The need to understand the concept of critical thinking grows out of the requirements for a modern person, in addition, critical thinking is an important component of the state strategy for the development of education and science of the Republic of Kazakhstan. We are convinced that this topic will develop together with the educational system of our country. The monitoring study presented in the article is the first in Kazakhstan, its purpose is to find out how successfully the concept of critical thinking as a way of thinking has been conveyed to students over the years since the adoption and implementation of the updated content of secondary education program. The study compared two groups of students: those who studied and those who did not study according to the updated content of secondary education, in order to find out how effectively the concept of critical thinking was learned by students. According to the monitoring results, there was no significant difference between the two groups of students, but the respondents' answers showed that there is a persistent non-distinction between such concepts as decision-making in emergency and critical situations, analysis, conclusions, self-regulation, speed of decision-making and success in the exact sciences in the perception of the concept of "critical thinking". At the end of the article, recommendations are given for further use of the obtained data for other studies.

In this paper, linear multi-step hybrid block methods with three-, four- and five-step numbers are developed for approximating directly the solution of second order Initial and Boundary Value Problems (IBVPs). Multiple finite difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to second order IBVPs over sub-intervals. A new class of orthogonal polynomials constructed as basis function to develop the hybrid block methods adopting collocation technique with a non-negative weight function. The scheme is applied as simultaneous integrator to second order initial value and boundary value problems of ODEs. The properties and convergence of the proposed method are discussed. The derived schemes were used to solve some problems and the numerical result shows the effectiveness, accuracy and superiority of the method over the existing methods found in the literature.

In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean-$CVaR$ portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-at-risk and Conditional-Value-at-risk curves were simulated by three copula models: full Gaussian, Student's $t$ and regular vine copula. These risk curves are lower than historical values of the risk measures curve. All three models have superior prediction ability than a usual empirical method. Further directions of research are described.

The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer linear programming problem and includes an objective payoff function and a system of constraints. In order to demonstrate the performance of the proposed model, we have constructed the portfolio on the European call and put options of Taiwan Futures Exchange. The optimum solution was obtained using the MATLAB software. Our approach is quite general and has the potential to design options portfolios on financial markets.

A method for mapping a two-dimensional color image of the microstructure of the material to a complex network is proposed. Each image elements is assigned to node network. A weighted combination of distance metrics - the Euclidean distance and the Manhattan distance defines whether there is or not an edge between corresponding nodes. The first metric is used to calculate the spatial distance between the picture elements (pixels), the second metric takes into account the contrast between the brightness of pixels in the gray scale. On the basis of the topological properties of the constructed network the edge pixels were detected that allows us to identify the border areas in the microstructure of materials. The proposed method can be used in automated systems of materialographic analysis.

History of loading is the result of interaction of the material microstructure evolution and the loading conditions. The present work aims at an investigation of the behavior in face-centered cubic (FCC) metals under loading with a strain rate jump at different stages. In order to describe the behavior of FCC metals under loading we propose a mathematical model. This model is based on a system of ordinary differential equations (ODEs) and realized as software.

The purpose of this study is to detect project teams in a group. A key point in considering group’s relationships is the reciprocal influence, whereby group’s members influence each other. There was conducted a survey based on reciprocal nomination method, and then a social network was constructed. Participants were first-year bachelor students of Tomsk Polytechnic University. Various social network analysis algorithms were used to cluster network in communities. The results of analysis were discussed with the teachers and students, and then detected community teams were adjusted within the key actors of group. The results of the study may be used to create project teams, which can make successful collective actions in educational projects.

This article presents the results of investigation into changes in the stored energy during the process of plastic deformation. It has been shown that the value of stored energy increases with the degree of deformation and the higher this value the lower the deformation temperature. The stored energy decreases with increasing temperature. Intervals of strong and weak temperature dependence are associated with changes in the intensity of accumulation of deformation defects of different types. The stored energy also increases with increasing stress and the degree of deformation, which corresponds to the experimental data.

In this study, the phenomenon of creep of face-centered cubic (FCC) crystals have been studied by mathematical modeling. The effect of applied stress on creep curves of copper at different temperatures and stress were performed. We have found that steady-state creep rate is proportional to the applied stress and observed the Stages I-III of creep.

The problem of decision making in training-testing systems using fuzzy-logic elements is discussed. The authors present the background and formulate the problem. The technique for passing training, testing, and controlling is described. An informal description of the algorithm for constructing mixed diagnostic tests during simultaneous decision making is given. The use of an intelligent training-testing system constructed on the basis of the IMSLOG software tool is proposed.

A mathematical model of plastic deformation in face-centered cubic (FCC) materials based on a balance model taking into account fundamental properties of deformation defects of a crystal lattice was developed. This model is based on a system of ordinary differential equations (ODE) accounting for various mechanisms of generation and annihilation of deformation defects for different external conditions. In-house developed software, SPFCC (Slip Plasticity of Face-Centered Cubic), was employed to solve the system of ordinary differential equations. The implemented code solves efficiently the stiff ODE system and provides a user-friendly interface for investigation of various features of plastic deformation in FCC materials. Simulation of plastic deformation in the FCC metals was performed for the case of constant strain rate. The modelling results were validated by comparing experimental data and simulation results (stress-strain curves) and good agreement was obtained.

Relevance of computer based learning and testing of students are discussed. Construction of mixed diagnostic tests that are a compromise between unconditional and conditional components is used in order to develop blended education and training. It is proposed for control, monitoring students' knowledge, professional and personal skills and abilities, and designing learning trajectory of courses for every student. We suggest a technique for construction of optimal mixed diagnostic tests that is based only on the experts' knowledge about problem area.

A numerical simulation of creep in metals with FCC structure is done. The influence of various factors on the curves of creep for constant stress and constant load in tension and compression is investigated.