Abstract: A method of extracting mathematical concepts from mathematical exercise representations includes the steps of accessing at least one document including a plurality of mathematical exercise representations, wherein each mathematical exercise representation comprises one or more algorithmic, linguistic, geometric, and graphic mathematical exercise representations; extracting each mathematical exercise representation to identify one or more mathematical concepts; identifying a relationship between a first mathematical concept and a second mathematical concept to identify a plurality of concept groups; populate an optimization table to associate at least one of the mathematical concepts and concept groups with one or more of the plurality of mathematical exercise representations; and optimize the optimization table to remove redundancies.

Abstract: A method of extracting mathematical concepts from mathematical exercise representations includes the steps of accessing at least one document including a plurality of mathematical exercise representations, wherein each mathematical exercise representation comprises one or more algorithmic, linguistic, geometric, and graphic mathematical exercise representations; extracting each mathematical exercise representation to identify one or more mathematical concepts; identifying a relationship between a first mathematical concept and a second mathematical concept to identify a plurality of concept groups; populate an optimization table to associate at least one of the mathematical concepts and concept groups with one or more of the plurality of mathematical exercise representations; and optimize the optimization table to remove redundancies.

Abstract: An extensive computer based online math research system (the “Research System”) having as its foundation an Ontology of mathematics, and utilizing unique and intensive computer support, coordination, data structuring, data storage, computer processing, retrieval capabilities, and data-mining capabilities, and an Ontology editing system that runs on computer software with computer processors and data storage capabilities (the “Ontology Editor System”). The Research System also includes a methodology to enable online reference and data manipulation of the Ontology, and an Internet based search of the concepts of mathematics and applications of mathematics to the sciences on the basis of the Ontology.

Abstract: An extensive computer based online math research system (the “Research System”) having as its foundation an Ontology of mathematics, and utilizing unique and intensive computer support, coordination, data structuring, data storage, computer processing, retrieval capabilities, and data-mining capabilities, and an Ontology editing system that runs on computer software with computer processors and data storage capabilities (the “Ontology Editor System”). The Research System also includes a methodology to enable online reference and data manipulation of the Ontology, and an Internet based search of the concepts of mathematics and applications of mathematics to the sciences on the basis of the Ontology.

Abstract: An extensive computer based online math research system (the “Research System”) having as its foundation an Ontology of mathematics, and utilizing unique and intensive computer support, coordination, data structuring, data storage, computer processing, retrieval capabilities, and data-mining capabilities, and an Ontology editing system that runs on computer software with computer processors and data storage capabilities (the “Ontology Editor System”). The Research System also includes a methodology to enable online reference and data manipulation of the Ontology, and an Internet based search of the concepts of mathematics and applications of mathematics to the sciences on the basis of the Ontology.

Abstract: An extensive computer based online math research system (the “Research System”) having as its foundation an Ontology of mathematics, and utilizing unique and intensive computer support, coordination, data structuring, data storage, computer processing, retrieval capabilities, and data-mining capabilities, and an Ontology editing system that runs on computer software with computer processors and data storage capabilities (the “Ontology Editor System”). The Research System also includes a methodology to enable online reference and data manipulation of the Ontology, and an Internet based search of the concepts of mathematics and applications of mathematics to the sciences on the basis of the Ontology.