Rm. Jacobian matrix. Chain rule of differentiation.

- Higher order partial derivatives. Taylor's formula. Theorem on the locally inverse function and on

implicit functions. Local extremal problems, constrained extremal problems.

- Double and multiple integrals. Properties. The conditions on the existence. The introduction of

new variables.

- Calculation and application.

- Proper and generalized integrals with parameter. Beta and Gamma functions. Stirling formula.

Course name: PHYSICSPHYSICSPHYSICSPHYSICS



Course topics: Physical Measurement, Linear movement, The movement in three dimensions, Forces

and motion, Newton's laws, Friction, The kinetic energy and work, Potential energy, energy

conservation, A system of particles, The centre of gravity, Momentum, Rotation, The angular

momentum, Balance and elastic properties, Gravity, Fluid Mechanics, Oscillation, Waves, General

characteristics and types of waves, Sound, Heat, Temperature, The thermodynamic laws, The

thermal conductivity, The kinetic theory of gases, Entropy, The electric charge, The electric field,

Electric Potential, Capacitance, Electrical resistance, The magnetic field, Induction, Alternating

currents and electromagnetic oscillations, Electromagnetic waves, Geometrical optics, Interference

and diffraction, Basic concepts of modern physics, Photons and material waves, Material waves,

atomic physics, The core of the atom, Special Theory of Relativity.

Course name: INTRODUCTION TO NUMEINTRODUCTION TO NUMEINTRODUCTION TO NUMEINTRODUCTION TO NUMERICAL CALCULATIONSRICAL CALCULATIONSRICAL CALCULATIONSRICAL CALCULATIONS



- Fundamentals of numerical computing. The floating point and rounding errors. Calculations in

floating points. Stable computational processes and the problem sensitivity. The total error.

- Non-linear equations. Bisection. Tangent method: derivatives, implicit functions, systems

- nonlinear equations. Secant method. Algebraic equations.

- Systems of linear equations. LU decomposition and Cholesky decomposition. Gaussian

elimination. Diagonally dominant and tridiagonal matrices. Problem sensitivity. Aposteriori error

estimation. Neumann series and iteratively improvement of the accuracy.

- Eigenvalues. Power method, Inverse power method. Schur and Gershogorin theorem.

- Function approximation. Polynomial interpolation. Divided difference. Hermite interpolation.

- Numerical integration. Integration with polynomial interpolation. Composite rules. Gaussian

quadrature formulas. Euler-Maclaurin formula

- Numerical solution of ordinary differential equations. Solving differential equations of the first

order. The Taylor series method of obtaining solution. Simple methods, the order of the method.

Methods of type Runge-Kutta.

- A linear programming. Convexity and linear inequalities. Simplex algorithm.

Course name: PROBABILTYPROBABILTYPROBABILTYPROBABILTY


ContenContenContenContent: t: t: t:



- Basics of combinatorics

- Fundamental Theorem of combinatorics.

- Variations and variations with repetition.

- Combinations and combinations with repetition.

- Permutations and permutations with repetition.

- The binomial formula and generalizations.

- Outcomes and Events

- The sample space, events, definition of probability.

- Calculations with the events.

- Conditional probability and independence.

- Random Variables

- Random variables and their distributions.

- Overview of some discrete distributions.

- Mathematical expectation and variance.

- Continuous random variables.

- Multidimensional distribution

- Definition of multi-dimensional discrete distribution.

- The independence of random variables.

- covariance, the sum of random variables.

- Conditional distributions and conditional mathematical expectation.

- Multidimensional continuous distributions.

- Generating functions

- Definition and examples.

- The process of diversification.

- Aproximations of distributions

- Convergence of random variables in the distribution.

- The normal distribution approximation of sums of random variables.

- Poisson approximation

Course name: MATHEMATICAL TOPICS MATHEMATICAL TOPICS MATHEMATICAL TOPICS MATHEMATICAL TOPICS IN ENGLISH IIIN ENGLISH IIIN ENGLISH IIIN ENGLISH II



- Basic methods of combinatorics: Classification of discrete problems, basic rules of

combinatorics, Selections, Inclusion-exclusion principle, generating functions, rook polynomials

- Combinatorics and recursion: Distributions, Polynomial sequences, Descending powers, Stirling

number of first and second kind, Lah numbers and antidifferences, Sums, linear recursion

- Theory of discrete probability, experiment, event, conditional probability, independence, Relay

experiments, random variables, Mathematical expectation and variance.

Course name: MATHEMATICAL MODELINMATHEMATICAL MODELINMATHEMATICAL MODELINMATHEMATICAL MODELINGGGG



- Optimization (Minima, maxima, saddle points. Taylor's formula for scalar fields. Types of critical

points. Finding optima under constraints. Discrete catenary. Newton's method. Method of

continuation. Stability of trusses.

- Calculus of variations (Standard problem of variation calculus. Isoperimetric problems. Truss

oscillations. Rotating axes.)



- Torsion (Navier equations. Torsion load. Torsion.)

- Statistics (χ2 test. Unbiased estimation. Statistical simulations.)

- Combinatorial optimization (Optimization problems. The matching problem. The transport

problem. The shorest path on a graph. The maximal flow problem. The traveling salesman

problem. Combinatorial optimization.)

- Linear programming (Linear program. Non-standard forms of linear programs. Terminology.

Combinatorial nature of linear programming. The simplex method. The revised simplex

algorithm).

- Sawing (Formulation of the problem. Algorithm. Avoinding the inverse matrix. The rucksack

problem).

- Duality (Definition. Duality theorem. Optimality of simplex method.)

- Algebraic graph theory (The concept of a graph. Transitive envelope. Network. Cycles and co-

cycles. Dimensions of subspaces in C and K. Basis in K. Solving Ax=χ. Basis in C.)

- Out of Kilter (The problem. Reduction. Duality. Minty's theorem.)

Course name: COMPUTERCOMPUTERCOMPUTERCOMPUTER SCIENCESCIENCESCIENCESCIENCE II II II II Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction Introduction to programming languages, concepts of programming languages, Meta-language, Chomski hierarchy, computability, overview of programming language history.

- Lambda calculus History of λ-calculus, λ-abstraction, definition of λ-calculus, evaluation, substitution, alpha reductions, beta reductions, programming in λ-calculus, Church numbers, recursion, uses of λ-calculus.

- Syntax Grammars, parsing, parse trees, BNF, grammar definition, operator, priority of operator, asociativity, dangling else, abstract syntax tree, BNF variations.

- Basic structures Values, basic types, variable declaration, global declaration, local declaration, implementation of variables, symbol tables, name-spaces.

- Functional languages Mathematical and logic foundations, function expressions, function definition, recursive functions, polymorphism, higher-order functions, examples of functions.

