Gröbner bazı ve uygulamaları

MSc Thesis Abstract FormName of the Student : Bilge ŞipalProgram of Study : MathematicsThesis Title : Gröbner Bases And Some ApplicationsAbstractIn this thesis, we give comprehensive introduction to definition andconstruction of Gröbner Basis and discuss applications of Gröbner Basisby presenting computational methods to solve problems which involverings of polynomials. We demonstrate some solutions in IntegerProgramming Problem and N-Coloring Problem of a finite graph.Then we present characterization of border bases of zerodimensional ideals that are analogous to the characterization of GröbnerBasis and a a totally different characterization.Consequently we give an algorithm to compute border basis andapply it to an example. And also compare Gröbner Basis with Border Basis.Advisor: Assistant Prof. Müfit Sezer Date:Director: Prof.Dr. Süleyman Özekici Date: