21. When Are Two Proofs Essentially The Same? « Gowers's Weblog Oct 4, 2007 How about the usual approaches to the fundamental theorem of algebra? http//en. wikipedia.org/wiki/fundamental_theorem_of_algebra Proofs http://gowers.wordpress.com/2007/10/04/when-are-two-proofs-essentially-the-same/

22. ARMENIANS - Web Fundamental Theorem of Algebra encyclopedia article One important case of the Fundamental en.citizendium.org/wiki/fundamental_theorem_of_algebra http://www.armenians.net/mobile/search/web?search=theorem&type=web&start

23. Polynomial Root Finder - C++ Forums 7 posts 3 authors - Last post 2 days ago where n is the degree of the polynomial (http//en.wikipedia.org/wiki/ fundamental_theorem_of_algebra). If you only need the real roots, http://www.cplusplus.com/forum/general/17664/

C++ Forums General C++ Programming : Polynomial Root Finder Search: C++ Information Documentation Reference ... Jobs Polynomial Root Finder When(1261572455) Oct 31, 2010 at 7:53am UTC I've been having problems with a program I'm writing for finding the roots of any polynomial. I use Newton's method which gives accurate roots sometimes, but quite often it fails to give me a root for a polynomial (which has roots), and quite frequently it fails to give me all the roots of a polynomial. I can get more roots if I increase the value of BIG_EPSILON_COMPARE, but then I get a lot of duplicate roots like 0.99995, 0.99996 and 1 for a polynomial whose root is 1. What should I do to get more roots? (Assuming the polynomial has more roots of course.) PS: poly.Evaluate(x) gives the value of the polynomial poly at x. #define EPSILON 1e-10 #define BIG_EPSILON_STEP 5e-2 #define BIG_EPSILON_COMPARE 1e-3 const int //Maximum number of iterations const int //Maximum number of roots (arbitrary) const double RANGE = 10000.0; void // still need to finish this double NewtonsMethodPolynomial( const double double double guess = approx_root;

24. Fundamental Theorem Of Algebra - Academic Kids In mathematics, the fundamental theorem of algebra states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. http://www.academickids.com/encyclopedia/index.php/Fundamental_theorem_of_algebr

Fundamental theorem of algebra From Academic Kids In mathematics , the fundamental theorem of algebra states that every complex polynomial of degree n has exactly n zeroes , counted with multiplicity. More formally, if (where the coefficients a a n can be real or complex numbers), then there exist ( not necessarily distinct) complex numbers z z n such that This shows that the field of complex numbers , unlike the field of real numbers , is algebraically closed n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by Carl Friedrich Gauss in 1799. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. All proofs of the fundamental theorem necessarily involve some analysis , or more precisely, the concept of continuity of real or complex polynomials. The main difficulty in the proof is to show that every non-constant polynomial has at least one zero. We mention approaches via complex analysis topology , and algebra Find a closed disk D of radius r p z p z r p z D is therefore achieved at some point z in the interior of D p z m p z ) is a holomorphic function in the entire complex plane. Applying

25. Fundamental Theorem Of Algebra In Korean - Dictionary And Translation Translate this page fundamental theorem of algebra. Dictionary terms for fundamental theorem of algebra in Korean, Korean definition for fundamental theorem of algebra, http://www.babylon.com/definition/fundamental_theorem_of_algebra/Korean

26. Page 20: The Math/Science Help Thread! @ Ultimate-Guitar.Com Forum Archive 100+ posts 54 authors - Last post Jun 16Well, the http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra says that every polynomial can be written as (x-a)(x-b). http://www.ultimate-guitar.com/forum/archive/index.php?t-658547-p-20.html

27. Fundamental Theorem Of Algebra - Wikinfo frTh or me de d'AlembertGauss The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial http://www.wikinfo.org/index.php/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From Wikinfo Jump to: navigation search [[fr:Th�or�me de d'Alembert-Gauss]] The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if (where the coefficients a a n can be real or complex numbers), then there exist ( not necessarily distinct) complex numbers z z n such that This shows that the field of complex numbers , unlike the field of real numbers , is algebraically closed n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by Carl Friedrich Gauss in 1799. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. All proofs of the fundamental theorem necessarily involve some analysis , or more precisely, the concept of continuity of real or complex polynomials. The main difficulty in the proof is to show that every non-constant polynomial has at least one zero. We mention approaches via

28. 대수학의 기본정리 - 수학이 알고싶은 중고대딩들을 위한 수 Translate this page 2009 1 29 The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) http //en.wikipedia.org/wiki/fundamental_theorem_of_algebra http://pythagoras0.springnote.com/pages/1991726