- Imperative languages Variables, sequential control, structured control, if statement,loops, patterns, function implementation, parameters, activation records, array, functions on arrays.

- Types Introduction to types, type declaration, products, records, unions, vectors, recursive types, parametrized types, type checking, type inference, examples of use of types.

- Modules Modules as units of compilation, interface and implementation, separate compilation, language of modules, information hiding, sharing types among modules, functors, examples of module implementations.

- Objects and classes Introduction to object-oriented languages, object logic, class definition, aggregation, specialization, inheritance, self and super, object initialization, method overloading, dynamic binding, abstract classes, polymorphism, parametrized classes, introspection, exceptions, implementation of classes and objects.



Course name: COMPUTER SCIENCECOMPUTER SCIENCECOMPUTER SCIENCECOMPUTER SCIENCE IIII Number of ECTS credits: 6666 Content: Content: Content: Content: Basic building blocks of a computer program (using the syntax of the programming language Java):

- Variables, types and expressions. Basic I/O operations. Decision statements. Control structures. Functions and parameters. Programs. Structural decomposition.

Basic data structures:

- Simple types. Arrays. Records. Characters and strings. Data representation in computer memory. Memory allocation. Linked structures. Stack. Queue. List. Tree.

Algorithms and problem solving:

- What is an algorithm? Problem solving strategies. The role of algoirithms in problem solving. Algorithm implementation strategies. Debugging. Recursion – recursive functions, divide-and-conquer principle, backtracking, implementation of recursion.

Programming languages overview:

- Types of programming languages. Flow control. Functions. Subprograms. Namespaces. Declarations and types:

- Types. Declarations of types. Safe typing. Type checking. Subtypes. Classes. Polymorphism. Abstraction mechanisms:

- Data abstractions. Simple types. Composite types. Flow abstractions. Subprograms and functions. Abstract data types. Objects and classes. Patterns. Modules.

Course name: COMPUTER PRACTICUMCOMPUTER PRACTICUMCOMPUTER PRACTICUMCOMPUTER PRACTICUM Number of ECTS credits: 6666 Content: Content: Content: Content: The faculty network and basic usage rules:

- Description of the faculty computer network, login methods, password changing procedure, e-mail and mailing list usage, access to e-materials.

- OS Linux basics:

- Description of the Linux OS and its Slovenian version – Pingo Linux. BASH shell usage basics.

- Programming language C:

- The syntax of the C programming language. Usage of programming language C to solve example problems.

ELECTIVEELECTIVEELECTIVEELECTIVE COURSESCOURSESCOURSESCOURSES

Course name: ALGEBRAIC THEORYALGEBRAIC THEORYALGEBRAIC THEORYALGEBRAIC THEORY OF GRAPHSOF GRAPHSOF GRAPHSOF GRAPHS



- Eigenvalues of the graph;

- Automorphism group of graph;

- Symmetries of the graph;

- Graphs with transitive automorphism group (vertex-transitive graphs, edge-transitive graphs, arc-

transitive graphs, distance-transitive graphs);

- Strongly regular graphs.



Course name: ALGEBRA IV ALGEBRA IV ALGEBRA IV ALGEBRA IV ---- ALGEBRAIC STRUCTURESALGEBRAIC STRUCTURESALGEBRAIC STRUCTURESALGEBRAIC STRUCTURES



- Rings. Ideals. Ring homomorphisms. Quotient rings. Integral domains. Euclidean

- rings. Principal ideal domains. Gaussian rings. Gaussian numbers. Chinese remainder theorem.

- Fields. Subfields. Extensions. Finite extensions.

- The extension degree. Tower Theorem. Simple algebraic extension. Splitting field.

- Constructions with ruler and compass. Squaring the circle. Trisecting the angle. Doubling the

Cube.

- Constructions of regular polygons.

Course name: ANALYSIS IV ANALYSIS IV ANALYSIS IV ANALYSIS IV ---- REAL ANALYSISREAL ANALYSISREAL ANALYSISREAL ANALYSIS



- Fourier series. Bessel inequality of vector spaces with inner product.

- Orthonormal system and ortnormirana base. Fourier integral and Fourier transform.

- Differential geometry of curves in the plane and space. The length of the curve. Natural

parameter.

- Frenet formulas. Surfaces. Curvilinear coordinates, tangentna plane. The first fundamental

form.Area of the surface. Surface curvature and second fundamental form.

- Vector analysis. Scalar and vector fields. Gradient, divergence, curl. Potential and solenoid field.

Line integrals and surface integrals of the first and second types. Gauss and Stokes theorem.

Course name: DIFFERENTIAL EQUATIODIFFERENTIAL EQUATIODIFFERENTIAL EQUATIODIFFERENTIAL EQUATIONSNSNSNS



- Differential Equations. Examples from geometry and physics. Cauchy problem and Euler's

method of solution.

- The elementary integration methods for ordinary differential equations. Existence theorems.

Differential equations of higher orders. Linear differential equations. Systems of differential

equations. Separable variables. Homogeneous right-hand side. Linear equation. Bernoulli and

Riccati equatin.

- Calculus of variations. The basic problem of calculus of variations. Euler's equation. Isoperimetric

problem.

- Bessel differential equation. Solution with the series. Representation with series and integrals.

- Numerical solutions.

- Laplace transform. Inverse formula, properties. Application.

- Boundary problems for differential equations of second order. Sturm-Liouville operator

Course name: FINANCING FINANCING FINANCING FINANCING HEALTH CARE HEALTH CARE HEALTH CARE HEALTH CARE SYSTEMSYSTEMSYSTEMSYSTEM



- Health.

- Basic definition.



- Indicators of population health.

- Public and private.

- Sources of health care financing.

- The role of co-existence of public and private health care financing.

- Health care systems.

- Bismarck's system of statutory health insurance.

- Beveridge’s national health care system.

- The market system of health insurance.

- Classification of health insurance.

- Public statutory health insurance.

- Historical data about the development.

- Content of the statutory health insurance.

- Dilemmas and trends.

- Private health insurance.

- The insurance business.

- Risk factors and premium determination.

- Dilemmas and trends.

- Case studies.

- The growth of health care expenditure and management of growth.

- Offer of private health insurance.

- Absence from work due to illness or injury.

- Health financing and longevity.

- Other current themes.

Course name: FUFUFUFUNCTIONAL ANALYSISNCTIONAL ANALYSISNCTIONAL ANALYSISNCTIONAL ANALYSIS



- Topological vector spaces. Normed spaces. Banach spaces. Finite dimensional normed spaces.

Seminorms and local convexity. Minkowsky functional. Closed subspaces and quotient space.

- Linear operators and linear functionals. Boundedness of the operator.

- Baire theorem. Uniform boundedness theorem. Open mapping theorem. Closed graph Theorem

on the separation of closed convex sets. Weak and weak - * topology. Banach-Alaoglu theorem.

