This article provides an overview of existing solutions for semantic analysis of mathematical documents, and also presents a method for automatic semantic analysis of documents in PDF format. This method searches for local variables in the text of the article, extracts their definitions and connects concepts with formulas. The advantage of the method over the existing ones is independence from the markup of the original PDF document, which expands the scope of the method. We provide estimates of recall, precision and F-measure for algorithms for finding variables and linking local variables with formulas. The resulting semantic markup of the document will be used to create a collection of documents suitable for the semantic formula search service, which is part of the set of services of the Lobachevskii-DML digital publishing system.

The enrichment of educational texts with semantic content (in particular, adding hyperlinks to the pages of the service that displays detailed information about concepts in the text) helps to increase the efficiency of students' assimilation of the material. The existing methods of semantic markup of educational texts do not take into account the structural features of such documents, which leads to excessive recognition of concepts. This article describes the development of the method of automatic annotation of mathematical concepts in educational mathematical texts by adding functionality to account for the structure of an educational document. The main purpose of the method is to process educational materials of the distance education course "Technology for solving planimetric problems". Following a single template when creating course pages allows you to apply an analysis of the web page markup and keywords used by the course creators. The main task in this process is to determine the type of table cell containing text fragments of educational materials. In accordance with the recommendations of the course creators, definitions should be highlighted in the cells containing the task statement, as well as in those blocks where the input data of the task is indicated. The type of table cells is determined by analyzing their attributes and searching for keywords in their contents. This limitation of recognizable text fragments will improve the student's perception of the course pages and improve the quality of learning.

The article provides an overview of existing digital publishing systems, existing ways to expand the functionality of such systems, and also proposes a project for a set of services to expand the functionality of the Open Journal Systems publishing system on the platform of the Lobachevskii-DML digital mathematical library. The proposed set of services includes services aimed at the authors of articles and intended for the editorial staff of the journal. The existing developments in individual parts of the project are described, and the main ideas for the development of all services are proposed.

We present a set of semantic services developed by us to support the educational process in mathematics. The functionality of these services is based on the use of mathematical ontologies OntoMath^Edu and OntoMath^PRO. The ontology of professional mathematical knowledge OntoMath^PRO is designed to classify and systematize the concepts of professional mathematics and includes several important areas of mathematics. Educational mathematical ontology OntoMath^Edu systematically represents knowledge on the training course “Planimetry”. For the use of ontologies in educational applications, an approach to the design of prerequisite relations in these ontologies has been developed. To support mathematical education, we have developed: a service for semantic search by mathematical formulas, a service for semantic annotation of educational materials, a service for visualizing subgraphs of the OntoMath^Edu ontology semantic network, a parallel formal/informal corpus of mathematical statements, a system for automatically generating test questions in mathematical disciplines.

We provide examples of successful application of the developed software tools.

The created software tools are built into the OntoMath digital ecosystem. This ecosystem implements the interaction of semantic services for managing mathematical knowledge.

A service for generating and visualizing educational cards of mathematical concepts based on the ontology of school mathematics OntoMathEdu is presented. The main stages of collecting information for displaying the concept card are given. The developed service is used as a recommendation system in the distance education course of KFU "Technology for solving planimetric problems". Mathematical concepts located in the texts of lecture materials are enriched with links to the corresponding concept card on the service.