5. The simplest ciphers, their resistancy to ctyptoanalysis, the «absolute unbreakable»

cryptographic system.

6. Modern stream and block ciphers, classification, principles and examples.

7. Modern asymmetric cryptosystem, purpose, principles and examples.

8. Authentication in local and network systems.

9. Main principles and protocols of information protection in networks.

Computer graphics

1. Important topics in computer graphics. Applications of computer graphics. Image

types. Raster and vector graphics. Human vision system.

2. Color models (RGB, CMYK, HSV, HLS). Input and output devices used for

computer graphics.

3. Bresenham's line drawing algorithm. Algorithms for drawing circles and ellipses.

Bezier curve. Filling algorithms.

4. Affine transformation.

5. Graphical projection. Parallel projection. Perspective projection.

6. Image processing. Image filtering. Contour detection. Vectorization of raster images.

Hough transform.

7. 3D visualization. Polygon mesh. Voxels. Hidden Surface and Hidden Line Removal.

Painter algorithm. Z-buffer algorithm. Floating horizon algorithm.

8. Computer graphics lighting. Ray tracing.

9. Lossless compression. Run-Length Coding. LZW.

10. Lossy data compression. JPEG image compression. Wavelet compression. Fractal

image compression.

Mathematical logic and theory of algorithms

1. Statements, formulas, tautologies. Identically true formulas. Identically false formulas.

Equivalence of formulas. The ratio of the logical consequence.

2. Formal (axiomatic) systems. Consistency, independence and completeness of

axiomatic systems. Conclusion in the axiomatic system. The problem of the solution of

the propositional calculus.

3. Calculus of statements. The alphabet, the rules for constructing formulas, the system of

axioms, and the rules for the derivation of the propositional calculus. Interpretation of

formulas.

4. The deduction theorem and the converse theorem. The proof of the theorem is by

contradiction. Phrases of Horn. The method of resolutions in the propositional calculus.

5. First-order predicate calculus. The alphabet, rules for constructing formulas, the

system of axioms and the rules for deducing the predicate calculus. Interpretation of

formulas.

6. Theorems on the logical consequence. Gödel's theorem. The Church theorem. Prefixed

normal forms. The algorithm for converting to the normal form.

7. Skoolem's standard forms. Algorithm of transformation into a Skoolem standard form.

Rule of unification. The method of resolutions in the predicate calculus.

8. Algorithms. Turing machines. Operations with Turing machines. The duality principle.

Sequential connection of Turing machines. Iteration of the Turing machine. Branching of

Turing machines. The Turing thesis.

9. The simplest primitive recursive functions. Superposition operation. The operation of

primitive recursion. Definition of primitive recursive functions. Minimization operations.

Definition of partial-recursive functions. Definition of an effectively computable

function. Thesis Church.

10. Normal Markov algorithms. The scheme of the algorithm. Dictionary functions that

are computable by Markov. The principle of Markov normalization.

Modeling of information-computing systems

1. Modeling as the basic method for the complex systems research. Classification of the

models. Types of the models: analytical, simulation models.

2. Structure of the simulation model.

3. Simulation of the random values with given laws of probability distribution. Method of

the inverse functions. Simulation of the random values with exponential and uniform law

of probability distribution.

4. Obtaining of the realizations of the stationary ordinary random information flows of

homogeneous events. Obtaining of the realizations of the simplest flow, a flow with a

uniform law of distribution of time intervals between the events.

5. Three types of time in simulation modeling. Methods for recalculation of the model

time. Models with continuous and discrete states changes.

6. The concept of events. The structure of the events calendar.

7. The concept of states. The combined graph of transitions and descriptions of the

simulated system dynamics. The structure of the simulation monitor supporting the auto-

event model.

8. The process-oriented approach for system modeling. The concept of the process. The

concept of the objects-transacts.

9. The basic functions and properties of the simulation languages. Classification of the

modeling languages. The basic concepts for describing dynamic processes in the

modeling languages.

10. Accuracy and validity of the statistical experiment. Calculation of the realizations

number for the simulation experiment.

Object-Oriented Programming

1. Three directions for the development of the Java platform. Typical features of the Java

language. Three principles of OOP. Example. Advantages and disadvantages of OOP.

Classes and objects. Properties of objects. Example.

2. Members of the class. Class declaration modifiers. Packages. Namespaces. The

compilation module.

