Algebraic hyperstructures on the plane: τhe case of P-hyperstructures (Master thesis)

Ηλιού, Ιωάννα/ Iliou, Ioanna

This dissertation, in its main part, aims at the algebraic study of the P-hyperstructures and on the other hand at their visualization on the plane, using the Geogebra Dynamic Geometry Software. This study is conducted, introducing three hyperoperations and focuses on the documentation of the type of each hyperstructure, the unit and inverse elements and the Join Space structure, wherever it exists. Specifically, the algebraic and mainly the geometric proof is exploited, since, Geometry or Linear Algebra in a 2-dimensional real vector space, with their continuous references to fundamental intuitively comprehensible principles, are tools of teaching and educational value. Furthermore, through interviews and a test, an empirical research took place in the spring of 2017, concerning the way the concepts of operation and hyperoperation are approached by first- year and final- year students of Primary Education School, which revealed several difficulties. In relation to these, conclusions have been drawn that promote their previous knowledge and experiences as important and examine the role of mental maturity in relation to their performance
Institution and School/Department of submitter: Δημοκρίτειο Πανεπιστήμιο Θράκης. Σχολή Επιστημών Αγωγής. Παιδαγωγικό Τμήμα Δημοτικής Εκπαίδευσης
Subject classification: Algebra
Keywords: Υπερπράξεις,Υπερδομές,HV-δομές,Ρ-υπερδομές,Hyperstructures,Hv-structures,P-hyperstructures
URI: https://repo.lib.duth.gr/jspui/handle/123456789/10631
http://dx.doi.org/10.26257/heal.duth.7113
http://dx.doi.org/10.26257/heal.duth.7113
Appears in Collections:Π.Μ.Σ. "ΕΠΙΣΤΗΜΕΣ ΤΗΣ ΑΓΩΓΗΣ: ΕΚΠΑΙΔΕΥΣΗ ΣΤΑ ΜΑΘΗΜΑΤΙΚΑ ΚΑΙ ΣΤΙΣ ΦΥΣΙΚΕΣ ΕΠΙΣΤΗΜΕΣ"

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