Abbreviations

**p-sz** - obligatory module of common theoretical basis, obligatory for all specialisations,

**pv-ob** - elective branch module, obligatory for selected branches,

**pv-za** - elective specialisation module, obligatory for selected specialisations,

**p-hu** - obligatory humanity module,

**p-em** - iobligatory economical-management module,

**p-pr** - obligatory project,

**pv-hu** - elective humanity module,

**v** - elective module.

module (abbreviation) | dimension | completion | type of module | lecturer | recom. year |

Statistics for Informatics ( MIE-SPI ) | 4+1 | z,zk | p-sz | Blažek, Ph.D. | 1. |

Parallel Computer Architectures ( MIE-PAR ) | 3+1 | z,zk | p-sz | prof. Tvrdík | 1. |

Systems Theory ( MIE-TES ) | 2+1 | z,zk | p-sz | prof. Moos | 1. |

Parsing and Compilers ( MIE-SYP ) | 2+1 | z,zk | pv-ob | prof. Melichar | 1. |

Linear Optimization and Methods ( MIE-LOM ) | 2+1 | z,zk | pv-za | Černý, Ph.D. | 1. |

Cybernality ( MIE-KYB ) | 2+0 | zk | p-hu | doc. Jirovský | 1. |

Mathematics for Informatics ( MIE-MPI ) | 4+1 | z,zk | p-sz | doc. Šolcová | 1. |

Functional and Logical Programming ( MIE-FLP ) | 2+1 | z,zk | pv-ob | Janoušek, Ph.D. | 1. |

Advanced Algorithms ( MIE-PAL ) | 2+1 | z,zk | pv-za | prof. Kučera | 1. |

Automata in Text Pattern Matching ( MIE-AVY ) | 2+1 | z,zk | pv-za | prof. Melichar | 1. |

elective module | 2+1 | z,zk | v | 1. | |

elective module | 2+1 | z,zk | v | 1. | |

Project Management ( MIE-PRM ) | 1+2 | z | p-em | Vala | 1. |

Complexity Theory ( MIE-CPX ) | 3+1 | z,zk | pv-ob | prof. Kučera | 2. |

Computational Intelligence Methods ( MIE-MVI ) | 2+1 | z,zk | pv-za | Kordík, Ph.D. | 2. |

Nonlinear Continuous Optimization and Numerical Methods ( MIE-NON ) | 2+1 | z,zk | pv-za | doc. Kruis | 2. |

Master Project ( MIE-MPR ) | z | p-pr | 2. | ||

elective module | 2+1 | z,zk | v | 2. | |

elective module | 2+1 | z,zk | v | 2. | |

Information Security ( MIE-IBE ) | 2+0 | zk | p-em | Čermák, CSc. | 2. |

elective module | 2+1 | z,zk | v | 2. | |

IT Support to Business and CIO Role ( MIE-CIO ) | 3+0 | zk | p-em | prof. Dohnal | 2. |

obligatory humanity module | zk | pv-hu | 2. | ||

Master Thesis (MIE-DIP) | z | p-pr | 2. |

- Text systems, basic notions, taxonomy of text pattern matching problems.
- Codirectional searching, models of searching algorithms.
- Nondeterministic search automata.
- Simulation of nondeterministic search automata, bit parallelism, dynamic programming.
- Prefix and suffix automata.
- Factor automata, factor oracle, suffix oracle.
- Boundaries and periods in texts.
- Repetitions in texts, exact and inexact.
- Simulation of nondeterministic search automata, fail function, the MP a KMP algorithms.
- Simulation of nondeterministic search algorithms, fail function, the AC algorithm.
- Contradirectional single pattern matching, the BM algorithm, the CW algorithm.
- State-of-the-art in text pattern matching (e.g., matching in a multidimensional text, searching in a compressed text).

