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• Joining an ARML team
  ...nds. Please email Xinke Guo-Xue at xinkeguoxue@gmail.com, or message Xinke's AoPS account "hurdler", if you are interested in trying out for the Alabama ...at the San Diego Math Circle (SDMC), and most of the students on last year's team were regular attendees at SDMC. Also, since the 2007 team contained no
  22 KB (3,533 words) - 20:58, 2 June 2024
• Community Service Scholarships
  ...they can finance their educations! If you are unfamiliar with how to edit a Wiki and don't have time to learn, please contact [[Mathew Crawford]] using * Kohl's Kids Who Care Scholarship Program [http://www.kohlscorporation.com/communit
  3 KB (350 words) - 01:18, 19 June 2016
• Mu Alpha Theta
  ...national Mu Alpha Theta convention is held during the summer that includes a large competition. The test is a multiple choice test with 4 choices and an extra choice called NOTA, which
  4 KB (632 words) - 17:09, 11 October 2020
• Power Mean Inequality
  The '''Power Mean Inequality''' is a generalized form of the multi-variable [[Arithmetic Mean-Geometric Mean]] I The Power Mean Inequality follows from [[Jensen's Inequality]].
  3 KB (606 words) - 23:59, 1 July 2022
• Wilson's Theorem
  In [[number theory]], '''Wilson's Theorem''' states that if [[integer ]]<math>p > 1</math> , then <math>(p-1) Suppose first that <math>p</math> is composite. Then <math>p</math> has a factor <math>d > 1</math> that is less than or equal to <math>p-1</math>.
  4 KB (639 words) - 01:53, 2 February 2023
• Trivial Inequality
  For all [[real number]]s <math>x</math>, <math>x^2 \ge 0</math>. <cmath>ax^2+bx+c = a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})+c-\frac{b^2}{4a} = a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}.</cmath>
  3 KB (560 words) - 22:51, 13 January 2024
• Heron's Formula
  ...rmula) is a [[mathematical formula | formula]] for finding the [[area]] of a [[triangle]] given only the three side lengths. ...any triangle with side lengths <math>{a}, {b}, {c}</math>, the area <math>{A}</math> can be found using the following formula:
  4 KB (675 words) - 00:05, 22 January 2024
• Polynomial
  ...algebra]] often an arbitrary [[field]]). Note that a [[constant]] is also a polynomial. ===A More Precise Definition===
  6 KB (1,100 words) - 01:44, 17 January 2024
• Simon's Favorite Factoring Trick
  ...of the equation and a product of variables with each of those variables in a linear term on the other side. An example would be: <cmath>xy+66x-88y=23333 ...Factoring Trick, this equation can be transformed into: <cmath>(x+k)(y+j)=a+jk</cmath>
  7 KB (1,130 words) - 18:48, 3 June 2024
• Factoring
  ...rs, is to write the expression (often an [[integer]] or [[polynomial]]) as a product of different terms. This often allows one to find information abou Using the formula for the sum of a [[geometric sequence]], it's easy to derive the general formula for difference of powers:
  3 KB (532 words) - 22:00, 13 January 2024
• Proof by contradiction
  ...fs look better --> This technique usually works well on problems where not a lot of information is known, and thus we can create some using proof by con ...d as a rational fraction of the form <math>\frac{b}{a}</math>, where <math>a</math> and <math>b</math> are two [[relatively prime]] integers. Now, sinc
  2 KB (374 words) - 14:01, 21 August 2022
• Mathematical problem solving
  ...ng]] involves using all the tools at one's disposal to attack a problem in a new way. == A Historical Example ==
  2 KB (314 words) - 06:45, 1 May 2014
• Pigeonhole Principle
  ...ts, the principle may be referred to as the '''Dirichlet box principle'''. A common phrasing of the principle uses balls and boxes and is that if <math> ...nhole principle is as follows: suppose for contradiction that there exists a way to place <math>n</math> balls into <math>k</math> boxes where <math>n>k
  11 KB (1,985 words) - 21:03, 5 August 2023
• 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
• Geometric mean
  .../math> and <math>c</math> is the number <math>a</math> such that <math>a + a = b + c</math>, while the geometric mean of the numbers <math>b</math> and ...length of [[line segment]] <math>AM</math> is the geometric mean of <math>a</math> and <math>b</math>.
  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. ...counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem solving.
  9 KB (1,703 words) - 07:25, 24 March 2024
• Mill's Constant
  ...>\theta</math> such that <math>\lfloor\theta^{3^n}\rfloor</math> is always a prime number for all natural n. ...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
  ...'binomial coefficient''', is a way of choosing <math>r</math> objects from a set of <math>n</math> where the order in which the objects are chosen is ir ...ons are, their various types, and how to calculate each type! It serves as a great introductory video to combinations, permutations, and counting proble
  4 KB (615 words) - 11:43, 21 May 2021
• Cauchy-Schwarz Inequality
  ..._2 + \cdots + a_nb_n)^2,</cmath> with equality if and only if there exists a constant <math>t</math> such that <math>a_i = t b_i</math> for all <math>1 ...cdot \overrightarrow{w}|</cmath> with equality if and only if there exists a scalar <math>t</math> such that <math>\overrightarrow{v} = t \overrightarro
  13 KB (2,048 words) - 15:28, 22 February 2024

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