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Cross Domain Mathematical Concept Formation

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Original languageEnglish
Title of host publicationAISB 2000
Publication statusPublished - 2000
EventAISB 2000 Convention - Birmingham, United Kingdom
Duration: 17 Apr 200020 Apr 2000


ConferenceAISB 2000 Convention
CountryUnited Kingdom


Many interesting concepts in mathematics are essentially ‘cross-domain’ in nature, relating objects from more than one area of mathematics, e.g. prime order groups. These concepts are often vital to the formation of a mathematical theory. Often, the introduction of cross-domain concepts to an investigation seems to exercise a mathematician’s creative ability. The HR program, (Colton et al., 1999), proposes new concepts in mathematics. Its original implementation was limited to working in one mathematical domain at a time, so it was unable to create cross-domain concepts. Here, we describe an extension of HR to multiple domains. Cross-domain concept formation is facilitated by generalisation of the data structures and heuristic measures employed by the program, and the implementation of a new production rule. Results achieved include generation of the concepts of prime order groups, graph nodes of maximal degree and an interesting class of graph.


AISB 2000 Convention


Birmingham, United Kingdom

Event: Conference

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