Header home - FAQ 복소계수를 갖는 n차 다항방정식은 언제나 복소수체 안에서 해를 갖는다. The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) Benjamin Fine (Author), Gerhard Rosenberger (Author) http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) by Benjamin Fine (Author), Gerhard Rosenberger (Author) 에서 가져옴. proof_of_FTA_1.pdf proof_of_FTA_2.pdf proof_of_FTA_3.pdf proof_of_FTA_4.pdf winding number의 개념을 통한 위상수학적 증명 proof_of_FTA_5.pdf degree 개념을 이용하는 대수적 위상수학을 통한 증명 proof_of_FTA_6.pdf 예) springnote, abc@gmail.com, cool, abc.myid.net PC방 등 공용컴퓨터에서는 체크하지 마세요. 오픈ID 로그인 오픈ID 오픈ID 찾기 XXXX@mail.com

29. What Are Some Correct Results Discovered With Incorrect (or No) Proofs? - MathOv The fundamental theorem of algebra was given incomplete proofs by d Alembert http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra http://mathoverflow.net/questions/27749/what-are-some-correct-results-discovered

login faq how to ask meta ... What are some correct results discovered with incorrect (or no) proofs? Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points Many famous results were discovered through non-rigorous proofs, with correct proofs being found only later and with greater difficulty. One that is well known is Euler's 1737 proof that Another example, of a different type, is the Jordan curve theorem. In this case, the theorem seems obvious, and Jordan gets credit for realizing that it requires proof. However, the proof was harder than he thought, and the first rigorous proof was found some decades later than Jordan's attempt. Many of the basic theorems of topology are like this. Then of course there is Ramanujan, who is in a class of his own when it comes to discovering theorems without proving them. I'd be interested to see other examples, and in your thoughts on what the examples reveal about the connection between discovery and proof. Clarification . When I posed the question I was hoping for some explanations for the gap between discovery and proof to emerge, without any hinting from me. Since this hasn't happened much yet, let me suggest some possible explanations that I had in mind:

30. Fundamental Theorem Of Algebra - Tamil Word - தமிழ் விக்சன 15 Jul 2010 fundamental theorem of algebra. . http://ta.wiktionary.org/wiki/fundamental_theorem_of_algebra

fundamental theorem of algebra fundamental theorem of algebra fundamental theorem of algebra http://ta.wiktionary.org/wiki/fundamental_theorem_of_algebra New features Text is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply. See for details.

31. Fundamental Theorem Of Algebra - The Dalton Math Wiki Complex Numbers . Complex numbers were originally thought of as formal (i.e., not actual) solutions to equations lacking real number solutions. For example, i can be defined by http://wikis.dalton.org/math/index.php?title=Fundamental_Theorem_of_Algebra

32. La Teoremo De Liouville (kompleksa Analitiko) - Wikipedia's Liouville's Theorem span class= mwheadline id= fundamental_theorem_of_algebra algebra ? eng=Fundamental theorem of algebra Complex-analytic_proofs title= Algebra http://epo.wikitrans.net/show.php?id=312293&source=1

33. Kids.Net.Au - Encyclopedia > Fundamental Theorem Of Algebra The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has http://encyclopedia.kids.net.au/page/fu/Fundamental_theorem_of_algebra

Search the Internet with Kids.Net.Au Encyclopedia > Fundamental theorem of algebra Article Content Fundamental theorem of algebra The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if (where the coefficients a a n can be real or complex numbers), then there exist (not necessarily distinct) complex numbers z z n such that This shows that the field of complex numbers , unlike the field of real numbers , is algebraically closed . An easy consequence is that the product of all the roots equals (-1) n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by Carl Friedrich Gauss in the early 19th century. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. It is possible to prove the theorem by using only algebraic methods, but nowadays the proof based on complex analysis seems most natural. The difficult step in the proof is to show that every non-constant polynomial has at least one zero. This can be done by employing

34. Fundamental Theorem Of Algebra In Encyclopedia Fundamental theorem of algebra in Encyclopedia in Encyclopedia Fundamental theorem of algebra. In mathematics, the fundamental theorem of algebra states that every nonconstant single http://www.tutorgig.com/ed/Fundamental_theorem_of_algebra

35. - O Translate this page 27 posts - 5 authors - Last post Jun 25 sosad adore . http//en.wikipedia.org/wiki/ fundamental_theorem_of_algebra Reply icon 6/25/2010 354 PM http://forum2.hkgolden.com/view.aspx?type=ED&message=2400386&page=20&

