Fundamental Theorems
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Fundamental Theorems: Fundamental Theorem of Algebra, Fundamental Theorem of Arithmetic, Finitely-Generated Abelian Group

Fundamental Theorems: Fundamental Theorem of Algebra, Fundamental Theorem of Arithmetic, Finitely-Generated Abelian Group


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 27. Chapters: Fundamental theorem of algebra, Fundamental theorem of arithmetic, Finitely-generated abelian group, Fundamental theorem on homomorphisms, Thermodynamic potential, Fundamental theorem of calculus, Fundamental theorems of welfare economics, Fundamental theorem of Galois theory, Fundamental theorem of combinatorial enumeration, Helmholtz decomposition, Collineation, Fundamental theorem of cyclic groups, Fundamental theorem of Riemannian geometry, Fisher's fundamental theorem of natural selection, Fundamental theorem of poker, Fundamental theorem of linear algebra, Fundamental lemma of calculus of variations, Fundamental theorem of arbitrage-free pricing, Fundamental theorem of linear programming, Fundamental theorem of curves. Excerpt: The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed. Sometimes, this theorem is stated as: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity. Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors. In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time in which algebra was mainly about solving polynomial equations with real or complex coefficients. Peter Rothe (Petrus Roth), in his book Arithmetica Philosophica (published in 1608), wrote ...


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Product Details
  • ISBN-13: 9781155448756
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Weight: 68 gr
  • ISBN-10: 1155448758
  • Publisher Date: 17 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Fundamental Theorem of Algebra, Fundamental Theorem of Arithmetic, Finitely-Generated Abelian Group
  • Width: 189 mm


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