3. Fields. Access modifiers. Methods. Access modifiers. The main method.

4. Creating objects. Constructors. Initialization blocks. Static initialization.

5. Exceptions. The parent exception class. Throwing exceptions. Declared and non-

declared exceptions. Example. Synchronous and asynchronous exceptions. Example. The

throws clause. Try, catch, and finally.

6. Interfaces. Modifiers in interface declarations. An example of a simple interface.

Interface declaration. Constants and methods in interfaces.

7. Data streams. Byte streams. Basic abstract classes of byte streams. Character streams.

Basic abstract classes of character streams. Examples of byte and character stream

classes. Standard streams. InputStreamReader and OutputStreamWriter.

8. Generic types and their features. Generic types with constraints. A metasymbol

argument. A metasymbol with constraints. Generic methods, constructors, interfaces.

Examples.

9. Collections. Interface Collection. Class Collections. Synchronized and unmodified

wrappers. Interface Set. . Interface List. Interface Iterator. Interface Map. Classes of

collections.

10. Problems of a single-threaded approach. Features of multithreading. Using the Thread

class. Using the Runnable interface. Priorities of threads.

Operating Systems

1. Give the definition of the operating system in terms of the functions it performs. Give

examples of operating systems for various purposes.

2. Describe the basic architectures of operating systems.

3. What is the multitasking? Describe the types of multitasking from the point of: (1)

reasons of processes switching; (2) types of scheduling algorithms.

4. Describe the mechanism for implementing multitasking in time-sharing systems

outlining: data structures in use; algorithm for selecting the next running process;

scheduling priorities.

5. Give a definition of the deadlock state. List the necessary conditions for the deadlock

occurrence in the process-resource system.

6. List and briefly outline ways to prevent the deadlock.

7. Briefly outline the following concurrent programming issues: race condition; false

sharing; aggressive optimization.

8. Describe how the operating system interacts with external devices.

9. Briefly describe the main ways of logical and physical organization of files.

10. Briefly describe the memory managment in modern operating systems.

Development of Web-applications

1. JDBC. Types of drivers. The main objectives of the JDBC interface. Examples of

using JDBC. Fundamentals of programming JDBC. Prepared statements. Metadata.

2. XML. Differences between XML and HTML. The structure of the XML document.

XML example. Creation of XML-documents. Example.

3. DTD and XML schema. Examples.

4. Dom and SAX. Examples.

5. ORM. Advantages and disadvantages. Hibernate. File hibernate.cfg.xml. Example.

6. Servlet. Servlet container. Distributed servlet container. Servlet context. Servlet

mapping. The lifecycle of servlets. Features of servlets. Request and Response Objects.

HTTP Servlet. An example of a servlet. Session support. The common deployment

descriptor web.xml. Filtration.

7. JSP. Principle of operation, error handling, JSP views, JSP page elements. Expression

Language. Types of expressions EL. Literals, operators, objects of access to other

objects.

8. JavaScript. Areas of usage. Placement in HTML document. Browser processing.

Comments. Literals and variables. Managing the order of execution. Examples.

9. JavaScript. Functions. Objects. Functions-constructors. Built-in objects. Inheritance.

Throwing and handling exceptions. User arrays. Methods of user arrays.

10. JavaScript. Types of objects. BOM and DOM. The window object. Create and close

new windows. Running new threads. Properties window. The document object. Direct

entry into the document. Events of objects. Work with forms. Programming of

hyperlinks.

9. Networks and telecommunications

1. Open System Interconnection.

2. Topologies of local area networks.

3. Cables. Coaxial cables, twisted pairs, fiber optic.

4. Information Encoding. Synchronization. NRZ, RZ, Manchester encoding.

5. TCP/IP.

6. IP, TCP and their functions.

7. Addressing in Internet. IP addresses. Domain Name System. Classless Internet Direct

Routing.

8. Routing.

9. Access methods in local area networks. Token Passing Multiple Access. Frequency

Division Multiple Access. Time Division Multiple Access. Carrier Sense Multiple

Access with Collision Detection.

10. Ethernet, Fast Ethernet and Gigabit Ethernet.

11. WiFi. 802.11a/b/g/n.

10. Systems of artificial intelligence

1. Classification of artificial intelligence systems. Characteristics of knowledge. Logical,

network, product and frame models of knowledge representation.