36. Fundamental Theorem Of Algebra - AoPSWiki The fundamental theorem of algebra states that every nonconstant polynomial with complex coefficients has a complex root. In fact, every known proof of this theorem involves http://www.artofproblemsolving.com/Wiki/index.php/Fundamental_Theorem_of_Algebra

Art of Problem Solving LOGIN/REGISTER Home Bookstore AoPS Curriculum ... Articles You are here: Resources AoPSWiki Search Wiki Page Tools Page Discussion View source History Personal tools Talk for this IP Log in Navigation Main Page Community portal Current events Recent changes ... Help Toolbox What links here Related changes Special pages Printable version ... Permanent link Fundamental Theorem of Algebra From AoPSWiki The fundamental theorem of algebra states that every nonconstant polynomial with complex coefficients has a complex root . In fact, every known proof of this theorem involves some analysis , since the result depends on certain properties of the complex numbers that are most naturally described in topological terms. It follows from the division algorithm that every complex polynomial of degree has complex roots, counting multiplicities. In other words, every polynomial over splits over , or decomposes into linear factors. Contents Proofs Proof by Liouville's Theorem Algebraic Proof References ... See also Proofs Proof by Liouville's Theorem We use Liouville's Boundedness Theorem of complex analysis , which says that every bounded entire function is constant Suppose that is a complex polynomial of degree with no complex roots; without loss of generality, suppose that

37. Ό�ѹ����� ��Ե��ʵ�� Marathon [Archive] - Mathcenter Forum Translate this page (fundamental theorem of algebra. (http/ /en.wikipedia.org/wiki/fundamental_theorem_of_algebra)) http://www.mathcenter.net/forum/archive/index.php/t-2880.html

Mathcenter Forum PDA View Full Version : Ό�ѹ����� ��Ե��ʵ�� Marathon nooonuii M@gpie �͵ͺ��� Leibnitz ��Ѻ�� ˹ѧ��ͺҧ�����͡��� Newton �繼��ش��С���Ԫ��Ť���ʤ�Ѻ TOP ��� Newton ��� Leibnitz ����� ����ͧ����ҧ������Ѻ��� ���Ф��Դ Calculus ������ͧ��ԧ� �˹������繡�з���������Ҹ͹�����¡�з������ ��Ͷ���Ӷ������ǡѺ���Ҹ͹�ѡ˹��� :yum: �繷���Һ�ѹ����� ���зҧ����Ѻ���������Ҹ͹��鹤�� 42.195 �������� :rolleyes: ���Һ�ѹ�����ҵ���Ţ��� �շ�������ҧ�� �´�˹ѧ����ͧ 300 ��ҧ������ �ش������鹢ͧ�ѹ��������¹���� :laugh: kanakon The name, "marathon", comes from the legend of Pheidippides, a Greek soldier, who was sent from the town of Marathon to Athens to announce that the Persians had been miraculously defeated in the Battle of Marathon. It is said that he ran the entire distance without stopping, but moments after proclaiming his message to the city he collapsed dead from exhaustion. The account of the run from Marathon to Athens first appears in Plutarch's On the Glory of Athens in the 1st century AD who quotes from Heraclides Ponticus' lost work, giving the runner's name as either Thersipus of Erchius or Eucles.[1] Lucian of Samosata (2nd century AD) also gives the story but names the runner Philippides (not Pheidippides).[2] The Greek historian Herodotus, the main source for the Greco-Persian Wars, mentions Pheidippides as the messenger who ran from Athens to Sparta asking for help. In some Herodotus manuscripts the name of the runner between Athens and Sparta is given as Philippides.

38. - Translate this page http//www.clarku.edu/~djoyce/complex http //en.wikipedia.org/wiki/fundamental_theorem_of_algebra http://gifted.cet.ac.il/GIFTED/skira/numbers/numbers8.asp dir=rtl

39. Mat_pavli Zanimive Spletne Strani Translate this page 7 jan 2010 http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra. (osnovni izrek algebre). 2. RACIONALNE FUNKCIJE http://e.stanislav.si/mod/resource/view.php?id=428

40. Polynom N-ten Grades Nur N Nullstellen Translate this page 27 posts - 8 authors - Last post Jun 16, 2004http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra. 13.06.2004, 1146, Auf diesen Beitrag antworten �. Thomas, Auf deutsch http://www.matheboard.de/archive/4135/thread.html

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