Dokazi prebrojavanjem

Štimac, Helena

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master's thesis

Dokazi prebrojavanjem

Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:100418

Štimac, Helena

University of Zagreb
Faculty of Science
Department of Mathematics

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APA 6th Edition

Štimac, H. (2024). Dokazi prebrojavanjem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:100418

MLA 8th Edition

Štimac, Helena. "Dokazi prebrojavanjem." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:100418

Chicago 17th Edition

Štimac, Helena. "Dokazi prebrojavanjem." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:100418

Harvard

Štimac, H. (2024). 'Dokazi prebrojavanjem', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:100418

Vancouver

Štimac H. Dokazi prebrojavanjem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2025 January 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:100418

IEEE

H. Štimac, "Dokazi prebrojavanjem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:100418

Cite this item: https://urn.nsk.hr/urn:nbn:hr:217:100418

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Metadata

Title	Dokazi prebrojavanjem
Author	Helena Štimac
Mentor	Vedran Krčadinac (mentor)
Committee member	Vedran Krčadinac (predsjednik povjerenstva)
Committee member	Mea Bombardelli (član povjerenstva)
Committee member	Nina Kamčev (član povjerenstva)
Committee member	Goran Igaly (član povjerenstva)
Granter	University of Zagreb Faculty of Science (Department of Mathematics) Zagreb
Defense date and country	2024-11-27, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics
Abstract	U radu se kroz tri poglavlja upoznajemo s kombinatornim interpretacijama Fibonaccijevih brojeva, verižnih razlomaka te binomnih koeficijenata i kombinacija s ponavljanjem. Poglavlje o Fibonaccijevim brojevima posebno približava tehnike dokazivanja prebrojavanjem te služi kao temelj u razmišljanju o daljnjim poglavljima i složenijim problemima. Iskazano je mnoštvo identiteta. Svaki identitet dokazujemo na elegantan način temeljen na konceptu prebrojavanja. U radu dokaze provodimo na dva načina, dvostrukim prebrojavanjem istog skupa ili prebrojavanjem dva različita skupa, a zatim uspostavljanjem bijekcije između njih. U oba slučaja slijedit će jednakost između lijeve i desne strane identiteta. Iako nije uvijek najjednostavniji pristup, prebrojavanje nam omogućuje potpuno drugačije shvaćanje i razumijevanje problema. Ovim radom želimo čitatelju dočarati moć prebrojavanja kada je u pitanju dokazivanje kombinatornih identiteta.
Abstract (english)	In this thesis, through three chapters, we introduce combinatorial interpretations of Fibonacci numbers, continued fractions, binomial coefficients and combinations with repetition. In the chapter on Fibonacci numbers we get acquainted with proof techniques by counting. It serves as a foundation for further chapters and more complex problems. Many identities are expressed. We give an elegant proof based on counting for each identity. In this thesis, counting arguments are carried out in two ways, by double counting the same set or by counting two different sets and then establishing a bijection between them. In both cases, equality between the left and right side of the identity will follow. Although it is not always the simplest approach, counting allows us to see and understand the problem in a completely different way. With this thesis, we want to convey to the reader the power of counting arguments when it comes to proving combinatorial identities.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:217:100418
Study programme	Title: Financial and Business Mathematics Study programme type: university Study level: graduate Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Repository	Repository of the Faculty of Science
Created on	2024-11-11 13:22:02