2. Theoretical foundations of the Prolog programming language. Initialize variables.

Scope of names. The concept of an anonymous variable. Types of sentences in Prolog.

Unification of variables in Prolog. Calculation of the goal. The mechanism of return.

Managing the search for solutions.

3. Repetition and recursion in Prolog. Use the return mechanism. Return method after

failure. A repeat rule that uses an infinite loop. Methods for organizing recursion.

Optimization of tail recursion. Examples.

4. Representation of binary trees in the Prolog language. Definition of a binary tree.

Program for traversing a binary tree. Representation of graphs in Prolog. Determining the

connectedness of the vertices of a graph. Finding a way on the graph.

5. Basic strategies for solving problems in Prolog. Search for solutions in the state space.

The search algorithm «in depth», the search algorithm «in width». Algorithm A *,

modified algorithm A *. Example.

6. Basic properties of neural networks. Biological basis of artificial neural networks.

Model of the neuron McCulloch-Pits. Perceptron. Rule of the perceptron. Sigmoidal

neuron. Neuron of WTA type. Neuron of Hebb.

7. Multilayer perceptron. Structure of a two-layer sigmoidal network. The algorithm of

steepest descent. The algorithm of steepest descent with moments. Choice of training

factor. The algorithm for back propagation of the error. Simulation algorithm for

annealing.

8. Self-organizing network Kohonen. Normalization of input vectors. The problem of

dead neurons and methods for solving it. The WTA algorithm. WTM algorithms.

Kohonen's algorithm.

9. Hopfield's recurrent network. The Hebb rule. The projection method and the delta

projection method. Recurrent Hemming network. Training and functioning of the

network.

11. Real-Time Systems

1. Definition, purpose, basic properties, typical structure and examples of real-time

systems.

2. A typical structure of the measuring channel, the purpose and characteristics of the

components, the Metrology aspects.

3. The time measuring methods and hardware.

4. Operating systems (RTOS) and programming languages used in real-time systems:

structure and principles.

5. Structure and arrangement of the multitasking RTOS.

6. The principles of task synchronization in the RTOS.

7. Algorithms of buffering, data compression and data integrity control in real-time

systems.

8. The purpose and principles of PID-controller.

9. The simplest algorithms of data preprocessing and processing.

12. Information theory

1. Formal knowledge representation. Forms of information. Definition of entropy as a

measure of uncertainty. Properties of entropy.

2. Entropy of a system. Joint entropy. Conditional entropy.

3. Mutual information and entropy. Properties of the mutual information

4. Source coding. Fixed length codes.

5. Source coding. Variable length codes. Shannon–Fano coding.

6. Communications over a channel. Channel types, properties, noise, and channel

capacity.

7. Channel capacity. Shannon's theorems. Error detection and correction. Error

correcting codes.

8. Cryptography. Cipher types. Kinds of cryptosystems: symmetric and asymmetric.

Public-key cryptography. Digital signature.

9. Data compression. Lossless compression. Huffman coding. Arithmetic coding.

10. Data compression. Lossless compression. Adaptive Huffman coding. Dictionary

based compression algorithms. LZ77. LZSS. LZ78.

13. Formal language theory

1. Formal language theory as a section of Mathematical Linguistics. Notions of “formal

language” and “grammar”.

2. Chomsky hierarchy. Technique for constructing finite-state and context-free

grammars.

3. Finite-state grammars and finite-state machines. Algorithm for the transformation of

finite-state grammars and finite-state machines into DFA.

4. Equivalent transformations of context-free grammars. Elimination of dead-end rules.

5. Theorem about the general form of context-free grammars and its corollaries.

6. Operations over languages. Closure of finite-state and context-free grammars

concerning operations.

7. Methods of analyses for context-free grammars. Precedence grammars of Wirth and

Floyd.

8. Precedence functions. Methods of constructing precedence functions.

9. Reverse Polish notation (RPN). Interpreting RPN. The algorithm for translating

expressions into RPN.

14. Computers and Peripherals

1. Computer and computer system.

2. The cycle of the command.

3. Architecture and levels of detalization.

4. The concept of the machine with a program stored in memory.

5. Machine cycle with interruption.

6. The principle of binary coding. The principle of program management. The principle

of uniformity of memory. The principle of targeting.

7. The main indicators of computers.

8. Von Neumann architecture.