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.

The results on the creation of methods for managing mathematical knowledge in the context of digital mathematical libraries are presented. The software tools developed on the basis of these methods are part of the OntoMath digital ecosystem, within which they interact. A brief description of the architecture of the OntoMath ecosystem is given, the levels of subject ontologies and external ontologies are highlighted, as well as the level of software tools and services. Semantic services are separated into a separate category. This term denotes software tools, in the functionality of which queries to subject ontologies are used to ensure the management of knowledge objects. General descriptions of developed subject ontologies are given: educational mathematical ontology OntoMath^Edu and ontology of professional mathematics OntoMath^PRO. The development of educational ontology is reflected in the direction of including educational prerequisite links between classes. Among the software tools of the digital ecosystem, search services for mathematical electronic collections, a service for semantic annotation of mathematical documents, tools for semantic marking of educational mathematical documents, as well as a system for automatically generating testing tests in mathematical educational disciplines are highlighted. As part of the OntoMath digital ecosystem, special-purpose recommender systems are being developed. The current version of the ecosystem includes a recommender system for generating a list of related articles based on the OntoMath^PRO ontology, a recommender system for appointing experts to support the scientific review process, and recommender systems for selecting subject classifiers UDC and Mathematics Subject Classification codes for mathematical documents. The results are also presented in the direction of creating a digital library metadata factory, which includes services and tools for extracting, refining, replenishing and normalizing the metadata of electronic mathematical collections. Note that the OntoMath ecosystem is being developed as the technological basis for the Lobachevskii Digital Mathematical Library.