Editing Fundamental theorem of algebra (section)

==References==
===Citations===
{{Reflist}}

===Historic sources===
*{{Citation|last = Cauchy|first = Augustin-Louis|author-link = Augustin-Louis Cauchy|publication-date = 1992|year = 1821|title = Cours d'Analyse de l'École Royale Polytechnique, 1<sup>ère</sup> partie: Analyse Algébrique|url = http://gallica.bnf.fr/ark:/12148/bpt6k29058v|place = Paris|publisher = Éditions Jacques Gabay|isbn = 978-2-87647-053-8}} (tr. Course on Analysis of the [[École Polytechnique|Royal Polytechnic Academy]], part 1: Algebraic Analysis)
* {{citation|last = Euler|first = Leonhard|author-link = Leonhard Euler|year = 1751|title = Recherches sur les racines imaginaires des équations|periodical = Histoire de l'Académie Royale des Sciences et des Belles-Lettres de Berlin|location = Berlin|volume = 5|pages = 222–288|url = http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=02-hist/1749&seite:int=228|access-date = 2008-01-28|archive-date = 2008-12-24|archive-url = https://web.archive.org/web/20081224062952/http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=02-hist%2F1749&seite%3Aint=228|url-status = dead}}. English translation: {{citation|last = Euler|first = Leonhard|author-link = Leonhard Euler|year = 1751|title = Investigations on the Imaginary Roots of Equations|periodical = Histoire de l'Académie Royale des Sciences et des Belles-Lettres de Berlin|location = Berlin|volume = 5|pages = 222–288|url = http://eulerarchive.maa.org/docs/translations/E170en.pdf}}
* {{citation|last = Gauss|first = Carl Friedrich|author-link = Carl Friedrich Gauss|year = 1799|title = Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse|place = [[Helmstedt]]|publisher = C.&nbsp;G.&nbsp;Fleckeisen}} (tr. New proof of the theorem that every integral rational [[algebraic function]] of one variable can be resolved into real factors of the first or second degree).
* {{Citation|last=Gauss|first=Carl Friedrich|year=1866|title=Carl Friedrich Gauss Werke|publisher=Königlichen Gesellschaft der Wissenschaften zu Göttingen|volume=Band III|url={{Google books|WFxYAAAAYAAJ|Werke: Analysis|plainurl=yes}}}}
*#{{Google books|WFxYAAAAYAAJ|Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (1799), pp. 1–31.|page=1}} – first proof.
*#{{Google books|WFxYAAAAYAAJ|Demonstratio nova altera theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (1815 Dec), pp. 32–56.|page=32}} – second proof.
*#{{Google books|WFxYAAAAYAAJ|Theorematis de resolubilitate functionum algebraicarum integrarum in factores reales demonstratio tertia Supplementum commentationis praecedentis (1816 Jan), pp. 57–64.|page=57}} – third proof.
*#{{Google books|WFxYAAAAYAAJ|Beiträge zur Theorie der algebraischen Gleichungen (1849 Juli), pp. 71–103.|page=71}} – fourth proof.
* {{citation|last = Kneser|first = Hellmuth|author-link = Hellmuth Kneser|year = 1940|title = Der Fundamentalsatz der Algebra und der Intuitionismus|url = https://eudml.org/doc/168904|periodical = Mathematische Zeitschrift|volume = 46|pages = 287–302|issn = 0025-5874|doi = 10.1007/BF01181442|s2cid = 120861330}} (The Fundamental Theorem of Algebra and [[Intuitionism]]).
* {{citation|last = Kneser|first = Martin|year = 1981|title = Ergänzung zu einer Arbeit von Hellmuth Kneser über den Fundamentalsatz der Algebra|url = http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN266833020_0177|periodical = Mathematische Zeitschrift|volume = 177|pages = 285–287|issn = 0025-5874|doi = 10.1007/BF01214206|issue = 2|s2cid = 122310417}} (tr. An extension of a work of [[Hellmuth Kneser]] on the Fundamental Theorem of Algebra).
* {{citation|last = Ostrowski|first = Alexander | author-link = Alexander Ostrowski | year = 1920 | chapter = Über den ersten und vierten Gaußschen Beweis des Fundamental-Satzes der Algebra | title = Carl Friedrich Gauss ''Werke'' Band X Abt. 2 | chapter-url = http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN236019856&DMDID=dmdlog53}} (tr. On the first and fourth Gaussian proofs of the Fundamental Theorem of Algebra).
* {{citation|last=Weierstraß|first= Karl|author-link=Karl Weierstrass|contribution=Neuer Beweis des Satzes, dass jede ganze rationale Function einer Veränderlichen dargestellt werden kann als ein Product aus linearen Functionen derselben Veränderlichen|title=Sitzungsberichte der königlich preussischen Akademie der Wissenschaften zu Berlin|pages = 1085–1101|year=1891}} (tr. New proof of the theorem that every integral rational function of one variable can be represented as a product of linear functions of the same variable).

