Create the page "%s" on this wiki! See also the search results found.

Page title matches

• Carleman's Inequality
  '''Carleman's Inequality''' states that for [[nonnegative]] [[real numbers]] <math>\{a_n\
  2 KB (278 words) - 16:39, 29 December 2021
• Vieta's formulas
  ...its roots can be easily expressed as a ratio between two of the polynomial's coefficients. It is among the most ubiquitous results to circumvent finding a polynomial's roots in competition math and sees widespread usage in many math contests/t
  3 KB (514 words) - 06:47, 15 June 2024
• Euclid's Elements
  ...ct should have been either common notions or postulates, as some of Euclid's methods of proof were faulty. Euclid's work is split into thirteen volumes. It covers not only geometry, but numbe
  12 KB (2,094 words) - 15:42, 1 December 2015
• Euclid's proof on the infitude of primes
  #REDIRECT [[Euclid's proof of the infinitude of primes]]
  56 bytes (8 words) - 15:35, 11 February 2015
• Lagrange's Mean Value Theorem
  '''Lagrange's mean value theorem''' (often called "the mean value theorem," and abbreviat We reduce the problem to [[Rolle's theorem]] by using an auxiliary function.
  1 KB (210 words) - 12:53, 20 February 2024
• Zassenhaus's Lemma
  ...s proof of the lemma in 1934 to provide a more elegant proof of [[Schreier's Theorem]]. He was a doctorate student under Emil Artin at the time. In th ...up of <math>K' \cdot (H \cap K)</math>; furthermore, the [[quotient group]]s
  2 KB (414 words) - 12:13, 9 April 2019
• Schreier's Theorem
  ...[[Zassenhaus's Lemma | lemma]], which gives an improved proof of Schreier's Theorem. ...gma_1</math> and <math>\Sigma_2</math>, respectively. Again by Zassenhaus's Lemma, the quotients <math>H'_{im+j}/H'_{im+j+1}</math> and <math>K'_{jn+i}
  2 KB (337 words) - 12:13, 9 April 2019
• Lagrange's Theorem
  '''Lagrange's theorem''' is a result on the indices of [[coset]]s of a [[group]]. so the index and order of <math>H</math> are [[divisor]]s of <math>g</math>.
  2 KB (303 words) - 12:24, 9 April 2019
• Burnside's Lemma
  ...rial]] result in [[group theory]] that is useful for counting the [[orbit]]s of a [[set]] on which a [[group]] [[group action|acts]]. ...led the '''Cauchy-Frobenius Lemma''', or '''the lemma that is not Burnside's'''. The lemma was (mistakenly) attributed to Burnside because he quoted an
  5 KB (757 words) - 18:11, 23 October 2023
• Cayley's Theorem
  ...characterizes group structure as the structure of a family of [[bijection]]s.
  1 KB (214 words) - 16:56, 19 February 2024
• Legendre's Formula
  '''Legendre's Formula''' states that ...of <math>n!</math> and <math>S_p(n)</math> is the [[sum]] of the [[digit]]s of <math>n</math> when written in [[base]] <math>p</math>.
  4 KB (699 words) - 17:55, 5 August 2023
• Routh's Theorem
  ...be the intersection of <math>CF</math> and <math>AD</math>. Then, '''Routh's Theorem''' states that <cmath>[GHI]=\dfrac{(rst-1)^2}{(rs+r+1)(st+s+1)(tr+t+1)}[ABC]</cmath>
  2 KB (267 words) - 00:02, 24 March 2021
• Bezout's Lemma
  #REDIRECT[[Bézout's Identity]]
  31 bytes (4 words) - 13:34, 3 May 2023
• Carnot's Theorem
  '''Carnot's Theorem''' states that in a [[triangle]] <math>ABC</math>, the signed sum o label("$O_C$",f,S);
  4 KB (723 words) - 01:45, 18 February 2021
• Karamata's Inequality
  '''Karamata's Inequality''' states that if <math>(a_i)</math> [[Majorization|majorizes]] ...ming <math>a_i\geq a_{i+1}</math> and similarily with the <math>b_i</math>'s, we get that <math>c_i\geq c_{i+1}</math>. Now, we know:
  2 KB (370 words) - 03:39, 28 March 2024
• Aczel's Inequality
  '''Aczél's Inequality''' states that if <math>a_1^2>a_2^2+\cdots +a_n^2</math> or <mat * Popoviciu, T., Sur quelques inégalités, Gaz. Mat. Fiz. Ser. A, 11 (64) (1959) 451–461
  2 KB (428 words) - 16:36, 29 December 2021
• Gauss's Lemma
  * [[Gauss's Lemma (polynomial)]] * [[Quadratic reciprocity|Gauss's Lemma (quadratic reciprocity)]]
  292 bytes (32 words) - 13:14, 30 September 2020
• Gauss's Lemma (polynomial)
  '''Gauss's Lemma for Polynomials''' is a result in [[abstract algebra | algebra]]. The original statement concerns [[polynomial]]s with [[integer]] coefficients. Such a polynomial is called ''primitive'' i
  3 KB (483 words) - 12:23, 30 May 2019
• Fermat's Two Squares Theorem
  '''Fermat's Two Squares Theorem''' states that that a [[prime number]] <math>p</math> c Since 0 and 1 are the only [[quadratic residue]]s mod 4, it follows that if <math>p</math> is a prime number represented as t
  4 KB (612 words) - 12:10, 30 May 2019
• De Morgan's Laws
  '''De Morgan's Laws''' are two very important laws in the fields of [[set theory]] and [[b
  3 KB (448 words) - 19:53, 19 February 2022

