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master's thesis
Konačne geometrije i primjene
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:173729
Novosel, Iva
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Novosel, I. (2019). Konačne geometrije i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:173729

Novosel, Iva. "Konačne geometrije i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:173729

Novosel, Iva. "Konačne geometrije i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:173729

Novosel, I. (2019). 'Konačne geometrije i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 18 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:173729

Novosel I. Konačne geometrije i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 18] Available at: https://urn.nsk.hr/urn:nbn:hr:217:173729

I. Novosel, "Konačne geometrije i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:173729

Metadata
TitleKonačne geometrije i primjene
AuthorIva Novosel
MentorMatija Bašić (mentor)
Committee memberMatija Bašić (predsjednik povjerenstva)
Committee memberTihomir Vukelja (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
Committee memberMatko Milin (član povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Blok dizajni su konačne strukture u kojima su elementi konačnih skupova raspoređeni po zadanim pravilima. Specijalni slučajevi blok dizajna su konačne afine i projektivne ravnine. U radu su prikazane konstrukcije konačnih afinih i projektivnih ravnina pomoću konačnih polja, npr. Fanove ravnine kao najmanje projektivne ravnine. Na nekoliko načina prikazana je veza između afine i projektivne ravnine. Posebni naglasak stavljen je na prilagođavanje koncepata konačnih polja, afinih i projektivnih ravnina te dizajna učenicima u školi. Uz to, dane su aktivnosti kojima konačna polja, afine i projektivne ravnine te dizajne možemo približiti učenicima u školi. Rad je podijeljen u četiri dijela. Prva tri poglavlja donose osnovne teorijske rezultate o konačnim poljima, projektivnim i afinim ravninama i blok dizajnima. Svako poglavlje sadrži konstrukcije raznih struktura i rješenja nekih poznatih problema, npr. Kirkmanov problem 15 učenica. U četvrtom poglavlju promatramo na koji način učenicima možemo približiti teme iz prva tri poglavlja u svrhu razvijanja mišljenja i poticanja kognitivne aktivnosti. U tome je najbitnija prilagodba materijala i izražavanje prilikom izvođenja nastave. U dodacima se nalaze nastavni listići za provođenje aktivnosti na nastavnom satu.
Abstract (english)
Block designs are finite structures in which the elements of finite sets satisfy some properties. Special cases of block designs are affine and projective planes. In this thesis we present the construction of affine and projective plane using the finite fields, for example Fano plane as the smallest finite projective plane. In several ways connection between affine and projective plane is shown. Particular emphasis is given on the adaptation concepts of finite fields, affine and projective planes and designs to students in school. Also, activities are given which can be used to bring finite fields, affine and projective planes and designs closer to students. The thesis consists of four parts. First three chapters bring basic theoretical results of finite fields, affine and projective planes and block designs. Every chapter contains constructions of different structures and solutions of some familiar problems, such as Kirkman’s schoolgirl problem. In chapter four we discuss how to bring topics from first three chapters closer to students in order to encourage cognitive activities. In order to do so, most important is good adjustment of materials and expression during class. Appendices contain sheets for teaching in the class.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:173729
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-14 13:08:34