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master's thesis
Grafički prikaz binarnih kvadratnih formi
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:810974
Vidolin, Marina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Vidolin, M. (2020). Grafički prikaz binarnih kvadratnih formi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:810974

Vidolin, Marina. "Grafički prikaz binarnih kvadratnih formi." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:810974

Vidolin, Marina. "Grafički prikaz binarnih kvadratnih formi." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:810974

Vidolin, M. (2020). 'Grafički prikaz binarnih kvadratnih formi', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:810974

Vidolin M. Grafički prikaz binarnih kvadratnih formi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:810974

M. Vidolin, "Grafički prikaz binarnih kvadratnih formi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:810974

Metadata
TitleGrafički prikaz binarnih kvadratnih formi
AuthorMarina Vidolin
MentorTomislav Pejković (mentor)
Committee memberTomislav Pejković (predsjednik povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-02-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Binarna kvadratna forma je preslikavanje \(f:\mathbb{R}^2\rightarrow \mathbb{R}\) oblika \[f(x,y)=ax^2+bxy+cy^2, \quad a,b,c \in \mathbb{Z},\] tj. homogeni polinom dviju varijabli drugog stupnja s cjelobrojnim koeficijentima. U prvom poglavlju rada predstavljamo osnovne pojmove i rezultate o binarnim kvadratnim formama, poput ekvivalencije formi, njihovog matričnog zapisa i diskriminante. Također se bavimo problemom reprezentacije cijelog broja nekom kvadratnom formom i redukcijom pozitivno definitnih i indefinitnih formi. U drugom poglavlju opisujemo pojam topografa kojeg je osmislio engleski matematičar J. H. Conway. Topograf je izvanredan grafički pristup kvadratnim formama pomoću kojeg u trećem i četvrtom poglavlju opisujemo osnovna svojstva definitnih, semidefinitnih i indefinitnih kvadratnih formi s cjelobrojnim koeficijentima.
Abstract (english)
A binary quadratic form is a function \(f:\mathbb{R}^2\rightarrow \mathbb{R}\) of the general form \[f(x,y)=ax^2+bxy+cy^2, \quad a,b,c \in \mathbb{Z},\] In other words, binary quadratic form is a homogeneous polynomial of degree two in two variables with integer coefficients. In the first chapter of this master’s thesis we present the basic concepts and results on binary quadratic forms, such as the equivalence of forms, their matrix notation, and the discriminant. We also deal with the problem of the representation of an integer by some quadratic form and the reduction of positive definite and indefinite forms. In the second chapter, we describe the concept of topograph invented by the English mathematician J. H. Conway. A topograph is an extraordinary visual approach to quadratic forms by which we describe in the third and fourth chapter the basic properties of definite, semidefinite and indefinite quadratic forms with integer coefficients.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:810974
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-10-28 16:52:08