- Dual. Hahn-Banach theorem. Reflexive spaces. Anihilator of the space. The spectrum of the

operator. Arsela-Ascoli theorem. Compact operators. The spectrum of the compact operator

- Hilbert spaces. Orthogonality. Parallelogram identity. Riezs theorem on the representation of the

bounded functional. Adjoint operator. Orthonormal bases. Self adjoint, unitary and normal

operators.

- Banach algebra. Spectrum. Adjunction of identity. Gelfand-Mazur theorem.

- Unbounded operators. Closed operator. Adjpoint of densely defined operator.

Course name: SELECTED TOPICS IN DSELECTED TOPICS IN DSELECTED TOPICS IN DSELECTED TOPICS IN DISCRETE MATHEMATICSISCRETE MATHEMATICSISCRETE MATHEMATICSISCRETE MATHEMATICS



- Association schemes: definition, basic properties, examples, intersection numbers.

- Bose-Mesner algebra: basis, properties.

- Primitive idempotents: definition, Krein parameters.

- Distance-regular graphs: definition, examples, intersection numbers.



- Some necessary conditions for the existence of distance-regular graphs with prescribed

intersection numbers.

- Primitive and imprimitive distance-regular graphs.

Course name: SELECTED TOSELECTED TOSELECTED TOSELECTED TOPICS IN COMPUTING MEPICS IN COMPUTING MEPICS IN COMPUTING MEPICS IN COMPUTING METHODS AND APPLICATIOTHODS AND APPLICATIOTHODS AND APPLICATIOTHODS AND APPLICATIONSNSNSNS



- Hamiltonian Systems

- Numerical Integration Methods and Algorithms

- Lie Formalism

- Symplectic Integration Methods

- Numerical Experiments

Course name: SELECTED TOPICS SELECTED TOPICS SELECTED TOPICS SELECTED TOPICS FROMFROMFROMFROM STATISTISTATISTISTATISTISTATISTICSCSCSCS



- Graphical methods

- Empirical distribution function.

- Probabilistic diagrams.

- Histograms.

- Models for categorical data

- Contingency tables.

- χ^2 tests.

- Logit and probit models.

- Time series analysis

- Time series.

- Stationary processes.

- ARMA models.

- Parameter estimation.

- Model testing

- Time series and forecasting

Course name: COMBINATORICSCOMBINATORICSCOMBINATORICSCOMBINATORICS



- Basic methods of combinatorics: Classification of discrete problems, basic rules of

combinatorics, Selections, Inclusion and exclusion principle, generating functions, rook

polynomials

- Combinatorics and recursion: Distributions, Polynomial sequences, Descending powers, Stirling

number of first and second kind, Lah numbers and antidifferences, Sums, linear recursion

- Theory of discrete probability, experiment, event, conditional probability, independence, Relay

experiments, random variables, Mathematical expectation and variance.

Course name: COMPLEX ANALYSISCOMPLEX ANALYSISCOMPLEX ANALYSISCOMPLEX ANALYSIS





- A complex plane. The extended plane and stereographic projection. Power series with complex

arguments. Exponential function. Logarithmic function and root functions.

- Differentiation of complex functions. Cauchy-Riemann equations. Entire functions.

Integration of complex functions along the path. Cauchy- theorems. Morera’s theorem. Liouville's

theorem and the fundamental theorem of algebra. The principle of maximum modulus.

Homotopy.

- Isolated singularities. Laurent series. Residues and its applications.

- Harmonic functions. Poisson kernel and Poisson integrals. Solution of Dirichlet problem on the

circle. Harnack's theorem. Average value property and harmonic functions. Subharmonic

functions.

- Schwarz's Lemma. Principle of maximum modulus. Rado's theorem.

- Approximation of rational functions. Runge's theorem. Conformal mappings. Normal family.

Riemann theorem on the conformal equivalence.

- Infinite products. Zeros of holomorphic mappings. Weierstrass factorization theorem.

Meromorphic functions and Mittag-Leffler's theorem.

- Jensen's formula. Blaschke products and functions in H∞.

Course name: FINITE GEOMETRIESFINITE GEOMETRIESFINITE GEOMETRIESFINITE GEOMETRIES



- Steiner systems

- Designs

- Almost linear spaces

- Linear spaces

- Configurations, Pappus and Desargues configurations

- Projective spaces

- Affine spaces

- Polar spaces

- Generalized quadrangles

- Partial geometries

Course name: CRYPTOGRAPHY AND COMCRYPTOGRAPHY AND COMCRYPTOGRAPHY AND COMCRYPTOGRAPHY AND COMPUTER SPUTER SPUTER SPUTER SAFETYAFETYAFETYAFETY



- Classical ciphers and hoistorical development.

- Fiestel's cipher and AES (Advanced Encryption Standard).

- Finite fields and Extended Euclidean algorithm.

- Public crypto systems, one-way functions and related problems from number theory (testing

primality, factorization of integers, discrete logarithm problem)

- Hash functions and message integrity (authentication)

- Key exchange protocols and identification protocols

- Pseudo random number generator



- Other protocols (flipping a coin over the telephone, mental poker, secret sharing, verification

codes, vizual cryptography, zero knowledge proofs)

- Public key infrastructure (PKI), certificate authority (CA)

- Broader view on cryptography – security of information and network security

Course name: MATHEMATICAL METHODSMATHEMATICAL METHODSMATHEMATICAL METHODSMATHEMATICAL METHODS IN PHYSICSIN PHYSICSIN PHYSICSIN PHYSICS



- Software: Introduction. Comparison of MATLAB and OCTAVE. Mathematica.

Numerical differentiation, Numerical integration

- Ordinary differential equations: differential equations of first order. Radioactive decay.

Differential equations of second order. The movement of the projectile. Fluctuations. Movement

of the planets.

Partial differential equations: Laplacova equation. Wave equation. The heat equation.

Fourirer’s types: Fast Fourier Transform. Power spectrum.

Course name: MATHEMATICAL PRACTIMATHEMATICAL PRACTIMATHEMATICAL PRACTIMATHEMATICAL PRACTICUMCUMCUMCUM IIIIIIII



- Lectures are given on the most current program packages for mathematical computations:

- Magma, Computational Algebra System,

- Symbolic Computation (Mathematica, Maple, Derive), using built-in functions and help system,

formatting text which includes computations,

- using program system Mathematica for solving concrete problems (systems of equations, finding

zeros of polinomials, rules of logarithms, differentiation, integration, limits, etc.)

- program system Matlab, program language GNU Octave and basics for numerical computation

(basics of system Matlab and GNU Octave, solving simple problems about matrix algebra).

