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master's thesis
Osnovni teorem algebre
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:799040
Kišić, Nika
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Kišić, N. (2014). Osnovni teorem algebre (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:799040

Kišić, Nika. "Osnovni teorem algebre." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:799040

Kišić, Nika. "Osnovni teorem algebre." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:799040

Kišić, N. (2014). 'Osnovni teorem algebre', Master's thesis, University of Zagreb, Faculty of Science, accessed 01 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:799040

Kišić N. Osnovni teorem algebre [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:799040

N. Kišić, "Osnovni teorem algebre", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:799040

Metadata
TitleOsnovni teorem algebre
AuthorNika Kišić
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberDragutin Svrtan (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu obradili smo nekoliko dokaza osnovnog teorema algebre. Na samom početku rada naveli smo povijesni pregled ovog teorema. U drugom smo poglavlju iskoristili svojstva kompleksnih polinoma te dali prvi dokaz. U sljedećem poglavlju smo interpretirali kompleksne polinome kao algebarske objekte. Na taj smo način mogli dokazati teorem primijenivši svojstva polja i njihovih proširenja. Posljednje poglavlje posvećeno je kompleksnoj analizi. Pokazali smo da se osnovni teorem algebre može dokazati primjenom Liouvilleova teorema. Na kraju rada izložili smo još dva dokaza koji se temelje na teoriji kompleksne analize. U prvom smo koristili nejednakost srednje vrijednosti, a u drugom princip maksimuma modula.
Abstract (english)
In this graduate thesis we prove the fundamental theorem of algebra in several ways. In the first chapter we give a historical overview of this theorem. In the second chapter we outline the first proof using properties of complex polynomials. In the next chapter, we interpret complex polynomials as algebraic objects. In this way we are able to present the second proof by applying field and extension field properties. The final chapter is dedicated to complex analysis. We demonstrate that the fundamental theorem of algebra can be proved by using Liouville’s theorem. At the end of the work, we give two additional proofs rooted in complex analysis. The first one uses the mean value inequality and the second one is based on the maximum modulus principle.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:799040
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-12 13:48:13