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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

Institutional repository: Repository of the Faculty of Science

Cite this document

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

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

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

Štimac, H. (2024). 'Dokazi prebrojavanjem', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:100418

Štimac H. Dokazi prebrojavanjem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:100418

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

Metadata
TitleDokazi prebrojavanjem
AuthorHelena Štimac
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberNina Kamčev (član povjerenstva)
Committee memberGoran Igaly (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-11-27, 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)
Languagecroatian
URN:NBNurn:nbn:hr:217:100418
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-11-11 13:22:02