Course name: MATHEMATICS: METHOD MATHEMATICS: METHOD MATHEMATICS: METHOD MATHEMATICS: METHOD AND ARTAND ARTAND ARTAND ART



- Generating mathematical truths.

- Mathematics: method and art. Numbers 1, 2, 3, 5, 7 and basic principles of thinking. Real and

virtual. Restriction, extension and symmetry. Mathematization of science.

- Mathematics in natural sciences, social sciences, arts and politics. Concrete examples:

Parliamentary elections and geometric configurations; Genome, Chinese I-Ching and the

hypercube; symmetries of molecular graphs and fullerenes; Sports tournaments and graph

manipulation; Albrecht Durer - Melancholy, truncated cube, and Pappus configuration; Durer and

magic squares. Primes, factorization, and secret codes.

Course name: MOLECULAR MODELINGMOLECULAR MODELINGMOLECULAR MODELINGMOLECULAR MODELING





- The concepts of molecular modelling

- Introduction to Classical and Quantum Mechanics

- Potential field and molecular mechanics

- Computer simulation methods

- Molecular dynamics simulations

- Monte Carlo methods

- Using molecular modeling techniques in chemistry, pharmacy, biophysics, etc..

Course name: OPTIMIOPTIMIOPTIMIOPTIMIZZZZATION METHODATION METHODATION METHODATION METHOD



Basic definitions and examples. Linear programming.

- Mathematical model.

- Simplex method.

- Application examples from production.

- The theory of duality.

- The transshipment problem.

- Integer linear programming. Nonlinear programming.

- Extremum of a function from Rn to R.

- Gradient and the Hesse matrix.

- Unconstrained minimization.

- Gradient method.

- Constrained minimization.

- Transformation to the unconstrained problem.

- Karush-Kuhn-Tucker conditions. Discrete optimization.

- Graphs and digraphs.

- The shortest path problem.

- Breath-first search.

- Dijkstra’s, Prim’s and Kruskal’s algorithm.

- Network flows.

- Ford-Fulkerson’s algorithm.

- Matching and weighted matching problems in bipartite graphs. Approximation algorithms and heuristics.

- Local optimization.

- 2-approximation algorithm for the vertex cover problem.

- 2-approximation algorithm for the metric traveling salesman problem.

- Christofides algoritem. Applications on concrete examples of discrete optimization (NP-hard) problems and continuous optimization problems.

Course name: OPTIMIZATION METHODSOPTIMIZATION METHODSOPTIMIZATION METHODSOPTIMIZATION METHODS IN LOGISTICSIN LOGISTICSIN LOGISTICSIN LOGISTICS



The basic areas of logistics systems. Theoretical characteristics of logistics and distribution supply chains

- Material flow.

- Information flow.

- Cash flow.



Major decisions on supply chains. - Location. - Production. - Inventories. - Transportation. Linear and nonlinear programming. Discrete optimization. Construction algorithms. The use of heuristics and metaheuristics. Specific examples of the tasks in logistics and distribution supply chains. - Warehousing and storage planning. - Compiling of - preparation of transport units. - Transportation - Carp (road, rail, ship)

Course name: INTRODUCTION TOINTRODUCTION TOINTRODUCTION TOINTRODUCTION TO FINANCIAL MATHEMATICFINANCIAL MATHEMATICFINANCIAL MATHEMATICFINANCIAL MATHEMATICSSSS



Mathematics of life insurance: Interest, the current value, The principle of equivalence, Models of survival, Determination of net premiums., Determination of the net mathematical reserves., Risk management in life insurance. Market models: Types of securities, Stochastic models of markets, The concept of strategy. Asset management, Dimensions of risk, An optimal strategy for one period, Dynamic Strategy, CAPM model. Options: Types of options, The principle of arbitration, The protection and the fundamental theorem of evaluation options, European and American options, Exotic options, Practical aspects of security. Models of interest rates: The importance of stochastic modeling, Basic designs for current interest rates, Options on interest rates.

Course name: INTRODUCTION TOINTRODUCTION TOINTRODUCTION TOINTRODUCTION TO STATISTICSSTATISTICSSTATISTICSSTATISTICS



Sampling:

- The concept of random sampling

- Sampling distribution and standard error

- Examples of sampling and their standard errors

- Stratified sampling and examples of allocations Parameter estimation:

- The concept of a statistical model

- Parameter space, estimators, sampling distribution

- Maximum likelihood method

- Asymptotic properties of the maximum likelihood method

- Rao-Cramér inequality, optimality of estimates, factorization theorem Hypothesis testing:

- Problem formulation

- Statistical tests, test size, power of tests

- Examples of statistical tests

- Wilks' Theorem

- Neyman-Pearson lemma, theory of optimality Linear models:

- Assumptions of linear models and examples

- Parameter estimation



- Gauss-Markov theorem

- Generalizations of linear models Applications

Course name: SOSOSOSOLVING LVING LVING LVING EQUATION: FROM ALEQUATION: FROM ALEQUATION: FROM ALEQUATION: FROM AL----KHWARIZMI TO GALOISKHWARIZMI TO GALOISKHWARIZMI TO GALOISKHWARIZMI TO GALOIS



- Classical algebra and art of solving equations. - Musa al-Khwarizmi and quadratic equation. - Renaissance Italy and the formula for the equation of the third and fourth degree. - Battling with equations. - Cardano, Ferrari and Fontana - Tartaglia. - Abel, Galois and the birth of modern algebra. - Basic elements of Galois theory. Automorphisms. Galois extensions. Fundamental theorem

of Galois theory. - Symmetric polynomials. - Regular pentagon. Regular Heptadecagon. - Solvability of equations by radicals.

Course name: SYMMETRICSYMMETRICSYMMETRICSYMMETRICALALALAL CODESCODESCODESCODES



- history of the classical symmetric key encryption schemes - fundamental concepts in the design of block and stream ciphers, - modes of operation of symmetric key ciphers, - cryptographic criteria for encryption schemes, - security evaluation and generic attacks, - basic building blocks of symmetric key encryption schemes, - state-of-art ciphers and their security

Course name: STOCHASTIC STOCHASTIC STOCHASTIC STOCHASTIC PROCESSESPROCESSESPROCESSESPROCESSES



- Discrete-time Markov chains, classification of states, strong Markov property, hitting probabilities, ergodic properties.

- Continuous time Markov chains: definitions, strong Markov property, left and right equations, birth and death processes, branching processes, ergodic properties, applications.

- Martingales, optional stopping times, convergence theorems, applications. - Brownian motion: construction of Brownian motion, properties of trajectories, Markov

property, the reflection principle, martingales connected with Brownian motion - Poisson processes: abstract definitions, transformations of Poisson process, excursion

theory.