- Introduction. IT trends and business support. CIO and CEO relationship. ICT Management (categorization, management models, services, processes).
- CIO role, responsibility. CIO Decision Cycle (business goals, innovation, strategy, plan, execution, measurement).
- The value chain and ICT support. Marketing and selling processes, business cycle.
- CIO priorities: Team management. Understanding of the business environment. ICT vision. Shape ICT demand and communicate expectations. IT Governance.
- CIO priorities: Bring business and ICT strategies together. Communication of the ICT value to business. Risk Management.
- CIO priorities: Creation of a new ICT. Change in the profile of ICT people. ICT competencies (technical, business, behavioral).
- ICT business cases on workforce (time management, meeting management, delegation).
- ICT business cases on workforce (appraisal, coaching, mentor, mentee).
- CRM as an example of ICT support of business processes. CRM and enterprise culture.
- CRM processes.
- CRM Technology. CRM innovation and the role of ICT.
- Specific tasks of ICT management (sourcing, cost cutting).
- Invited lecturer – CIO of a selected company, discussion.

- Models of computation.\r
- Algorithmic undecidability.\r
- Nondeterminism, the class NP, the existence of an NP-complete problem.\r
- NP-complete problems.\r
- Problem P=NP, relativization, classes coNP and NP intersection coNP.\r
- The class PSPACE, Savitch theorem, hierarchy in PSPACE.\r
- PSPACE-complete problem (quantified formulae and games), complete problem for the hierarchy classes.\r
- Circuit and algebraic complexity.\r
- Randomized algorithms, complexity classes of randomized algorithms (classes BPP, ZP, RP).\r
- One-way functions, pseudorandom sequences, discrete logarithm, cryptography.\r
- Interactive proofs, probabilistically verifiable proofs, expanders, gap problem, PCP theorem, non-aproximability of 3SAT.\r

- Declarative programming languages. Lambda calculus as a formalism for functional programming.
- Basic data types and functions in Lisp, lists.
- Variables, type predicates, recursion and iteration in Lisp.
- Mapping functionals, control statements.
- Input and output, macros.
- Structures, vectors, arrays, hash tables.
- Implementation of Lisp.
- Predicate logic, Horns clauses and SLD resolutions as an introduction to Prolog.
- Predicates, clauses, facts, operators in Prolog.
- Control of the computation in Prolog, lists.
- Data structures, input, output.
- Implementation of Prolog.
- Logic programming and proof trees - relation to attributed grammars.

- Management, management and governance, IT management.
- Information security management system, IS/ICT governance, international standards on IS/ICT security, legislation in the Czech Republic.
- Risk management.
- Physical security, access control system, information resource valuation, internal and external threats, evaluation of countermeasures,
- Administration security (guidelines, training).
- Disaster recovery planning, business continuity management, incident management,
- IS/IT audits, application security testing, penetration testing, certifications.
- Certification according ISO 27001, Best practises (ISO 17999),
- Information security trends.

- Basic leslative norms relevant for operation of computer systems and networks, basic notions.
- Classification of attacks.
- Systems for computer network operation monitoring.
- Cybernetic attacks, psychologic and social aspects of a cybernetic attack, life cycle of exploiting the system weaknesses.
- Hackers - hacker comunity, types and motivations of the hacker behaviour.
- Cyberterorism, its demonstration and methods.
- Principles of infoware, the role of intelligent agents, strategic information warfare.
- Principles of attacks on the web, trends of attacks and attackers, phases of an attack, coordination and management of an attack.
- Basic types of attacks - DoS, forged node, manipulation with address sequences.

- Classification of optimization techniques: linear and integer programming, nonlinear optimization, continuous optimization, special forms of linear programs, general convex programming, multicriteria optimization.
- Mathematical formulation of optimization problems (optimization and combinatorics, distribution, allocation, network, statistical problems, etc.).
- Models of conflicting situations, introduction to the game theory.
- Linear algebra: matrices and linear mappings, eigenvalues and eigenvectors, basic bounds, positive (semi)definiteness, $L_k$-norms, matrix norms.
- Fundamentals of theory of linear and integer programming and their geometry, forms of linear programs.
- The simplex algorithm.
- Duality in linear programming.
- Applications of duality in combinatorics and algorithmic design.
- Classifications of optimization problems using the complexity theory.
- The ellipsoid algorithm.
- Interior point algorithms.
- Algorithms for integer programming.
- Implementation issues (numerical stability, sparse matrices, approximate and exact solutions, date structures).

