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undergraduate thesis
Nejednakosti na matematičkim natjecanjima
Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Applied Mathematics and Informatics, 2023. urn:nbn:hr:126:678373
Dumenčić, Ena
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Computer Science

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Dumenčić, E. (2023). Nejednakosti na matematičkim natjecanjima (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:678373

Dumenčić, Ena. "Nejednakosti na matematičkim natjecanjima." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:678373

Dumenčić, Ena. "Nejednakosti na matematičkim natjecanjima." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:678373

Dumenčić, E. (2023). 'Nejednakosti na matematičkim natjecanjima', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 17 July 2024, https://urn.nsk.hr/urn:nbn:hr:126:678373

Dumenčić E. Nejednakosti na matematičkim natjecanjima [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 July 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:678373

E. Dumenčić, "Nejednakosti na matematičkim natjecanjima", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:678373

Metadata
TitleNejednakosti na matematičkim natjecanjima
Title (english)Inequalities In Mathematical Competitions
AuthorEna Dumenčić
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovom završnom radu prezentirane su neke od osnovnih nejednakosti i tehnike pri rješavanju zadataka koji se pojavljuju na matematičkim natjecanjima. Navedene su i dokazane nejednakosti medu sredinama, nejednakost trokuta i Ptolomejeva nejednakost. Također vrlo važne Cauchy-Schwarz-Buniakowskyjeva nejednakost, Čebiševljeva nejednakost, Bernoullijeva ne jednakost, Holderova nejednakost i nejednakost Minkowskog. Svaka navedena nejednakost potkrijepljena je primjerima i rješenjima zadataka sa županijskih, državnih, internacionalnih natjecanja ili međunarodnih olimpijada.
Abstract (english)
This paper examines some fundamental inequalities and techniques for solving problems that arise in mathematical competitions. Mean inequalities, the triangle inequality, and Ptolomey’s inequality are stated and proved. Additionally, the Cauchy-Schwarz-Buniakowsky inequality, Chebyshev’s inequality, Bernoulli’s inequality, H¨older’s inequality, and Minkowski’s inequality are highlighted as very important. These mentioned inequalities are supported by examples and solutions from county, national, and international competitions, or international Olympiads
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:678373
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-10-19 11:35:09