Home  - Theorems_And_Conjectures - Fundamental Theorem Of Algebra

Books Baby Camera Phones Computers Games DVD Electronics Kitchen Magazines Music Garden Software Tools Toys Video Apparel & Accessories Jewelry & Watches Musical Instruments Health & Personal Care Beauty Sports & Outdoors Office Products

e99.com Bookstore

Images

Newsgroups

41-60 of 89    Back | 1  | 2  | 3  | 4  | 5  | Next 20

Fundamental Theorem Of Algebra:     more books (18)

The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) by Benjamin Fine, Gerhard Rosenberger, 1997-06-20 Constructive aspects of the fundamental theorem of algebra. Proceedings of a symposium conducted at the IBM Research Laboratory by Bruno, Henrici, Peter, Editors Dejon, 1969 Constructive aspects of the fundamental theorem of algebra;: Proceedings of a symposium conducted at the IBM Research Laboratory, Zurich-Ruschlikon, Switzerland, June 5-7, 1967, Constructive aspects of the fundamental theorem of algebra. Proceedings of a symposium conducted at the IBM Research Laboratory by Bruno, Henrici, Peter, Editors Dejon, 1969-01-01 Abstract Algebra: Vector Space, Group, Linear Map, Polynomial, Euclidean Vector, Cauchy Sequence, Fundamental Theorem of Algebra, Power Set Fundamental Theorems: Fundamental Theorem of Algebra, Fundamental Theorem of Arithmetic, Finitely Generated Abelian Group Field Theory: Field, P-Adic Number, Fundamental Theorem of Algebra, Hyperreal Number, Galois Theory, Finite Field, Algebraically Closed Field Fundamental Theorem of Algebra Imaginary Unit: Real number, Complex number, Iota, Polynomial, Imaginary number, Root of unity, Algebraic closure, Complex plane, Fundamental theorem of algebra Constructive Aspects of the Fundamental Theorem of Algebra by Bruno & Peter Henrici. Eds. Dejon, 1969 Complex Analysis: Euler's Formula, Complex Number, Euler's Identity, Exponential Function, Polynomial, Fundamental Theorem of Algebra Constructive Aspects of the Fundamental Theorem of Algebra by Bruno and Peter Henrici. Eds. Dejon, 1969 Constructive aspects of the fundamental theorem of algebra. Proceedings ofa symposium conducted at the IBM Research Laboratory by Bruno, Henrici, Peter, Editors Dejon, 1969-01-01 Algebraic Analysis: Solutions and Exercises, Illustrating the Fundamental Theorems and the Most Important Processes of Pure Algebra by George Albert Wentworth, James Alexander McLellan, et all 2010-01-11

lists with details

41. Forumi FERI
    Translate this page 15 posts - 8 authors - Last post Sep 26, 2007http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra. Uporabniki, ki trenutno prebirajo to temo. gost. Pojdi na forum  
    http://forum.feri.uni-mb.si/Default.aspx?g=posts&t=3966

42. 007 Ja Kultasormi Goldfinger 007 Ja Kultasormi Goldfinger
    Algebran peruslause fundamental theorem of algebra Algebran peruslause fundamental_theorem_of_algebra Algebran peruslause Fundamental Theorem of Algebra  
    http://www.cs.helsinki.fi/group/smart/data/wikipedia/phrase_table/wikipedia_phra

43. ���������� -
    Translate this page 2010 9 12 http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra . (2010-09-11 210725) 1 / 0 IP211.42.200.110  
    http://todayhumor.co.kr/board/view.php?table=science&no=2465&page=11&

44. אם תרצו, אין זה דמיון « לא מדויק
    Translate this page 21 2007 http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra. ( Algebraic Proofs ). -Abstract Algebra Dummit  
    http://www.gadial.net/?p=31 dir=rtl

45. Mengapa Kita Menggunakan Bilangan Kompleks
    Translate this page 19 posts - 16 authors - Last post Sep 30, 2002http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra Dengan cara ini, akar F (x) = 0 mungkin Complex.Di sisi lain Transformasi  
    http://id.edaboard.com/index.php?topic=872240.0

46. The Fundamental Theorem Of Algebra.
    How to think of a proof of the fundamental theorem of algebra Prerequisites . A familiarity with polynomials and with basic real analysis. Statement  
    http://www.dpmms.cam.ac.uk/~wtg10/ftalg.html
    
