The article describes the problems and features of information retrieval activity of students amid the extreme transition of universities to remote education. The results of a student survey are described, allowing to gain some initial insights into the information retrieval competencies of students in a new reality, when the only opportunity for them is remote access to electronic information systems and electronic educational resources. The competencies necessary for effective information retrieval in a remote and blended teaching have been listed and characterized.

A new approach related to the extraction of terms of relative geological age from the metadata of scientific geological publications is described. Based on the developed and adapted approaches and technological solutions, a set of macros is implemented that implements the functions of searching, extracting and adding new metadata to scientific publications.

The paper presents the problem of the existence of a tree with certain numerical characteristics. It is clear that if a tree is given, it is possible to determine the number of node vertices of the tree and leaves, as well as to determine their degrees. Thus, for a tree, you can define a set of pairs whose coordinates are numbers corresponding to the number of node vertices and their degrees. We can form the inverse problem: we give pairs of natural numbers whose second coordinates are greater than 1, and we should determine whether there is at least one tree that the numbers of its node vertices and their degrees coincide with these pairs. The solution to this problem is presented in this paper.

This article focuses on improving the 3D reconstruction of a human model from a single pixel-aligned implicit function image presented by FaceBook Research. The drawbacks of the method are revealed, associated with limiting the quality of the original image, recommendations are presented to avoid its incorrect operation, and approaches to improve the original model are proposed, which increase the identity of the resulting model by 1.33 times. We also worked out the tactics of subsequent texture mapping and implementation of a set of animations.

The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMath^Edu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.

Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.

The OntoMath^Edu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.

The article proposes a methodology related to the use of integrated project tasks in teaching mathematics, based on the practical application of the acquired knowledge in mathematical disciplines in conjunction with computer modeling and programming. Examples of specific integrated project tasks are presented.

The article discusses the construction of a visual solution of boundary value problems for a linear differential equation of the second order by the tridiagonal sweep method in VBA in Excel. Creating macros in VBA allows you to visualize solutions to such boundary value problems.

The aim of the paper is to demonstrate how the techniques of one of the geometries indicated in the title can be used for solving problems formulated in the framework of one of the other geometries. In particular, it is shown how problems formulated in the framework of affine or projective geometry can be solved with an appropriate choice of Euclidean scalar product.