Cjelobrojne funkcije i primjene

master's thesis

• Author: Jana Čičko
• Mentor: Mario Krnić (mentor)
• Committee member: Mario Krnić (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opsežno smo obradili cjelobrojne funkcije. Najprije smo ih precizno matematički definirali i naveli njihova osnovna svojstva te smo zatim riješili velik broj primjera iz različitih područja (logaritmi, limesi, nizovi, raznoliki zadaci iz područja teorije brojeva, zadaci iz svakodnevnog života koje smo riješili primjenom Dirichletovog principa, itd.). U svim primjerima primjenjivali smo svojstva cjelobrojnih funkcija. Primjenjujući naučeno o cjelobrojnim funkcijama, postupno smo izgradili pojam binarne operacije mod. Velik dio rada posvetili smo rješavanju zadataka s identitetima, jednadžbama, nejednakostima i nejednadžbama među kojima su i zadaci s matematičkih natjecanja u Republici Hrvatskoj. Konačno, riješili smo i velik broj zadataka sa sumama i rekurzijama koje uključuju funkcije pod i strop.

Abstract (english)

In this thesis, we gave the extensive overview of the integer functions. In the beginning, we gave their strict mathematical definition and listed their main properties which we used throughout the whole thesis. Also, we solved a lot of examples from various mathematical areas (which included logarithms, limits, arrays, theory of numbers, Dirichlet's principle, etc.) in which we applied those properties. In great part of the thesis, we solved a lot of exercises which included identities, equations and inequalities. Within those exercises, there were a lot of those from mathematical competitions in the Republic of Croatia. Finally, we solved tasks that included sums and recursive relations with integer functions.

• Keywords: cjelobrojne funkcije; Dirichletov princip; matematička natjecanja
• Keywords (english): integer functions; Dirichlet's principle; mathematical competitions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:322542
• 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: 2020-01-23 10:26:38