    Extractions: A familiarity with polynomials and with basic real analysis. Every polynomial (with arbitrary complex coefficients) has a root in the complex plane. (Hence, by the factor theorem, the number of roots of a polynomial, up to multiplicity, equals its degree.) If you have heard of the impossibility of solving the quintic by radicals, or if you have simply tried and failed to solve such equations, then you will understand that it is unlikely that algebra alone will help us to find a solution of an arbitrary polynomial equation. In fact, what does it mean to solve a polynomial equation? When we `solve' quadratics, what we actually do is reduce the problem to solving quadratics of the particularly simple form x =C. In other words, our achievement is relative: if it is possible to find square roots, then it is possible to solve arbitrary quadratic equations. But is it possible to find square roots? Algebra cannot help us here. (What it can do is tell us that the existence of square roots does not lead to a contradiction of the field axioms. We simply "adjoin" square roots to the rational numbers and go ahead and do calculations with them - just as we adjoin i to the reals without worrying about its existence. See my

47. Gauss Summary
    One of the all-time greats, Gauss began to show his mathematical brilliance at the early age of seven. He is usually credited with the first proof of The Fundamental Theorem of Algebra.  
    http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Gauss.html
    
    Extractions: to see thirteen larger pictures Gauss worked in a wide variety of fields in both mathematics and physics incuding number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His work has had an immense influence in many areas. Full MacTutor biography [Version for printing] List of References (67 books/articles) Some Quotations Mathematicians born in the same country Show birthplace location Additional Material in MacTutor A comment from Thomas Hirst's diary Gauss's Disquisitiones Arithmeticae Honours awarded to Carl Friedrich Gauss (Click below for those honoured in this way) Fellow of the Royal Society Fellow of the Royal Society of Edinburgh Royal Society Copley Medal Lunar features Crater Gauss Popular biographies list Number 11 Other Web sites Encyclopaedia Britannica NNDB Gauss Werke (1863 in Latin and German) Nelly Cung (An [unacknowledged] copy of May's biography in the Dictionary of Scientific Biography Kevin Brown (Constructing the 17-gon) Kevin Brown (Geodesy) Sonoma H Kohler S D Chambless (An obituary of Gauss's son) and an account of his life in the USA Mathematical Genealogy Project Previous (Chronologically) Next Main Index Previous (Alphabetically) Next Biographies index JOC/EFR � December 1996 The URL of this page is:

48. Fundamental Theorem Of Algebra: Statement And Significance
    Fundamental Theorem of Algebra Statement and Significance. Any nonconstant polynomial with complex coefficients has a root  
    http://www.cut-the-knot.org/do_you_know/fundamental2.shtml

49. Fundamental Theorem Of Algebra - All Math Words Encyclopedia
    All Math Words Encyclopedia Fundamental Theorem of Algebra Every non-constant single-variable polynomial with complex coefficients has at least one complex root.  
    http://www.allmathwords.org/en/f/fundamentaltheoremalgebra.html
    
    Extractions: All Math Words Encyclopedia Home Pronunciation: /ˌfʌn dəˈmɛn tl ˈθi ər əm ʌv ˈæl dʒə brə/ The fundamental theorem of algebra states that every non-constant single variable polynomial with complex coefficients has at least one complex root. More importantly, for the level of math covered by this encyclopedia, the fundamental theorem of algebra implies that: Every non-constant polynomial with real coefficients can be factored over the real numbers into a product of linear factors and irreducible quadratic factors. A linear factor is a factor in the form bx+c where b and c are real numbers. A quadratic factor is a factor in the form ax +bx+c where a b and c are real numbers. A quadratic factor is irreducible if it can not be factored into two linear factors. The discriminant of a quadratic factor tells if the quadratic factor is reducible. If the discriminant is less than zero, the quadratic factor is irreducible. If the discriminant is greater or equal to zero, the quadratic factor can be reduce to two linear factors. The fundamental theorem of algebra is an existence theorem . While the fundamental theorem of algebra proves that the factors exist, it does not tell how to find the factors. For more information on factoring polynomials, see

50. Fundamental Theorem Of Algebra -- From Wolfram MathWorld
    Every polynomial equation having complex coefficients and degree =1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement  
    http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html
    