Course name: THE THEORY OFTHE THEORY OFTHE THEORY OFTHE THEORY OF GRAPHGRAPHGRAPHGRAPHSSSS





- Definitions and basic properties of graphs (paths and cycles in graphs, trees, bipartite graphs).

- Eulerian and Hamiltonian cycles. - Matchings in graphs (König's theorem). - Connectivity (Menger's theorem, Mader's theorem). - Planar graphs (Kuratowski's theorem). - Graph coloring (Four-Color Theorem, Vizing's theorem).

Course name: GAME THEORYGAME THEORYGAME THEORYGAME THEORY



- The decision problems in strategic situations. - Basic concepts of game theory: players, moves, income, matrix game with two players. - Games in normal form: dominating moves, the best answer, Nash balance. - Important examples of games in normal form: prisoners' dilemma, game of coordination,

partnership struggle, Coin game. - Random decisions: mixed moves, the existence of Nash balance. - Dynamic games, games in the branched form: strategies, Nash balance, reversible induction,

undergames, perfect balance of undergames. - Important examples of games in a branched form: centipede game, ultimatum game, the

game of negotiations, repeated prisoners' dilemma. - Comparison of decision theory and human decision making: experiments.

Course name: CODING THEORYCODING THEORYCODING THEORYCODING THEORY



- mathematical background (groups, rings, ideals, vector spaces, finite fields); - basic concepts in coding theory; - algebraic methods for the construction of error correcting codes; - Hamming codes; - Linear codes; - Binary Golay codes; - Cyclic codes; - BCH codes; - Reed-Solomon codes; - bounds (Hamming, Singleton, Johnson's bound , ...)

Course name: MEASURE THEORYMEASURE THEORYMEASURE THEORYMEASURE THEORY


ConteConteConteContent: nt: nt: nt:

- The concept of measureability. σ-algebra of measurable sets. Measurable functions. Borel sets and Borel measurable functions. Measureability of limit functions. Simple functions.

- Integral of nonnegative measurable functions and complex measurable functions. Fatou's lemma. Lebesgue's monotone convergence theorem and Lebesgue's dominated convergence theorem. Sets with measure zero and the concept of equality almost everywhere. Lp spaces.

- Positive Borel measures. Support of a function. Riesz's representation theorem for positive linear functional on algebra of continuous functions with compact support. Regularity of Borelovih measures. Lebesgu's measure.



- Approximation of a measurable function with continuous function. Lusin's theorem. - Complex measures. Total variation. Absolute continuity. Lebesgue-Radon-Nikodym's

theorem. Lp spaces as reflexive Banach spaces. - Differentiability of measure, symmetrical derivative of a measure. Absolute continuous

functions and fundamental theorem of calculus. Theorem on substitution in integration. - Product measure and Fubini's theorem. Completion of product Lebesgue measures.

Course name: THE THEORY OFTHE THEORY OFTHE THEORY OFTHE THEORY OFNUMBERNUMBERNUMBERNUMBERSSSS



- Divisibility of numbers. Greatest common divisor. Least common multiple. Euclid's algorithm. - Prime numbers. Writing numbers in other bases. - Divisibility criterions. Congruences. Theorems of Fermat and Euler. - Solving congruence equations. Quadratic reciprocity law. - Linear and quadratic Diophantine equations. Continued fractions. Arithmetical functions. - Möbius inversion formula.

Course name: TOPOLOGYTOPOLOGYTOPOLOGYTOPOLOGY



- Topological spaces. Topological structure on a set. Continuous mappings. Bases and subbases. Separation axioms.

- Compactness. Definition of a compactness. Compact metric spaces. Compact subspaces. Mappings of compact spaces. Locally compact spaces.

- Connectedness. An ordinary connectedness and connectedness with paths. Components. Local connectedness.

- Products. Topological product of finitely many factors. Topological properties of finite products. Topological product of infinitely many factors.

- Real-Valued Continuous Functions. Existence and Extension of Functions. Stone-Weierstrass Theorem.

- Quotient Spaces. Quotient Topology. Mappings of Quotient Spaces. Gluing. Projective Spaces. - Fundamental Theorems of Topology of Euclidean Spaces. Brouwer Fixed-Point Theorem.

Jordan Theorem. Invariant Open Sets. Schönflies Theorem.

Course name: THE THE THE THE HISTORY AND PHILOSOPHISTORY AND PHILOSOPHISTORY AND PHILOSOPHISTORY AND PHILOSOPHY OF MATHEMATICSHY OF MATHEMATICSHY OF MATHEMATICSHY OF MATHEMATICS


CCCContent: ontent: ontent: ontent:

- The history of the concept of number. Main and ordinal numbers in different languages. History of writing numbers: hieroglyphically, alphabetically, transition to positional (Chinese), positional. Algorithms, calculators.

- Number Theory - primes, Euclidean algorithm, Diophantine equations. Fractions, rational numbers. Roots, algebraic equations. The symbolism of algebra - unknowns.

- Famous design tasks. Pythagorean Theorem and related content. The number π. Famous curves. Trigonometry. Deductive method in mathematics.

- Rhind and Moscow Papyrus. Babylonian cuneiform script following Neugebauer. Ten classics (Suang-Ching). Euclid’s Elements. Archimedes' collected works. Bhaskara: Lilavati. Almagest. Fibonacci: Liber Abaci.

- A historical overview of computer science (from calculators to computing machines, from calculations to programs, from data to information, between mathematics and engineering).



- The history of mathematics in Slovenia (textbooks, scientific papers, e.g., Vega) - Historical development of mathematical and meta-mathematical terms.

Course name: INTRUDUCTION TOINTRUDUCTION TOINTRUDUCTION TOINTRUDUCTION TO BIOINFORMATICSBIOINFORMATICSBIOINFORMATICSBIOINFORMATICS



- Introduction - Basic biological background, comparison of samples - A comparison of two strings: algorithms for exact match - A comparison of two strings: heuristics - Finding patterns and the best match. - suffixal tree - A comparison of multiple sequences - Creation of evolutionary trees.

Course name: COMPUTER SECURITYCOMPUTER SECURITYCOMPUTER SECURITYCOMPUTER SECURITY



- Introduction and basic definitions. - symmetric and asymmetric cryptographic systems - Cryptographic protocols and an introduction to formal methods. - Public Key Infrastructure. - The elements of a comprehensive security infrastructure (defensive walls, intrusion detection

systems, - SSL, IPSec, and SET). - Managing the human factor (organizational and legal aspects).

