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We considered the problems of mathematical modeling of composite materials in the example of the development of materials for the protection against ionizing radiation. Construction materials are provided as a complex system with the appropriate attributes. The structure and physico-mechanical properties of the material were determined by the results of the modeling of kinetic processes. Process of forming properties is described by the differential equation in deviations from the equilibrium state (as for dispersion system). It is taken into account the elastic and damping properties of the material. To predict the behavior of the building material and the formation of his private mathematical models are used a representation of the processes as of time series. It is given the algorithm for studies (with considering prehistory) of formation of the basic physical and mechanical properties of epoxy composites for radiation protection. We present an example of the identification of building materials with special properties. Approaches used effectively in the development of materials with special properties.

The approaches to the cognitive modelling of education system as a complex system of modular architecture with the corresponding system attributes are defined. The modular hierarchical structure of educational system itself is based on the hierarchical structure of the set of particular criteria. The methodological principles for assessing the quality of the educational system are indicated. It is emphasised that measuring of indicator changes the system itself, thus making control ineffective. The insufficient performance of educational institutions' evaluation on the basis of radar chart is shown: education system deformation is possible through the redistribution of indicators. The possibility of aconsistent improvement in the quality indicators of an educational system based on the use of Pareto cumulative charts is assumed. The set of all formed competencies is considered as a vector criterion for assessing the quality of training of students. The illustration of the formation of competences is given on the example of the undergraduates studying the discipline "Complex systems mathematical modelling".