    Extractions: Fundamental Theorem of Algebra Every polynomial equation having complex coefficients and degree has at least one complex root . This theorem was first proven by Gauss. It is equivalent to the statement that a polynomial of degree has values (some of them possibly degenerate) for which . Such values are called polynomial roots . An example of a polynomial with a single root of multiplicity is , which has as a root of multiplicity 2. SEE ALSO: Degenerate Frivolous Theorem of Arithmetic Polynomial Polynomial Factorization ... Principal Ring REFERENCES: Courant, R. and Robbins, H. "The Fundamental Theorem of Algebra." §2.5.4 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 101-103, 1996. Krantz, S. G. "The Fundamental Theorem of Algebra." §1.1.7 and 3.1.4 in Handbook of Complex Variables. Smithies, F. "A Forgotten Paper on the Fundamental Theorem of Algebra." Notes Rec. Roy. Soc. London

51. Examples Fundamental Theorem Of Algebra | Tutorvista.com
    Introduction of fundamental theorem of algebra The Fundamental Theorem of Algebra is a for equation solving. It means that every polynomial equation over the field of  
    http://www.tutorvista.com/math/examples-fundamental-theorem-of-algebra

52. The Fundamental Theorem Of Algebra
    The multiplicity of roots. Let's factor the polynomial . We can pull out a term Can we do anything else? No, we're done, we have factored the polynomial completely; indeed  
    http://www.sosmath.com/algebra/factor/fac04/fac04.html
    
    Extractions: Let's factor the polynomial . We can "pull out" a term Can we do anything else? No, we're done, we have factored the polynomial completely; indeed we have found the four linear (=degree 1) polynomials, which make up f x It just happens that the linear factor x shows up three times. What are the roots of f x )? There are two distinct roots: x =0 and x =-1. It is convenient to say in this situation that the root x =0 has multiplicity 3 , since the term x x -0) shows up three times in the factorization of f x ). Of course, the other root x =-1 is said to have multiplicity 1. We will from now on always count roots according to their multiplicity. So we will say that the polynomial has FOUR roots. Here is another example: How many roots does the polynomial have? The root x =1 has multiplicity 2, the root has multiplicity 3, and the root x =-2 has multiplicity 4. All in all, the polynomial has 9 real roots! A degree 2 polynomial is called a quadratic polynomial. In factoring quadratic polynomials, we naturally encounter three different cases:

53. Fundamental Theorem Of Algebra
    Fundamental Theorem of Algebra. Complex numbers are in a sense perfect while there is little doubt that perfect numbers are complex. Leonhard Euler (17071783) made complex  
    http://www.cut-the-knot.org/do_you_know/fundamental.shtml

54. PlanetMath: Proof Of Fundamental Theorem Of Algebra (Rouché's Theorem)
    The fundamental theorem of algebra can be proven using Rouch 's theorem. Not only is this proof interesting because it demonstrates an important result, it also serves to provide an  
    http://planetmath.org/encyclopedia/ProofOfFundamentalTheoremOfAlgebraRouchesTheo
    
    Extractions: proof of fundamental theorem of algebra (Rouché's theorem) (Proof) The fundamental theorem of algebra can be proven using . Not only is this proof toy theorem ) for theorems on the zeroes of analytic functions . For a variant of this proof in terms of the argument principle consequence ), please see the proof of the fundamental theorem of algebra (argument principle) Proof . Let $n$ denote the degree of $f$ Without loss of generality , the assumption can be made that the leading coefficient of $f$ is . Thus, Let . Note that, by choice of $R$ , whenever . Suppose that . Since whenever . Hence, we have the following string of inequalities Since polynomials in $z$ are entire , they are certainly analytic functions in the disk for $z^n$ and $f(z)$ have the same number of zeroes in the disk . Since

55. Complex Numbers: The Fundamental Theorem Of Algebra
    Dave's Short Course on The Fundamental Theorem of Algebra As remarked before, in the 16th century Cardano noted that the sum of the three solutions to a cubic equation  
    http://www.clarku.edu/~djoyce/complex/fta.html
    
