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master's thesis
Polja, Galoisova teorija i primjene
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:004382
Milanović, Lada
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Milanović, L. (2022). Polja, Galoisova teorija i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:004382

Milanović, Lada. "Polja, Galoisova teorija i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:004382

Milanović, Lada. "Polja, Galoisova teorija i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:004382

Milanović, L. (2022). 'Polja, Galoisova teorija i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 07 October 2024, https://urn.nsk.hr/urn:nbn:hr:217:004382

Milanović L. Polja, Galoisova teorija i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 October 07] Available at: https://urn.nsk.hr/urn:nbn:hr:217:004382

L. Milanović, "Polja, Galoisova teorija i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:004382

Metadata
TitlePolja, Galoisova teorija i primjene
Title (english)Fields, Galois theory and applications
AuthorLada Milanović
MentorAna Prlić (mentor)
Committee memberAna Prlić (predsjednik povjerenstva)
Committee memberGoran Muić (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-12-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu opisana je Galoisova teorija te je ista primijenjena na klasične konstrukcijske probleme u geometriji - trisekciju kuta, duplikaciju kocke, kvadraturu kruga te konstrukciju pravilnog sedmerokuta. Rad se sastoji od tri cjeline. Prvi dio služi kao podsjetnik na važne definicije i teoreme potrebne za bolje razumijevanje same Galoisove teorije. U drugoj cjelini uvodimo Galoisovu teoriju koja se razvila iz klasičnog problema teorije polinomijalnih jednadžbi. Glavna ideja Galoisove teorije je povezati proširenje polja K ⊂ F s grupom svih automorfizama od F koji fiksiraju elemente polja K, odnosno Galoisovom grupom proširenja polja K. O postojanju bijekcije između ova dva spomenuta skupa govori upravo Fundamentalni teorem Galoisove teorije. U zadnjem, trećem dijelu, ovog rada primijenili smo opisanu teoriju na konstrukcijske probleme i algebarski dokazali kako konstrukcije uistinu nisu moguće.
Abstract (english)
In this thesis, Galois theory is described and applied to classical construction problems in geometry - angle trisection, doubling the cube, squaring the circle and construction of a regular heptagon. The work consists of three parts. The first part serves as a reminder of important definitions and theories necessary for a better understanding of Galois theory itself. In the second unit, we introduce the Galois theory, the origin of which begins with a classical problem in the theory of polynomial equations. The main idea of the Galois theory is to connect the field extension K ⊂ F to the group of all automorphisms of F that fix the elements of the field K, in other words, to the Galois group of the field extension K. The existence of a one-to-one correspondence between these two mentioned sets is exactly what the Fundamental theorem of Galois theory says. In the last, the third part of this paper, we applied the described theory to construction problems and proved algebraically that constructions are truly impossible.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:004382
Study programmeTitle: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education
Course: Mathematics and Computer Science Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-12-16 16:08:05