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master's thesis
Polimoni nad konačnim poljima
2020. urn:nbn:hr:166:691396
Bročić, Lucija
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Bročić, L. (2020). Polimoni nad konačnim poljima (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:691396

Bročić, Lucija. "Polimoni nad konačnim poljima." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:691396

Bročić, Lucija. "Polimoni nad konačnim poljima." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:691396

Bročić, L. (2020). 'Polimoni nad konačnim poljima', Master's thesis, University of Split, Faculty of Science, accessed 28 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:691396

Bročić L. Polimoni nad konačnim poljima [Master's thesis]. Split: University of Split, Faculty of Science; 2020 [cited 2024 December 28] Available at: https://urn.nsk.hr/urn:nbn:hr:166:691396

L. Bročić, "Polimoni nad konačnim poljima", Master's thesis, University of Split, Faculty of Science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:691396

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Metadata
TitlePolimoni nad konačnim poljima
Title (english)Polynomials over Finite Fields
AuthorLucija Bročić
MentorBorka Jadrijević (mentor)
Committee memberBorka Jadrijević (predsjednik povjerenstva)
Committee memberMarija Bliznac Trebješanin (član povjerenstva)
Committee memberDino Peran (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2020-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavili smo se polinomima i njihovim svojstvima, a posebno svojstvima polinoma nad konačnim poljima. U prvom poglavlju dane su osnovne definicije i tvrdnje vezane uz djeljivost polinoma, faktorizaciju, korijene i ireducibilnost polinoma jedne varijable. Promatrali smo i jedan poseban i važan oblik polinoma s više varijabli - simetrične polinome, koji su bitni u primjenama. U drugom poglavlju bavili smo se polinomima nad konačnim poljima. Prvo su dani su osnovni rezultati vezani uz konačna polja. Zatim smo promatrali ciklotomičke polinome i dali neka njihova svojstva. Nakon toga bavili smo se ireducibilnošću i traženjem korijena polinoma nad konačnim poljem.
Abstract (english)
In this master's thesis we dealt with polynomials and their properties, especially with properties of polynomials over finite fields. In the first chapter we gave basic definitions and results about divisibility, factorization, irreducibility and roots of polynomials in one variable. We also observed one special and important form of multivariate polynomials - symmetric polynomials, which are important in applications. The second chapter of this thesis deals with polynomials over finite fields. First, we gave the basic results about finite fields. Then we observed cyclotomic polynomials and gave some of their properties. After that, we dealt with irreducibility and finding the roots of polynomials over a finite field.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:691396
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-02-02 17:02:45