Povijest kompleksnih brojeva

master's thesis

• Title (english): History of complex numbers
• Author: Petra Bešlić
• Mentor: Franka Miriam Brückler (mentor)
• Committee member: Franka Miriam Brückler (predsjednik povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj diplomski rad daje pregled razvoja teorije kompleksnih brojeva i funkcija, od prvih pojava imaginarnih brojeva do utemeljenja kompleksne analize. Prva pojava kompleksnih brojeva seže još u doba renesanse, kada su matematičari Cardano i Bombelli, rješavajući kubne jednadžbe, otkrili da su za dobivanje realnih rješenja istih ponekad potrebni kvadratni korijeni negativnih brojeva te opisali kako s njima računati; tim prvim pojavama kompleksnih brojeva posvećeno je prvo poglavlje ovog rada. U drugom poglavlju opisano je kako su u 17: i 18: stoljeću matematičari pokušavali naći njihovu geometrijsku interpretaciju, što je konačno na prijelazu 18./19. st. pošlo za rukom Wesselu, Gaußu i Argandu. U ovom razdolju nastali su vrijedni rezultati za računanje s kompleksnim brojevima, poput Eulerovog produkta i De Moivreove formule. U posljednjem, trećem poglavlju, opisujemo kako su Cauchy, Laurent, Riemann i Weierstraß utemeljili teoriju kompleksnih funkcija, tj. kompleksnu analizu.

Abstract (english)

The subject of this thesis is the historical development of the theory of complex numbers and functions, from the first use of imaginary numbers up to the establishment of complex analysis. Complex numbers first appeared in the Renaissance period, when mathematicians Cardano and Bombelli, solving cubic equations, realized that, in order to get real solutions it was sometimes necessary to use square roots of negative numbers, and described how to calculate with them. This is the topic of the first chapter of this thesis. The second chapter describes the progress made during the 17th and 18th century when mathematicians tried to find their geometric interpretation, which was finally successfully done by Wessel, Gauß and Argandat the turn of the 18th to the 19th century. This period brought significant results for calculation with complex numbers, e.g. the Euler product and the De Moivre formula. The last, third, chapter describes how Cauchy, Laurent, Riemann and Weierstraß established the theory complex functions, i.e. complex analysis.

• Keywords: Cardano; Bombelli; Wessel; Gauss; Argand; Cauchy; Laurent; Riemann; Weierstrass; kompleksna analiza
• Keywords (english): Cardano; Bombelli; Wessel; Gauss; Argand; Cauchy; Laurent; Riemann; Weierstrass; complex analysis
• Language: croatian
• URN:NBN: urn:nbn:hr:217:271186
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-09-14 10:32:00