Page text matches

• Mathematical problem solving
  ...king. Mathematical [[problem solving]] involves using all the tools at one's disposal to attack a problem in a new way.
  2 KB (314 words) - 06:45, 1 May 2014
• Pigeonhole Principle
  ...ts, 2n}</math>. Show that if we choose <math>n+1</math> numbers from <math>S</math>, then there exist two numbers such that one is a multiple of the oth ...ath> integers. Prove that there exists distinct <math>a, b</math> in <math>S</math> such that <math>a - b</math> is a multiple of <math>n</math>.''
  11 KB (1,986 words) - 19:13, 19 June 2024
• Quadratic equation
  ...>, where <math>a</math>, <math>b</math> and <math>c</math> are [[constant]]s (that is, they do not depend on <math>x</math>) and <math>x</math> is the u ...of factoring is to turn a general quadratic into a product of [[binomial]]s. This is easier to illustrate than to describe.
  2 KB (264 words) - 12:04, 15 July 2021
• Relatively prime
  Two [[positive]] [[integer]]s <math>m</math> and <math>n</math> are said to be '''relatively prime''' or [[Euler's totient function]] determines the number of positive integers less than any
  2 KB (245 words) - 15:51, 25 February 2020
• Talk:MATHCOUNTS
  ...hink, for the safety of the users at AOPS, that the past winners' username's shouldn't be mentioned?
  822 bytes (123 words) - 18:10, 29 May 2011
• Vieta's Formulas
  #REDIRECT[[Vieta's formulas]]
  29 bytes (3 words) - 14:40, 5 November 2021
• Minnesota MathCounts
  * 2015 - Frank Han (11th written, S)
  995 bytes (131 words) - 18:02, 12 March 2023
• Geometric mean
  ...tric mean''' of a collection of <math>n</math> [[positive]] [[real number]]s is the <math>n</math>th [[root]] of the product of the numbers. Note that MC("a",D((-5,-0.3)--(3,-0.3),black,Arrows),S);
  2 KB (282 words) - 22:04, 11 July 2008
• Principle of Inclusion-Exclusion
  ...set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. Now, for <math>|A\cap B|</math>, that's just putting four guys in order. By the same logic as above, this is <math>
  9 KB (1,703 words) - 07:25, 24 March 2024
• Mill's Constant
  Mill's Constant is defined as the smallest real number <math>\theta</math> such th ...smallest element in that set. If the [[Riemann Hypothesis]] is true, Mill's constant is approximately <math>1.3063778838630806904686144926...</math> an
  794 bytes (105 words) - 01:59, 15 January 2022
• Combination
  ...ly that you choose the rest. This identity is also the reason why [[Pascal's Triangle]] is symmetrical. * [[Pascal's Triangle]]
  4 KB (615 words) - 11:43, 21 May 2021
• AoPS Wiki talk:Community portal
  What is the community portal supposed to be used for, and what's the difference between that and this discussion thing?
  2 KB (377 words) - 17:56, 3 April 2012
• Cauchy-Schwarz Inequality
  Its elementary algebraic formulation is often referred to as '''Cauchy's Inequality''' and states that for any list of reals <math>a_1, a_2, \ldots, ...as Sedrakyan's Inequality, Bergström's Inequality, Engel's Form or Titu's Lemma the following inequality is a direct result of Cauchy-Schwarz inequal
  13 KB (2,048 words) - 15:28, 22 February 2024
• Discriminant
  ...use if the discriminant is positive, the equation has two [[real]] [[root]]s; if the discriminant is negative, the equation has two [[nonreal]] roots; a ...s a polynomial of degree 3, which also makes possible to us to use Cardano's formula, by doing the substitution <math>x=z-\frac{a}{3}</math> on the poly
  4 KB (768 words) - 17:56, 24 June 2024
• Ceva's Theorem
  #REDIRECT[[Ceva's theorem]]
  27 bytes (3 words) - 16:06, 9 May 2021
• Menelaus' theorem
  First let's define some masses. * [[Ceva's theorem]]
  5 KB (804 words) - 03:01, 12 June 2023
• Number theory
  ...cs]] associated with studying the properties and identities of [[ integer]]s. *[[Prime number]]s
  3 KB (399 words) - 23:08, 8 January 2024
• Number theory/Intermediate
  ** [[Simon's Favorite Factoring Trick]] ** [[Euler's Totient Theorem]]
  1,016 bytes (108 words) - 21:05, 26 January 2016
• San Diego ARML
  Individually, San Diego Surf had 2 students who scored 7's and went to tiebreakers: In addition, there were multiple students (on both teams) who scored 6's and earned medals as team high scorers:
  2 KB (378 words) - 16:34, 5 January 2010
• ARML historical results
  | [[New York City ARML]] (New York City S)
  20 KB (2,642 words) - 21:23, 1 June 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)