Course name: COMPUTATIONAL GEOMETCOMPUTATIONAL GEOMETCOMPUTATIONAL GEOMETCOMPUTATIONAL GEOMETRYRYRYRY



- Introduction. - What is computational geometry? Motivations. Applications. Primitive operations. Convex

hull in two dimensions. - Line segment intersection. - Doubly connected edge list. Sweeping line paradigm. - Polynomial triangulation. - Partitioning polynomials in monotone pieces. Triangulation of monotone pieces. - Orthogonal range searching. - One-dimensional range searching. K-d trees. Range trees. Interval trees. Segment trees. - Point location. Trapezoidal maps. - Voronoi diagram and Delaunay trangulation. - Nearest neighbor problem. Voronoi diagram: definitions and basic properties. Delaunay

trangulation. Construction. - Arrangements and duality in computational geometry. - Line-point duality. Properties. Arrangements of lines. Construction.



Course name: ANDRAGOGY OF ICT ASSANDRAGOGY OF ICT ASSANDRAGOGY OF ICT ASSANDRAGOGY OF ICT ASSISTED EDUCATIONISTED EDUCATIONISTED EDUCATIONISTED EDUCATION Number of ECTS credits: 6666 Content: Content: Content: Content:

- Theoretical concepts for planning and realization of effective ICT assisted education for grown-ups.

- Regulations and socio-cultural conditions in the field of ICT assisted education for grown-ups. - Fundamental strategies and teaching techniques in ICT assisted education for grown-ups. - The use of ICT for assesment and evaluation of learning. - The role of ICT in the professional development of the teacher and the improvement of

quality, efficiency and productivity.

Course name: COMPILERSCOMPILERSCOMPILERSCOMPILERS Number of ECTS credits: 6666 Content: Content: Content: Content: Introduction

- basic structure of the compiler Regular languages and context-free grammars and parsers

- basics of regular languages and context free languages - lexical analysis and parsing

Block structure, scope and symbol tables - importance of the block structure - enviroment and variables in environment

The semantics - semantic analysis, types, variables - overloading, basics of polymorphism

Memory organization - stack during the program execution - calling records and subroutine call and return from it - parameter passing by value and by reference - heap organization (free memory)

Code generation - intermediate code, and its forms - basics of code generation analysis - code generation for parallel languages

Code optimization - overview of basic methods

Course name: COMPUTER NETWORKSCOMPUTER NETWORKSCOMPUTER NETWORKSCOMPUTER NETWORKS Number of ECTS credits: 6666 CoCoCoContent: ntent: ntent: ntent:

- Basic definitions and classification of computer networks

- The reference models ISO OSI and TCP/IP.

• The physical layer (signal tramsmission)

• The data-link layer (error detection and correction, medium access, flow control)

• The network layer (datagrams, routing, congestion control algorithms)

• The transport layer (connection oriented and connection-less service, protocols, multiplexing)



• The presentation layer (coding and security)

• The application layer (sample Internet applications)

- Communication technology integration (wired, wireless and mobile), modern information services (server/client model, P2P), web services.

Course name: CURRICULUM PLANNING CURRICULUM PLANNING CURRICULUM PLANNING CURRICULUM PLANNING IN ICT ASSISTED EDUCIN ICT ASSISTED EDUCIN ICT ASSISTED EDUCIN ICT ASSISTED EDUCATIONATIONATIONATION Number of ECTS credits: 6666 Content: Content: Content: Content:

- Basic concepts - The models of curriculum planning - The methods and phases of curriculum planning - Regulations in the field of curriculum planning in ICT assisted education - Curriculum planning for evaluation of ICT assisted education

Course name: DATA STRUCTURES AND DATA STRUCTURES AND DATA STRUCTURES AND DATA STRUCTURES AND ALGORITHMSALGORITHMSALGORITHMSALGORITHMS Number of ECTS credits: 6666 Content: Content: Content: Content:

- The basic mathematical tool

- Basic data structures

- The basic abstract types and their performance

- Sorting and frineds:

- Basic algorithmic techniques

- Algorithms on graphs and networks

- Selected algorithms

Course name: DATABASE DESIGNDATABASE DESIGNDATABASE DESIGNDATABASE DESIGN Number of ECTS credits: 6666 Content: Content: Content: Content:

- Relational data model. Overview, definition of relation, attributes, keys, data definition sentences, query language, SQL, SQL3, integrity constraints, indexes, clustered indexes.

- Data model ER. Entities, entity sets, identifier, relationships, relationship set, attributes, types of attributes, degree of relationship, cardinality.

- UML Conceptual model of UML, things in UML, relationships in UML, diagrams, rules, common mechanisms, structural design, examples of system design.

- Conceptual database design. Conceptual models, conceptual design methodology, schema integration, entity clustering, translation of ER to relations, translation rules, example of translating ER schema to relations, Case tools for conceptual design.

- Logical database design. Functional dependencies, normalization, Boyce-Codd normal form, 3. normal form, decomposition of relation, decomposition in BCNF or 3NF, lossles-join decomposition.

- Physical database design. Database design tuning, access path selection, indexes, denormalization of relations, distribution of relations, query tuning.



Course name: DIDACTICAL DESIGNDIDACTICAL DESIGNDIDACTICAL DESIGNDIDACTICAL DESIGN Number of ECTS credits: 6666 Content: Content: Content: Content:

- Historical view and technological possibilities for ICT supported learning materials. - The quality of electronic learning materials and their publishing in electronic media. - Regulations and socio-cultural framework in teh field of development and publishing of ICT

supported learning materials. - Planning and development of high-quality, effective ICT supported learning materials. - Teaching and learning methods using ICT supported learning materials. - ICT supported learning materials for assesment and evaluation of learning. - The role of ICT supported learning materials in the professional development of the teacher

and the improvement of quality, efficiency and productivity.

Course name: GEOGRAPHIC INFORMATIGEOGRAPHIC INFORMATIGEOGRAPHIC INFORMATIGEOGRAPHIC INFORMATION SYSTEMON SYSTEMON SYSTEMON SYSTEM Number of ECTS credits: 6666 Content: Content: Content: Content:

- Basic terms in geographical information systems. - Spatial data: Data structures, Data bases, Topological models. - Maintenance of special data: Entering and processing, Interactive queries, Analyses,

Presentation.

- Trends in development of geographical information systems.

Course name: ICT IN EDUCATIONICT IN EDUCATIONICT IN EDUCATIONICT IN EDUCATION Number of ECTS credits: 6666 Content: Content: Content: Content:

- Historical and technological development of ICT support in educational processes - Technological aspects of ICT supported education - Institutional framework for ICT supported education - Quality of electronic learning content and its publishing in electronic media - Systemic organization of social and cultural enviroment in the field of ICT supported

education. - The political importance of lifelong learning (LLL)

Course name: INFORMATION TECHNOLOINFORMATION TECHNOLOINFORMATION TECHNOLOINFORMATION TECHNOLOGY MANAGEMENTGY MANAGEMENTGY MANAGEMENTGY MANAGEMENT Number of ECTS credits: 6666 Content: Content: Content: Content:

- Principles of management.

