Metoda rekurzije

master's thesis

• Title (english): Recursion method
• Author: Emilija Višić
• Mentor: Ana Prlić (mentor)
• Committee member: Ana Prlić (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj diplomski rad posvećen je primjeni metode rekurzije u matematici. Rad je podijeljen na pet poglavlja. U prvom poglavlju navedene su definicije rekurzivnih relacija, opisane su poznate rekurzije (aritmetički i geometrijski niz) i riješeni su primjeri u kojima se primjenjuje metoda rekurzije. U drugom poglavlju opisan je postupak rješavanja linearnih rekurzija (homogenih i nehomogenih) s konstantnim koeficijentima koji je prikazan na riješenim primjerima. Također, opisana je i primjena rekurzivnih relacija pri računanju determinanti n–tog reda. Iduća dva poglavlja obuhvaćaju Fibonaccijeve i Catalanove brojeve. U posljednjem poglavlju ovog rada metodom rekurzije riješeno je nekoliko zadataka sa srednjoškolskih natjecanja.

Abstract (english)

This thesis describes the implementation of the recursion in mathematics and it is divided in five chapters. In the first chapter, definitions of recursive relations are stated, important recursions are described (arithmetic and geometric sequence) and several examples using recursion are given. In the second chapter, a procedure for solving linear recursions (homogeneous and non-homogeneous) with constant coefficients is described and several solved examples are shown. In addition, the implementation of the recursion in the calculation of nth order determinants is displayed. The following two chapters cover well-known two recursive relations: Fibonacci and Catalan numbers. Finally, the last chapter of this thesis includes a few solved tasks from high school competition in which recursion is applied.

• Keywords: rekurzivne relacije; aritmetički niz; geometrijski niz; linearne rekurzije; Fibonaccijevi brojevi; Catalanovi brojevi
• Keywords (english): recursion relations; arithmetic sequence; geometric sequence; linear recursions; Fibonacci numbers; Catalan numbers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:829599
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-11-09 11:35:30