- [2] Universal algebra: groups, finite groups, Cayley tables, group types, permutation, alternating, cyclic, and symmetry groups, normal subgroups.
- Finite fields, prime order of field, rings and their properties, integral domain, ideal. Lattices.
- Introduction to category theory, classes of objects, classes of morphisms and its properties, examples of categories: grupoid, category of all lattices, category of all commutative groups, category of all integral domains, category of all relations. Homomorphisms.
- Selected problems of graph theory, types of Hamiltonian problems. Algebraic solutions of combinatorial problems, Polya enumeration theorem.
- Algebra and algorithms (Algorithms for calculations of polynom roots - Newton' method, Lehmer-Schur's method, etc.).
- Convex sets, convex hull, pure convex set, theorem on partition of convex sets, Minkowski theorem on projection.
- Selected problems of number theory, quadratic congruence, Gauss algorithms. Special primes - factorial, palindromic, cyclic, Gauss', Eisenstein's primes. Examples of applications.
- Properties of Fermat primes, Little Fermat Theorem, primality tests, Pépin test, number theory and geometry, constructability of polygons.
- Selected numerical methods, Lagrange and Hermite interpolation, numerical integration, numerical solution of ordinary differential equations, calculating of eigenvalues of matrices, methods of solving of linear equations systems.
- Fast algorithms: multiplication, numerical searching of square roots, Fourier transformation, Fermat transformation.
- Axiomatic systems and their properties, recursive functions, proofs in the axiomatic system, examples of axiomatic systems, Peano's arithmetics, von Neumann's model of numbers.
- Special logics, multi-valued logics, modal logics, fuzzy logics.

- Introduction to computational intelligence, its uses.
- Algorithms of machine learning.
- Neural networks.
- Evolutionary algorithms, evolution of neural networks.
- [3] Computational intelligence methods: for clustering, for classification, for modeling and prediction.
- Fuzzy logic.
- Swarms (PSO, ACO).
- Model grouping and combining.
- Inductive modeling.
- Quantum and DNA computing.
- Case studies, new trends.

- Partial derivative, gradient, hessian.
- Continuous optimization of the 1st and 2nd order.
- Quasi-Newton method, conjugate gradient method.
- Application of methods of nonlinear continuous optimization.
- Introduction to ordinary and partial differential equations (taxonomy, the notion of the solution, physical interpretation).
- Ordinary differential equations – boundary value problem (exact solution, finite difference method, finite differences).
- Ordinary differential equations – boundary value problem (finite element method).
- Partial differential equations – stationary cases (finite difference method).
- Partial differential equations – stationary cases (finite element method).
- Ordinary differential equations – initial value problem.
- Partial differential equations – nonstationary problems.
- Iterative methods (Gauss-Seidel method, conjugate gradient method).
- Introduction to domain decomposition methods. Parallel solvers of sets of linear equations.

- Advanced algorithms for network flows.
- Matching: bipartite and general, minimum cost matching, parallel randomized algorithm.
- Planar graphs: planarity conditions, planarity testing, isomorphism of planar graphs.
- Digital signal processing: FFT and spectral compression.
- Geometric algorithms: convex hull, Voronoi diagram, and others.
- Streaming algorithms.
- Primality: randomized a deterministic testing, proof of primality.
- Approximation algorithms.
- Approximation schemes.
- Online algorithms.
- General heuristic methods: simulated annealing, tabu search, genetic algorithms.
- Specialized heuristic methods: spectral heuristics, TSP.
- Randomized algorithms and probabilistic analysis of algorithms.

- Performance characteristics of parallel computations.
- Models of parallel systems with shared memory.
- Interconnection networks of parallel computers.
- Embeddings and simulations of interconnection networks.
- Models for interprocessor communication and routing.
- Collective communication algorithms.
- Fundamental parallel algorithmics.
- Parallel sorting algorithms.
- Parallel algorithms for linear algebra.
- Parallel combinatorial space search.

- Project management, project, process. Definition of project participants, aims, metrics, quantification, planning, budget.
- Role of the project manager (presentation, levels of communication, duties). Life cycle and stages of a project.
- Project documents. Pre-business and business stages of a project.
- Preparation and realization stages of a project. Operation and closure of a project.
- Stabilization of a project, feedback, control mechanisms (methodical, contractual, or matter-of-fact supervision), risk management.
- Contractual arrangement of a project, business negotations, quality of delivery (SLA, security), warranty.
- Demand, definition of services, evaluation of proposals, the act of public contracts, evaluation criteria.
- Financial control.
- Project team management - human resources (roles, CIO, conducting a meeting, written records, tasks).
- Management of large projects (by area, by volume). Multiproject enviroment (reporting, coordination).
- Principles of methodology of poject management – Prince2, PMI. Quality management of project according to norms ISO 10006, ISO 9001.
- Setting up project management to company (linear x project management, process management).
- Particularities of project management of IS development.

- Basics of Probability Theory: Probability Space, Definitions, Properties, Sigma-continuity, etc.
- Basics of Probability Theory: Conditional Probability, Independence, Commented Examples
- Basics of Probability Theory: Random Variables, Cumulative Distribution Function, Probability Density Function, Dependence, Random Vectors, Marginal and Joint Distribution
- Basics of Probability Theory: Conditional Distribution, Conditional Expectation, Characteristics of Random Variables, Selected Examples of Probability Distributions
- Basics of Probability Theory: Poisson Process, Simulation Methods, Generating Functions
- Basics of Probability Theory: Strong Law of Large Numbers (SLLN), Central Limit Theorem (CLT), Large Deviations, Entropy
- Discrete-time Markov Chains with Finite State Space: Basic Concepts, Irreducibility and Periodicity of States, Absorption Probability, Stopping Times
- Discrete-time Markov Chains: Examples: Generalized Random Walk, Random Walk on a Graph, Gambler's Ruin, Coupon Collector
- Discrete-time Markov Chains: Asymptotic Stationarity, Uniqueness and Existence of Stationary Distributions, Convergence
- Discrete-time Markov Chains: Branching Processes, Birth & Death processes
- Monte Carlo Methods: Markov Chain Monte Carlo (MCMC) – Basic Concepts and Examples
- Monte Carlo Methods: Fast convergence of MCMC, Propp-Wilson Algorithm, Sandwiching, Simulated Annealing
- Monte Carlo Methods: Monte Carlo Estimates, Monte Carlo Tests, Reduction of Variance
- Stochastic Processes: Definition, Distribution Function, Characteristics of Stochastic Processes
- Stochastic Processes: Characteristics and Classification of Stochastic Processes, Examples
- Basics of Queueing Theory: Elements of Queueing Systems, Request Arrival Process, Queueing Policy, Service Policy, Kendall Notation
- Stochastic Processes: Application of the Poisson Process to Model Arrivals in Queueing Systems
- Stochastic Processes: Application of the Poisson Process in Queueing Theory
- Stochastic Processes: Non-homogeneous Poisson Process, Spatial Poisson Process, M/G/infinity Queue
- Continuous-time Markov Chains: Jump Rates, Timing Jumps by Poisson Process Arrivals, Kolmogorov Equations
- Basics of Queueing Theory: M/M/m Queues, Queueing Systems
- Basics of Queueing Theory: Open and Closed Queueing Systems
- Bootstrap Methods: Properties of Bootstrap Approximations, Bootstrap Correction of Estimation Bias
- Bootstrap Methods: Bootstrap Confidence Intervals, Permutation Bootstrap
- Bootstrap Methods: Bootstrap Confidence Intervals for Parameters in Linear Regression
- Estimation of Probability Density Functions: Histogram, Kernel Estimates, Maximum Likelihood Estimation, Estimation by the Method of Moments

- Recapitulaton of basic notions, LL parsing.
- Classification of LR parsers.
- Strong LR(k) parsing.
- LR(0) and SLR(1) parsing.
- LALR(k) and LR(k) parsing.
- Translation directed by an LR parser.
- Evaluation of attributes during LR parsing.
- LR attributed translation.
- Intermediate representation.
- Incremental LL parsing.
- Incremental LR parsing.
- Parallel LL parsing.
- Parallel LR parsing.

- System definition. Structural and functional concept of a system.
- Compositional and dynamic systems. Hard and soft systems.
- Identification of a system.
- Structural tasks of the system analysis. Paths and feedbacks.
- Tasks of decomposition and composition of a system and tasks of system goals.
- System behavior, behavior models, the notion of a process.
- Formalisms for the analysis of model behavior: Petri nets, decision tables.
- Bulk analysis and other methods of system analysis.
- Soft systems, methods of their analysis.
- Selected methodologies of system design, the SSADM method.
- System synthesis with discrete time.
- Decision and decision processes.
- Information in a system and in its neighborhood, system regularity, system viability.

Last modified: 11.11.2010, 19:23