81. Historia Matematica Mailing List Archive: [HM] The Fundamental Theorem Of Algebr The first substantial proof of the fundamental theorem of algebra, though notrigorous by modern standards, was given by Gauss in his http://sunsite.utk.edu/math_archives/.http/hypermail/historia/nov98/0015.html

[HM] The Fundamental Theorem of Algebra Samuel S. Kutler s-kutler@sjca.edu Tue, 3 Nov 1998 11:44:51 -0500 (EST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Martin Davis: "Re: [HM] The Fundamental Theorem of Algebra" Previous message: milo.gardner@24stex.com: "R: [HM] IS" Next in thread: Martin Davis: "Re: [HM] The Fundamental Theorem of Algebra" Friends: On page 598 of MATHEMATICAL THOUGHT FROM ANCIENT TO MODERN TIMES, Morris Kline writes The first substantial proof of the fundamental theorem [of algebra], though not rigorous by modern standards, was given by Gauss in his doctoral thesis of 1799 at Helmstadt. He criticized the work of d'Alembert, Euler, and Lagrange and then gave his own proof On the same page, Kline writes Gauss gave three more proofs. However, on page 224 of Modern Algebra, English translation 1949, 1953, B. L. Van der Waerden writes Gauss gave five proofs of the fundamental theorem. My questions: Did Gauss give four proofs or five?

82. The Fundamental Theorem Of Arithmetic Arithmetic (and, more generally, algebra) are essentially finite mathematics; The main point of the fundamental theorem of Mathematics is the uniqueness http://odin.mdacc.tmc.edu/~krc/numbers/fta.html

@import url(prime.css); The Fundamental Theorem of Arithmetic One of the surprising things about mathematics is its insistence that every assertion needs a justification. Non-mathematicians are often surprised by the extent to which mathematicians enforce this dictum. For example, consider the following result, which is usually called the Fundamental Theorem of Arithmetic. Theorem: Every integer can be written uniquely as a product of finitely many prime numbers Most people not only can't figure out where to start looking for a proof of this result, but also don't understand why it needs a proof. Of course it's true; it has been drilled into them since grade school. The whole issue of reducing a fraction to lowest terms doesn't make sense unless you can factor both numerator and denominator as a product of primes, and cancel the common factors. To a mathematician, however, it is precisely because this result is so basic that it needs to be questioned. Is it so fundamental that it needs to be made an axiom? Or is it a consequence of other, simpler statements? Another thing to keep in mind when confronted with the statement of a mathematical result is that mathematicians are laconic. They omit needless words. In particular, every word in the statement of a theorem is there for a reason. You won't really understand the statement until you ferret out the reason for the inclusion of each word.

83. Fundamental Theorem Of Linear Algebra fundamental theorem of Linear algebra. Inner Products and Orthogonality Thetheorem An Example. Up to Linear algebra Part II. http://www.ma.iup.edu/projects/CalcDEMma/linalg2/linalg218.html

Fundamental Theorem of Linear Algebra Inner Products and Orthogonality TheTheorem An Example Up to Linear Algebra Part II

84. The ``Pi Is Rational'' Page :) The fundamental theorem of Alternative algebra. Any two numbers are equal.Proof Consider two numbers, a and b, which do not equal zero. The steps follow http://dse.webonastick.com/pi/

webonastick Louisville Transportation Photos D. S. Embry Personal ... LiveJournal I was just wondering if you're really serious about your proof of the rationality of pi or whether you did it just so people like me would write to you to ask if you were really serious about your proof of the rationality of pi. Also featured on http://www.ihatecalculus.com/ Table Of Contents The Groundbreaking Research (31 August 1994) It all started when I offered my original proof that Pi was rational, using induction on the number of significant digits! Some Additional Research (6 September 1995) A fourteen-year-old (back then) genius gives us this proof based on the fact that there are no infinities in the physical universe! Using The Fundamental Postulate and Fundamental Theorem of Alternative Algebra (26 October 1995) Ben Guaraldi discovers a use for this new and wonderful branch of mathematics. On The Rationality of Infinite Sums of Rational Numbers (9 November 1995) Jacob Walker offers us his observations on why infinite sums of rational numbers are rational. I'm keeping his old comments here for historical reasons. If you have any additional information that you want to contribute, then please send me

85. GeoSci 236: The Fundamental Theorem Of Linear Algebra GeoSci 236 The fundamental theorem of Linear algebra. Gidon Eshel 491 Hinds Dept.of the Geophysical Sciences, 5734 S. Ellis Ave., The Univ. of Chicago, http://geosci.uchicago.edu/~gidon/geosci236/fundam/

GeoSci 236: The Fundamental Theorem of Linear Algebra Gidon Eshel 491 Hinds Dept. of the Geophysical Sciences, 5734 S. Ellis Ave., The Univ. of Chicago, Chicago, IL 60637 geshel@midway.uchicago.edu Figure 1: The forward problem (the fundamental theorem of linear algebra). A 's domain is the upper-left space, while its range is the lower-right one. In the domain, A 's row-space is shown in red , while its nullspace in blue . A generic vector comprising both a row-space and a nullspace components is the vector on which A operates, mapping it onto the adjoint space (lower-right). In the latter space, the shown b comprises components from A 's range (column-space) and left nullspace Figure 1 represents the operation of a matrix on a vector (the upper-left space). That is, it shows schematically what happens when an arbitrary vector from 's domain (the space corresponding dimensionally to 's row dimension N ) is mapped by onto the range space (the space corresponding dimensionally to 's column dimension M ). Hence the schematic shows what happens to from the upper-left space as transforms it to the range, the lower-right space. Put differently, this schematic represents the

86. Polynomial Interpolation And A Multivariate Analog Of Fundamental Theorem Of Alg Title Polynomial Interpolation and a Multivariate Analog of fundamental Theoremof algebra Authors Hakopian, H.; Tonoyan, M. Journal eprint http://adsabs.harvard.edu/abs/2004math......3492H

Smithsonian/NASA ADS arXiv e-prints Abstract Service Find Similar Abstracts (with default settings below arXiv e-print (arXiv:math/0403492) Also-Read Articles Translate Abstract Title: Polynomial Interpolation and a Multivariate Analog of Fundamental Theorem of Algebra Authors: Hakopian, H. Tonoyan, M. Journal: eprint arXiv:math/0403492 Publication Date: Origin: ARXIV Keywords: Numerical Analysis, 41A05 Comment: Symposium on Trends in Approximation Theory, Nashville, USA, (2000) Abstracts Bibliographic Code: Abstract Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy/Planetary Instrumentation Physics/Geophysics arXiv e-prints Smithsonian/NASA ADS Homepage ADS Sitemap Query Form Preferences ... FAQ

87. Www.math.utsa.edu/ecz/l_a_m.html http://www.math.utsa.edu/ecz/l_a_m.html

window.location="http://applied.math.utsa.edu/~gokhman/ecz/l_a_m.html";

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