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  • ...kind of "quality control" for the development of trustworthy theories and equations which are important to people in most modern technical discplines such as e ...ted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]].
    6 KB (902 words) - 17:16, 22 October 2024
  • ...d or subtracted without changing the inequality sign, much like [[equation|equations]]. However, when multiplying, dividing, or square rooting, we have to watc Linear inequalities can be solved much like linear equations to get implicit restrictions upon a variable. However, when multiplying/di
    12 KB (1,806 words) - 05:07, 19 June 2024
  • ...rational number]]s, etc. Some [[algebra]]ic topics such as [[Diophantine]] equations as well as some theorems concerning integer manipulation (like the [[Chicke
    3 KB (399 words) - 22:08, 8 January 2024
  • ...ted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]]. Algebra can be used to solve different types of equations, but algebra is also many other things
    3 KB (369 words) - 20:18, 18 June 2021
  • == Algebraic Number Theory == ...<math>\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})</math>. Famous problems in algebraic number theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fe
    5 KB (849 words) - 15:14, 18 May 2021
  • ...tions by means of [[abstract algebra]], and in particular [[ring theory]]. Algebraic geometry is most easily done over [[algebraically closed]] [[field]]s, but == Affine Algebraic Varieties ==
    2 KB (361 words) - 00:59, 24 January 2020
  • ...roblems, including finding solutions to [[Diophantine equation|Diophantine equations]], testing whether certain large numbers are prime, and even some problems ...ine{1}</math>, and <math>\overline{2}</math> as sets, we can treat them as algebraic objects -- like numbers -- with their own operations of addition and multip
    14 KB (2,317 words) - 18:01, 29 October 2021
  • ===Solution 5 (Pythagorean Theorem and little algebraic manipulation)=== ...ship <math>(a-b)^2+x^2=12^2</math>. Solving the system of 3 unknowns and 3 equations (One of the best ways to do it is to solve for <math>a</math> in the first
    14 KB (2,351 words) - 20:06, 8 December 2024
  • * [[Algebraic expression | Algebraic expressions]] ** [[Algebraic manipulation]]
    991 bytes (86 words) - 14:58, 24 August 2024
  • ...tions and dictate how sticky (viscous) a fluid is. Thus, the Navier-Stokes equations are a dynamical statement of the balance of forces acting at any given regi ...s, the analysis of the effects of pollution, etc. Coupled with [[Maxwell's Equations]] they can be used to model and study magnetohydrodynamics.
    3 KB (553 words) - 21:08, 2 May 2022
  • In [[algebra]], '''linear equations''' are algebraic [[equation]]s in which both sides of the equation are [[polynomials]] or [[
    1 KB (257 words) - 12:39, 14 July 2021
  • We can rewrite the equations as follows: ...A</math>. Then <math>\frac{1}{4}x=2A</math>; extend this for the other two equations. We can substitute into the first equation to obtain a value for <math>x</m
    6 KB (994 words) - 12:40, 3 December 2024
  • '''Algebraic manipulation''' involves doing opposite operations (undoing) to any equatio ...ing, we start by multiplying both sides by <math>x-5</math>. Then we used algebraic manipulation to get all terms to one side to form a [[quadratic]]. After [
    4 KB (562 words) - 17:49, 8 November 2020
  • Factoring this, we get <math>4</math> equations- Looking back at our equations for <math>m</math> and <math>n</math>, we can solve for <math>k = \frac{2m
    9 KB (1,522 words) - 22:41, 13 September 2024
  • ...winnerton-Dyer Conjecture]], the [[Hodge Conjecture]], the [[Navier-Stokes Equations]], [[P versus NP]], the [[Poincaré Conjecture]], the [[Riemann Hypothesis] ...ations of a given [[manifold]]'s topological properties, are composed of [[algebraic cycles]]. More rigorously, the common phrasing for the conjecture is "Given
    13 KB (1,969 words) - 16:57, 22 February 2024
  • Factoring this, we get <math>4</math> equations: Looking back at our equations for <math>m</math> and <math>n</math>, we can solve for <math>k = \frac{2m
    8 KB (1,426 words) - 13:14, 30 June 2024
  • Consider the system of equations After a little algebraic manipulation we can rewrite this as
    4 KB (626 words) - 17:58, 10 November 2024
  • ...tive integer <math>n</math>, or equivalently that <math>\alpha</math> is [[algebraic]] and its [[minimal polynomial]] has degree <math>2^n</math>. ...B,C\in K</math>. So now <math>\theta = x+yi</math> satisfies the system of equations:
    8 KB (1,305 words) - 07:39, 21 August 2009
  • ...ncoding=UTF8&qid=1556093238&sr=1-1-catcorr Advanced Olympiad Inequalities: Algebraic & Geometric Olympiad Inequalities] by '''Alijadallah Belabess'''. *''Algebraic Inequalities - Old And New Methods'' - '''Vasile Cirtoaje'''.
    19 KB (2,581 words) - 13:25, 1 November 2024
  • ...true. See this link: [http://math.stackexchange.com/questions/4323/are-all-algebraic-integers-with-absolute-value-1-roots-of-unity]). Since <math>P</math> has d ...ding this polynomial and comparing the coefficients, we have the following equations:
    11 KB (1,979 words) - 16:25, 6 September 2021

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