- Information technology and organization.

- Management IT services and activities.

- Legal regulations in EU and Slovenia.

- Systems approach to information systems projects.

- Selected chapters in information engineering and case studies.



Course name: INTELLIGENT INTELLIGENT INTELLIGENT INTELLIGENT SYSTEMS AND DATA MINSYSTEMS AND DATA MINSYSTEMS AND DATA MINSYSTEMS AND DATA MININGINGINGING Number of ECTS credits: 6666 Content: Content: Content: Content:

- Intelligent systems. What is the structure of a typical intelligent system and how it works. Examples of intelligent systems in computer science.

- Machine learning techniques. From basic to more advanced machine learning methods such as: decision trees, deciasion rules, regression, support vector macines, association rules … The use of these techniques on real-life problems – building and evaluation of prediction and description models from the data.

- Data mining. The use of machine learning techniques in the frame of the data mining process. Description of the CRISP methodology – data mining as a process consisting of the following steps: problem understanding, data understanding, data preparation, modeling, evaluation and deployment. The use of existing, open source data mining tools (e.g.: WEKA, Orange, A-Priori …)

Course name: INTRODUCTION TO DATAINTRODUCTION TO DATAINTRODUCTION TO DATAINTRODUCTION TO DATABASE SYSTEMSBASE SYSTEMSBASE SYSTEMSBASE SYSTEMS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction

- Logical data models: Entity-Relationship model, relational model, translation of ER into relational model, relational algebra, relational calculus, SQL, SQL3, QBE.

- DBMS implementation: Disks, files, index files, indexes, ISAM, B+ trees, hash indexes, evaluation of relational operations, query optimization, query evaluation, transactions, concurrency control, crash recovery.

- Database design: Logical database design, functional dependencies, normal forms, physical database design, denormalization, index selection.

- Application level: DBMS applications, embedded SQL, dynamic SQL, Internet databases.

Course name: LANGUAGE TECHNOLOGIELANGUAGE TECHNOLOGIELANGUAGE TECHNOLOGIELANGUAGE TECHNOLOGIESSSS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction and basics - short history of natural language processing, inspection of the resources for natural language

processing, corpora presentation - Slovenian language corpora, monolingual corpus, bilingual corpus, corpus construction,

corpora usage, presentation, labeling, network concordance - Computer tools - sharing of computer tools, - computer tools overview, - examples of computer tools - Machine Translation

techniques of machine translation techniques, evaluation of machine translation, statistical machine translation



- modern methods of collecting relevant linguistic information from computer manageable corpora

Course name: MMMMULTIMEDIA DESIGNULTIMEDIA DESIGNULTIMEDIA DESIGNULTIMEDIA DESIGN Number of ECTS credits: 6666 Content: Content: Content: Content: Nowadays, multimedia is widely used to transfer information between users – expecially those that are not »computer experts«. The state-ot-the-art communication technology enables the integration of different media such as: text, graphics, sound and video.

- Multimedia systems – basic concepts - Digitalization of information - Development of multimedia systems - The use of multimedia systems to produce multimedia content - The use of multimedia systems and multimedia content in other systems

Course name: MENTORSHIP IN ICT ASMENTORSHIP IN ICT ASMENTORSHIP IN ICT ASMENTORSHIP IN ICT ASSISTED EDUCATIONSISTED EDUCATIONSISTED EDUCATIONSISTED EDUCATION Number of ECTS credits: 6666 Content: Content: Content: Content:

- Teaching methods and the definition of mentorship. - The forms of mentorship in elementary, high-school, university and life-long ICT assisted

education. - The roles and activities of a mentor in ICT assisted education. - Test systems for assesment and evaluation the knowledge learned. - Leading styles and communication in ICT assisted education. - Professional development and ICT when using evaluation strategies.

Course name: PERMUTATIONAL GROUPSPERMUTATIONAL GROUPSPERMUTATIONAL GROUPSPERMUTATIONAL GROUPS Number of ECTS credits: 6666 Content: Content: Content: Content:

- group action. - orbits and stabilizers. - extensions to multiply transitive groups. - primitivity and imprimitivity. - permutation groups and graphs. - graph automorphisms, vertex-transitive and Cayley graphs. - graphs with a chosen degree of symmetry. - permutation groups and designs.

Course name: PROGRAMMING III PROGRAMMING III PROGRAMMING III PROGRAMMING III –––– CONCURRENT PROGRAMMICONCURRENT PROGRAMMICONCURRENT PROGRAMMICONCURRENT PROGRAMMINGNGNGNG Number of ECTS credits: 6666 Content: Content: Content: Content:

- Concurrent programming concepts; Techniques for parallelizing programs

- Synchronization, atomic actions.

- Critical sections: locks



- Parallel programming: barriers, barrier synchronization, bag of tasks paradigm

- Semaphores: basic concepts and uses, the method of passing the baton

- Introduction to Pthreads library

- Monitors and conditional variables: basic concepts, synchronization techniques, programming

- Distributed memory programming: message passing, remote procedure call, remote method invocation

- Introduction to MPI

- Examples of multithreaded, parallel and distributed programming.

Course name: SELECTED TOPICS IN ASELECTED TOPICS IN ASELECTED TOPICS IN ASELECTED TOPICS IN ALGORITHMSLGORITHMSLGORITHMSLGORITHMS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Models of computation, NP completeness. - Word-size parallelism and transdichotomous model of computation. - Linear programming. - Approximative and probabilistic algorithms. - Competitive algorithms and online algorithms. - Parallel algorithms and algorithms for distributed systems – algorithms for computer

networks (P2P etc.).

Course name: SELECTED TOPICS IN DSELECTED TOPICS IN DSELECTED TOPICS IN DSELECTED TOPICS IN DATA STRUCTURESATA STRUCTURESATA STRUCTURESATA STRUCTURES Number of ECTS credits: 6666 Content: Content: Content: Content:

- Models of computation. - Word-size parallelism. - Implicit data structures. - Succinct data structures. - Information coding entropy- - Data structures and memory hierarchy. - Practical examples from computer communications, embedded applications, massive data

storage etc.

Course name: SELECTED TOPICS IN SELECTED TOPICS IN SELECTED TOPICS IN SELECTED TOPICS IN COMPUTING METHODS ANCOMPUTING METHODS ANCOMPUTING METHODS ANCOMPUTING METHODS AND APPLICATIONSD APPLICATIONSD APPLICATIONSD APPLICATIONS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Hamiltonian Systems - Numerical Integration Methods and Algorithms - Lie Formalism - Symplectic Integration Methods - Numerical Experiments

Course name: SOFTWARE ENGENEERINGSOFTWARE ENGENEERINGSOFTWARE ENGENEERINGSOFTWARE ENGENEERING



Number of ECTS credits: 6666 Content: Content: Content: Content:

- Software process Software development life cycle. Software process (development) models (linear, evolutionary, RAD, etc.), software requirements, prototyping, analysis, design, implementation, software testing, software evolution.

