The article deals with the application of modern mathematical apparatus in information and cyber security namely fractal analysis. The choice of fractal modeling for the protection of information in the process of its digital processing is grounded. Based on scientific sources, the basic definitions of the research are analyzed: fractal, its dimension and basic properties used in the process of information protection. The basic types of fractals (geometric, algebraic, statistical) are presented and the most famous of them are described. The historical perspective of the development of fractal theory is conducted. Different approaches to the application of fractal theory in information and cyber security have been reviewed. Among them are: the use of fractal analysis in encryption algorithms; development of a method of protecting documents with latent elements based on fractals; modeling the security system of each automated workplace network using a set of properties that can be represented as fractals. The considered approaches to the application of fractal analysis in information and cyber security can be used in the preparation of specialists in the process of research work or diploma work.

The analysis of competences that should be formed in the future foreign language teachers by the tools of modern information and communications technologies is presented by the authors. It is been determined that generic (core) competences include: informatics, informational, organizational and methodological competences; profile (specific) competences include the abilities of information and communications technologies usage for such pupils` skills forming as: listening, speaking, reading and writing. The program of electronic study course to support the realization of abovementioned task is presented. The purpose of the program is to create a modern level of informational and computer culture, acquiring practical skills of application information technologies by teachers and philologists in order to increase the efficiency of the educational process; students of philological specialties and their preparation for the pedagogically effective use of information technology training in further professional activities. The content of the program modules has been given. Module 1. Network technologies in foreign languages, module 2. Office technologies in foreign languages, module 3. Multimedia technologies. The stages of using ICT in education have been identified, they are search, analysis and research of information, software, methodological resources for a lesson preparation with the further discussion; planning of organizational and methodological measures aimed at achieving goals and objectives of a certain lesson type; developing information materials according to the topic and type of lesson using ICT tools; assessment of future foreign language teachers readiness for the introduction of informational materials on the basis of software resources into The Modern Higher Education Review No. 2, 2017 ISSN 2518 the learning process. The usage of ICT for listening, speaking, reading and writing skills forming is demonstrated on the examples of software, on-line services and various podcasts.

The number and complexity of cybercrime are constantly growing. New types of attacks and competition are emerging. The number of systems is growing faster than new cybersecurity professionals are learning, making it increasingly difficult to track users' actions in real-time manually. E-commerce is incredibly active. Not all retailers have enough resources to maintain their online stores, so they are forced to work with intermediaries. Unique trading platforms increasingly perform the role of intermediaries with their electronic catalogs (showcases), payment and logistics services, quality control - marketplaces. The article considers the problem of protecting the personal data of marketplace users. The article aims to develop a mathematical behavior model to increase the protection of the user's data to counter fraud (antifraud). Profiling can be built in two directions: profiling a legitimate user and an attacker (profitability and scoring issues are beyond the scope of this study). User profiling is based on typical behavior, amounts, and quantities of goods, the speed of filling the electronic cart, the number of refusals and returns, etc. A proprietary model for profiling user behavior based on the Python programming language and the Scikit-learn library using the method of random forest, linear regression, and decision tree was proposed, metrics were used using an error matrix, and algorithms were evaluated. As a result of comparing the evaluation of these algorithms of three methods, the linear regression method showed the best results: A is 98.60%, P is 0.01%, R is 0.54%, F is 0.33%. 2% of violators have been correctly identified, which positively affects the protection of personal data.

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In this article, a mathematical apparatus for comparative analysis of the set of threats of state information resources (DIR) is proposed for consideration, which combines methods and approaches to assess their qualitative and quantitative indicators. The main feature of the study is that the proposed approach to solving the problem of choice does not require a complete restoration of the principle of optimality, but allows to limit only information that will be sufficient to select the "reference sample". The essence of the ranking procedure lies in the fact that the expert poses the threat of an IP in the order that, in his opinion, is the most rational. For each of them the expert assigns specific numbers from a natural series-ranks. In this case, the highest rank receives the threat that has the highest priority. The order scale to be obtained as a result of ranking should satisfy the condition of equality of the number of ranks of the number of ranked threats. In this case, the less complex value of the numerical value will correspond to the least dangerous threat. The essence of the method lies in the fact that the expert must put each threat considered in a certain place in accordance with the degree of availability of one or another property, or in accordance with the proposed by the same expert, the coefficient of significance. In this case, the larger value of a complex assessment corresponds to the least dangerous threat. The basic mathematical method for assessing the threat of threats from the "general population" of the IB classes of threats is the method of formation and research of generalized indicators (criteria), the results of complex combination of which determine the trends of qualitative growth of their significance. Methods of expert assessments are used to increase the reliability of the results of assessing the levels of potential hazards of each threat from the "general population" of IB threat classes. The application of the proposed method will reduce the time to assess the state of the security of information resources and will allow, firstly, to identify the most significant threats that could inflict the greatest damage to information security and, secondly, to direct them the necessary means and safeguards.