===Recent literature===
* {{citation|last1 = Almira|first1 = José María|last2 = Romero|first2 = Alfonso |year = 2007|title = Yet another application of the Gauss-Bonnet Theorem for the sphere|periodical = [[Bulletin of the Belgian Mathematical Society]]|volume = 14|pages = 341–342| url = http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.bbms/1179839226&view=body&content-type=pdf_1|mr=2341569}}
* {{citation|last1 = Almira|first1 = José María|last2 = Romero|first2 = Alfonso |year = 2012|title = Some Riemannian geometric proofs of the Fundamental Theorem of Algebra|periodical = Differential Geometry – Dynamical Systems|volume = 14|pages = 1–4| url = http://www.mathem.pub.ro/dgds/v14/D14-al.pdf|mr=2914638}}
* {{citation|last = de Oliveira|first = Oswaldo Rio Branco|year = 2011|title = The Fundamental Theorem of Algebra: an elementary and direct proof|periodical = [[The Mathematical Intelligencer]]|volume = 33|issue = 2|pages = 1–2|doi=10.1007/s00283-011-9199-2|s2cid = 5243991|mr=2813254}}
* {{citation|last = de Oliveira|first = Oswaldo Rio Branco|year = 2012|title = The Fundamental Theorem of Algebra: from the four basic operations|periodical = [[The American Mathematical Monthly]]|volume = 119|issue = 9|pages = 753–758|doi=10.4169/amer.math.monthly.119.09.753|arxiv = 1110.0165|s2cid = 218548926|mr=2990933}}
* {{citation|last1 = Fine|first1 = Benjamin|last2 = Rosenberger|first2 = Gerhard|title = The Fundamental Theorem of Algebra|publisher = [[Springer Science+Business Media|Springer-Verlag]]|place = Berlin|year = 1997|isbn = 978-0-387-94657-3|series = [[Undergraduate Texts in Mathematics]]|mr = 1454356}}
* {{citation|last1 = Gersten|first1 = Stephen M.|last2 = Stallings|first2 = John R.|author2-link=John R. Stallings|year = 1988|title = On Gauss's First Proof of the Fundamental Theorem of Algebra|jstor = 2047574|periodical = [[Proceedings of the American Mathematical Society]]|volume = 103|issue = 1|pages = 331–332|issn = 0002-9939|doi=10.1090/S0002-9939-1988-0938691-3 | doi-access=free|mr=0938691}}
* {{citation|last = Gilain|first = Christian|year = 1991|title = Sur l'histoire du théorème fondamental de l'algèbre: théorie des équations et calcul intégral|periodical = Archive for History of Exact Sciences|volume = 42|issue = 2|pages = 91–136|issn = 0003-9519|doi = 10.1007/BF00496870|s2cid = 121468210}} (tr. On the history of the fundamental theorem of algebra: [[theory of equations]] and [[integral calculus]].)
* {{citation|last1 = Netto|first1 = Eugen|last2 = Le Vavasseur|first2 = Raymond|author-link = Eugen Netto|year = 1916|chapter = Les fonctions rationnelles §80–88: Le théorème fondamental|editor-last = Meyer|editor-first = François|editor2-last = Molk|editor2-first = Jules|title = Encyclopédie des Sciences Mathématiques Pures et Appliquées, tome&nbsp;I, vol.&nbsp;2|publication-date = 1992|publisher = Éditions Jacques Gabay|isbn = 978-2-87647-101-6}} (tr. The rational functions §80–88: the fundamental theorem).
* {{citation|last = Remmert|first = Reinhold|author-link = Reinhold Remmert|year = 1991|chapter = The Fundamental Theorem of Algebra|editor-last = Ebbinghaus|editor-first = Heinz-Dieter|editor2-last = Hermes|editor2-first = Hans|editor3-last = Hirzebruch|editor3-first = Friedrich|title = Numbers|series = Graduate Texts in Mathematics 123|editor3-link = Friedrich Hirzebruch|place = Berlin|publisher = [[Springer Science+Business Media|Springer-Verlag]]|isbn = 978-0-387-97497-2|url-access = registration|url = https://archive.org/details/numbers0000unse_d4i8}}
* {{citation|last = Shipman|first = Joseph|year = 2007|title = Improving the Fundamental Theorem of Algebra|periodical = Mathematical Intelligencer|volume = 29|issue = 4|pages = 9–14|doi=10.1007/BF02986170|s2cid = 123089882|issn = 0343-6993}}
* {{citation|last = Smale|first = Steve|year = 1981|title=The Fundamental Theorem of Algebra and Complexity Theory|author-link = Stephen Smale|journal = Bulletin of the American Mathematical Society |series=New Series|volume = 4 | issue = 1|pages = 1–36|doi = 10.1090/S0273-0979-1981-14858-8|doi-access = free}} [http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183547848]
* {{citation|last = Smith|first = David Eugene|author-link = David Eugene Smith|title = A Source Book in Mathematics|publisher = [[Dover Publications|Dover]]|isbn = 978-0-486-64690-9|year = 1959|url-access = registration|url = https://archive.org/details/sourcebookinmath0000smit}}
* {{citation|last = Smithies|first = Frank|year = 2000|title = A forgotten paper on the fundamental theorem of algebra|periodical = Notes & Records of the Royal Society|volume = 54|issue = 3|pages = 333–341|issn = 0035-9149|doi = 10.1098/rsnr.2000.0116|s2cid = 145593806}}
* {{citation|last = Taylor|first = Paul|date = 2 June 2007|title = Gauss's second proof of the fundamental theorem of algebra|url = http://www.paultaylor.eu/misc/gauss-web.php}} – English translation of Gauss's second proof.
* {{citation | last = van der Waerden | first = Bartel Leendert | author-link = Bartel Leendert van der Waerden | title = Algebra | volume = I | edition = 7th | year = 2003 | publisher = [[Springer Science+Business Media|Springer-Verlag]] | isbn = 978-0-387-40624-4}}