- Languages and diagraming techniques for description of software products. UML (Unified modeling language). Functional model, object model, dynamic model. Use cases.

- Software requirements analysis. Requirements elicitation for software. Description of existing solutions. Interviews. Prototyping. Software system specification. Natural languages vs. diagramming methods. Data flow diagrams, Entity-relationship diagrams, State machines.

- Software system design. Software decomposition, software architecture patterns, design patterns. Object classification. Software modules design and reuse. Software libraries. Client-server model and distributed systems. Software security.

- Software implementation. Integrated development environments. Coding standards. Implementation of distributed systems. Software system integration. Software documentation, user documentation, project documentation and relation to software maintenance and evolution.

- Object – relational databases and persistent data storage. Persistency of objects. Relational and object-relational data model.

- Software testing. How to write software code to enable efficient testing. Testing methods, black-box and white-box testing. Unit testing. Testing strategies. Debugging.

Course name: SYSTEM PROGRAMMINGSYSTEM PROGRAMMINGSYSTEM PROGRAMMINGSYSTEM PROGRAMMING Number of ECTS credits: 6666 Content: Content: Content: Content: Unix:

- Users. Authentication. User administration. Groups. Files and permissions. User groups. Devices. Processes. Ports. Network file systems – NFS. Samba. Security. OS boot sequence. Services. Firewalls.

System programming languages: - Unix shell & programming. Perl & programming. Example of a system program.

Windows: - Users, groups and layers. Authentication. Active directory. Processes. Domein server.

Application server. Security. Open SSL. VPNs. Archiving.

Course name: SYSTEMS II SYSTEMS II SYSTEMS II SYSTEMS II –––– OPERATING SYSTEMSOPERATING SYSTEMSOPERATING SYSTEMSOPERATING SYSTEMS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction, what is operating system?, history of operating systems, computer hardware overview, concepts of operating systems, system calls, operating system structure.

- Processes, threads, inter-process communication, critical conditions, critical regions, classical IPC problems, scheduling.

- Deadlocks, resources, representation of processes and resources, deadlock modeling, Osterich algorithm, deadlock detection and recovery, deadlock avoidance, deadlock prevention.



- Memory, basic operations, swapping, virtual memory, page replacement algorithms, modeling page replacement algorithms, page management system, segmentation, Multics, Pentium.

- Input/output, principles of I/O hardware, principles of I/O software, sftware levels of I/O, disk, clock, character terminals, graphical interfaces, network terminals, other I/O equipment.

- File systems, directories, file system implementation, examples of file systems, Unix, Windows.

- Multimedia, multimedia files, video compression, JPEG, MPEG, scheduling multimedia processes, multimedia file systems, storing multimedia files, disk scheduling.

- Multi-processor systems, multi-computer systems, distributed systems, architectures and examples.

- Security, security environment, introduction to cryptography, user authentication, attacks from inside, attacks from outside, protection mechanisms, trusted systems.

- Unix-Linux, history of UNIX, overview of UNIX, UNIX processes and memory management, UNIX I/O and file system, UNIX security.

Course name: SYSTEMS I SYSTEMS I SYSTEMS I SYSTEMS I ---- HARDWAREHARDWAREHARDWAREHARDWARE Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction to information theory and coding.

- Computer arithmetic. Arithmetic in fixed and floating point. Basic operations: addition, subtraction, multiplication, division. Carry over. Booth's procedure.

- Switching functions and circuits.

- History of computer systems and an introduction to machine computing.

- Instructions. Basic properties of instructions. Instruction formats. The composition of instructions according to the addressing modes, the number of explicit operands, storage methods of operands in CPU, type of operations and type and length of operands. RISC and CISC computers.

- Central processing unit.

- Memory and cache.

- Virtual Memory

- Input and output: Operation of I/O devices. Connecting of I/O devices. Direct memory access and I/O processors.

- Parallel computer systems and advanced processor architectures.

Course name: SYSTEMS III SYSTEMS III SYSTEMS III SYSTEMS III –––– INFORMATION SYSTEMSINFORMATION SYSTEMSINFORMATION SYSTEMSINFORMATION SYSTEMS Number of ECTS credits: 6666 Content: Content: Content: Content:

- Information systems Basic definitions from the field of information systems. Introduction to business analysis. Analysis and design of business processes. Analysis and design of data. Database tools. Software development tools. Web technology. Definition of information system requirements. Definition of information system architecture. Implementation of information systems. Documenting information system.

- Data systems Database management systems (DBMS). Architecture of DBMS. SQL language. Database design. Data modeling, Database modeling tools. Information system development tools.



Course name: THEORETICAL COMPUTERTHEORETICAL COMPUTERTHEORETICAL COMPUTERTHEORETICAL COMPUTER SCIENCE III SCIENCE III SCIENCE III SCIENCE III –––– FORMAL LANGUAGES ANDFORMAL LANGUAGES ANDFORMAL LANGUAGES ANDFORMAL LANGUAGES AND COMPUTABILITYCOMPUTABILITYCOMPUTABILITYCOMPUTABILITY Number of ECTS credits: 6666 Content: Content: Content: Content:

- Finite automata and regular expressions: Computation model, finite automaton – DFA, NFA; Alphabet, language, regular expression/language; The relation between DFA, NFA and regular expressions; Using FA to solve problems; RE pumping lemma, non-regular languages

- Grammars, context (non)free languages and stack automata: Grammar, derivation tree, attribute grammar; Context-dependant and context-free grammars, stack automaton; Grammar normal forms: Greibach, Chomsky; Transforming grammars into CNF; CYK algorithm; Pumping lemma for CFG; Operations on languages (intersection, union …).

- Turing machines and their languages: Turing machine and its derivations, RAM; Church-Turing thesis; Recursively enumerable languages, Chomsky hierarchy; Unsolvable and undecidable problems, the stopping problem, Rice theorem and PCP.

- Introduction to the theory of complexity: P and NP – relation between them; Problem translation, NP completeness; NP complete problems.

Course name: THEORETICAL COMPTHEORETICAL COMPTHEORETICAL COMPTHEORETICAL COMPUTER SCIENCE II UTER SCIENCE II UTER SCIENCE II UTER SCIENCE II –––– INFORMATION THEORYINFORMATION THEORYINFORMATION THEORYINFORMATION THEORY Number of ECTS credits: 6666 Content: Content: Content: Content:

- Introduction to information theory

- Mathematical foundations of information theory

- Discrete entropy

- Data Compression

- Channel Capacity

- Differential Entropy

mathematics mathematics, undergraduate - up famnit

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