    Extractions: The Fundamental Theorem of Algebra As remarked before, in the 16th century Cardano noted that the sum of the three solutions to a cubic equation x bx cx d b , the negation of the coefficient of x . By the 17th century the theory of equations had developed so far as to allow Girard (1595-1632) to state a principle of algebra, what we call now "the fundamental theorem of algebra". His formulation, which he didn't prove, also gives a general relation between the n solutions to an n th degree equation and its n coefficients. An n th degree equation can be written in modern notation as x n a x n a n x a n x a n where the coefficients a a n a n , and a n are all constants. Girard said that an n th degree equation admits of n solutions, if you allow all roots and count roots with multiplicity. So, for example, the equation x x x + 1 = has the two solutions 1 and 1. Girard wasn't particularly clear what form his solutions were to have, just that there be n of them: x x x n , and x n Girard gave the relation between the n roots x x x n , and x n and the n coefficients a a n a n , and a n that extends Cardano's remark. First, the sum of the roots

56. Classroom Activities - Texas Instruments - US And Canada
    Students apply the Fundamental Theorem of Algebra in determining the complex roots of polynomial functions.  
    http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&

57. Fund Theorem Of Algebra
    The Fundamental Theorem of Algebra (FTA) states Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.  
    http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fund_theorem_of_algebra.h
    
    Extractions: Version for printing The Fundamental Theorem of Algebra (FTA) states Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers. In fact there are many equivalent formulations: for example that every real polynomial can be expressed as the product of real linear and real quadratic factors. Early studies of equations by al-Khwarizmi (c 800) only allowed positive real roots and the FTA was not relevant. Cardan was the first to realise that one could work with quantities more general than the real numbers. This discovery was made in the course of studying a formula which gave the roots of a cubic equation. The formula when applied to the equation x x Cardan knew that the equation had x = 4 as a solution. He was able to manipulate with his 'complex numbers' to obtain the right answer yet he in no way understood his own mathematics. Bombelli , in his Algebra , published in 1572, was to produce a proper set of rules for manipulating these 'complex numbers'. Descartes in 1637 says that one can 'imagine' for every equation of degree n n roots but these imagined roots do not correspond to any real quantity.

58. Lesson Plan
    Lesson On Pascal's Triangle Friedrich Gauss (17771855) Introduction. What is the 'Fundamental Theorem of Algebra', whom did it come from, and what is it good for?  
    http://ctap295.ctaponline.org/~kpenner/
    
    Extractions: Fundamental Theorem of Algebra 4.0 Students know the statement of, and can apply, the fundamental theorem of algebra. back to the top Instructional Objectives After exploring available resources related to the topic, the student will be able to identify the Fundamental Theorem of Algebra. The student, after studying and practicing proper application of the Fundamental Theorem of Algebra will be able to give examples demonstrating comprehension of the Fundamental Theorem of Algebra. Students will be able to determine whether or not a given algebraic expression is completely factored by applying the Fundamental Theorem of Algebra to a variety of polynomial expressions. The student will be able to break down a given polynomial into its component parts (factors) and be able to differentiate linear from irreducible quadratic factors.

59. Fundamental Theorem Of Algebra
    Fundamental Theorem of Algebra. The fundamental theorem of algebra (FTA) states Every polynomial of degree n with complex coefficients has n roots in the complex numbers.  
    http://www.und.edu/dept/math/history/fundalg.htm
    
    Extractions: The fundamental theorem of algebra (FTA) states Every polynomial of degree n with complex coefficients has n roots in the complex numbers. There are many other equivalent versions of this, for example that every real polynomial can be expressed as the product of real linear and real quadratic factors. Early work with equations only considered positive real roots so the FTA was not relevant. Cardan realized that one could work with numbers outside of the reals while studying a formula for the roots of a cubic equation. While solving x = 15x + 4 using the formula he got an answer involving the square root of -121. He manipulated this to obtain the correct answer, x = 4, even though he did not understand exactly what he was doing with these "complex numbers." In 1572 Bombelli created rules for these "complex numbers." In 1637 Descartes said that one can "imagine" for every equation of degree n n roots, but these imagined roots do not correspond to any real quantity. Albert Girard , a Flemish mathematiciam, was the first to claim that there are always n solutions to a polynomial of degree n in 1629 in . He does not say that the solutions are of the form a + b i , a, b real. Many mathematicians accepted Girard's claim that a polynomial equation must have

60. Fundamental Theorem Of Algebra Example | TutorVista
    Example 1 Factors completely f (x) = x 4 1 using fundamental theorem in algebra Solution We know that since n = 4, that there are exactly 4 complex zeros, roots  
    http://www.tutorvista.com/topic/fundamental-theorem-of-algebra-example

41-60 of 89    Back | 1  | 2  | 3  | 4  | 5  | Next 20