Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των ΜαθηματικώνLibrary of the School of Science
Author:
Kastani Anastasia
Supervisors info:
Ευάγγελος Ράπτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
∆ημήτριος Βάρσος, Καθηγητής , Τμήμα Μαθηματικών, Τομέας Άλγεβρας Γεωμετρίας, ΕΚΠΑ
Διονύσιος Λάππας, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Τομέας Άλγεβρας Γεωμετρίας, ΕΚΠΑ
Original Title:
Πολυώνυμα και επίλυση συστημάτων πολυωνυμικών εξισώσεων
Translated title:
Polynomials and solving systems of polynomial equations
Summary:
The aim of this work is to present the solution of linear and non-linear systems, through the perspective of polynomials and with short historical references.
First, the polynomials of many variables, their properties and the operations between polynomials, as they are defined, are studied. Next, the linear representations, their properties and basic theorems that govern their nature are examined. We then move on to solving a system of polynomial equations: one chapter examines the solution of a system of polynomial equations of a variable, while the next two chapters examine the solution of a system of polynomial equations of many variables. In these two chapters a distinction is made between linear systems and non-linear systems. In the latter, the definition and calculation of the Gröbner base, which is widely studied, plays a decisive role. Finally, a large part of the work is devoted to didactic approaches on systems of polynomial equations, through two didactic scenarios.
Main subject category:
Science
Keywords:
polynomials, polynomial equations, systems of polynomial equations
