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master's thesis
Teorija brojeva u nastavi matematike
2017. urn:nbn:hr:126:443360
Obradović, Srđana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

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Obradović, S. (2017). Teorija brojeva u nastavi matematike (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:443360

Obradović, Srđana. "Teorija brojeva u nastavi matematike." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:443360

Obradović, Srđana. "Teorija brojeva u nastavi matematike." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:443360

Obradović, S. (2017). 'Teorija brojeva u nastavi matematike', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:443360

Obradović S. Teorija brojeva u nastavi matematike [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:443360

S. Obradović, "Teorija brojeva u nastavi matematike", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:443360

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Metadata
TitleTeorija brojeva u nastavi matematike
AuthorSrđana Obradović
MentorLjerka Jukić Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2017-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Teme u ovome radu baziraju se na elementarnoj teoriji brojeva i većina primjera i zadataka koje dokazujemo obrađuju se na nastavi osnovnih škola. No, posljednja poglavlja najprirodnije se uklapaju u nastavu srednjih škola. Važno je napomenuti kako rad ne obuhvaća čitavu granu matematike. Najprije je uveden pojam djeljivosti kao jedan od najjednostavnijih, ali i ujedno najvažnijih pojmova u teoriji brojeva. Zadatcima i primjerima prikazane su djeljivosti s brojevima 2,3,4,6,11,5,8 i 9. Potom su uslijedili elementarni pojmovi prostih i složenih brojeva te najveći zajednički djeljitelj i najmanji zajednički višekratnik. Osvrnuli smo se i na Euklidov algoritam i temeljne sustave brojeva, a rad je zaokružen modularnom aritmetikom i diofantskom analizom. Svi teoremi popraćeni su dokazima, formulacije problema pogodne da učenike zainteresira za sadržaj, a cilj rada je ovladati teorijom brojeva i upoznati se s mnogim njezinim primjenama pokazanim u raznim maštovitim primjerima.
Abstract (english)
Topics in this paper are based on the elementary number theory and most examples and tasks and proofs are for primary school education of mathematics. But the last chapters are beter fit for teaching in high school. It is important to know that the complete knowledge of this branch of mathematics is not covered in this paper. First, concept of divisibility is introduced as one of the simplest, but also one of the most important concepts in number theory. Rules of divisibility by numbers 2,3,4,6,11,5,8 and 9 are shown through tasks and examples, followed by prime and composite numbers, greatest common divisor and least common multiple. We will also mention the Euclidean algorithm and different base number systems, and the work is completed by modular arithmetic and Diophantine analysis. All theorems are accompanied by proofs, problems suitable for students interested in the content who aim to master the number theory and become familiar with many of its applications demonstrated in different interesting examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:443360
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-05-10 06:03:54