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master's thesis
Teorija igara i nepristrane igre
2020. urn:nbn:hr:166:937203
Carić, Barbara
University of Split
University of Split, Faculty of science
Department of Mathematics

Cite this document

Carić, B. (2020). Teorija igara i nepristrane igre (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:937203

Carić, Barbara. "Teorija igara i nepristrane igre." Master's thesis, University of Split, University of Split, Faculty of science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:937203

Carić, Barbara. "Teorija igara i nepristrane igre." Master's thesis, University of Split, University of Split, Faculty of science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:937203

Carić, B. (2020). 'Teorija igara i nepristrane igre', Master's thesis, University of Split, University of Split, Faculty of science, accessed 26 May 2022, https://urn.nsk.hr/urn:nbn:hr:166:937203

Carić B. Teorija igara i nepristrane igre [Master's thesis]. Split: University of Split, University of Split, Faculty of science; 2020 [cited 2022 May 26] Available at: https://urn.nsk.hr/urn:nbn:hr:166:937203

B. Carić, "Teorija igara i nepristrane igre", Master's thesis, University of Split, University of Split, Faculty of science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:937203

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Metadata
TitleTeorija igara i nepristrane igre
Title (english)Game theory and impartial games
AuthorBarbara Carić
MentorDamir Vukičević (mentor)
Committee memberDamir Vukičević (predsjednik povjerenstva)
Committee memberSnježana Braić (član povjerenstva)
Committee memberTanja Vojković (član povjerenstva)
GranterUniversity of Split
University of Split, Faculty of science
(Department of Mathematics)
Split
Defense date and country2020-07-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavni cilj ovog rada je analiza nepristranih igara. U tu svrhu objašnjene su neke strategije koje se javljaju u kombinatornim igrama. Kako bi pokazali posebna svojstva koje imaju nepristrane igre, definirane su pozicije i opcije u igri, te suma igara. Poseban naglasak stavljen je na igru nim pomoću koje je definirana vrijednost pod nazivom nimberi. To je klasa beskrajno malih vrijednosti koje se ne ponašaju kao nijedna vrijednost s kojima smo se do sada susreli, a poprimaju je nepristrane igre. Jedan od najbitnijih rezultata ovog rada je Sprague-grundy teorem po kojem je svaka nepristrana igra ekvivalenta nim-hrpi. Zbog toga igra nim ima veliku ulogu u analizi nepristranih igara.
Abstract (english)
The main objective of this master’s thesis is the analysis of impartial games. For this purpose, some strategies that occur in combinatorial games are explained. In order to show the special properties that impartial games have, positions and options in the game are defined, as well as the sum of games. Special emphasis is placed on the game nim by which is defined the value nimbers. It is a class of infinitesimals that do not behave like any values that we have yet encountered. They occur naturally as the values of the impartial game. One of the most important results of this master’s is Sprague-grundy theorem according to which any impartial game is equivalent to a nim-heap. Therefore, nim plays a mayor role in the analysis of impartial games.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:937203
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 conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-02-02 16:04:42