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  • In [[number theory]], '''Wilson's Theorem''' states that if [[integer ]]<math>p > 1</math> , then <math>(p-1) ...e. Consider the [[field]] of integers modulo <math>p</math>. By [[Fermat's Little Theorem]], every nonzero element of this field is a root of the [[po
    4 KB (639 words) - 01:53, 2 February 2023
  • '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula | formula]] for finding the [[area]] o <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math>
    4 KB (675 words) - 00:05, 22 January 2024
  • Simon's Favorite Factoring Trick (SFFT) (made by AoPS user [https://artofproblemsol ...t 1, then divide the coefficient off of the equation.). According to Simon's Favorite Factoring Trick, this equation can be transformed into: <cmath>(x+
    7 KB (1,107 words) - 07:35, 26 March 2024
  • #REDIRECT[[Vieta's formulas]]
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  • 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
  • #REDIRECT[[Ceva's theorem]]
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  • '''Fermat's Little Theorem''' is highly useful in [[number theory]] for simplifying the A frequently used corollary of Fermat's Little Theorem is <math>a^p \equiv a \pmod {p}</math>. As you can see, it i
    16 KB (2,658 words) - 16:02, 8 May 2024
  • '''Chebyshev's inequality''', named after [[Pafnuty Chebyshev]], states that if ...nce of the [[Rearrangement inequality]], which gives us that the sum <math>S=a_1b_{i_1}+a_2b_{i_2}+...+a_nb_{i_n} </math> is maximal when <math>i_k=k</m
    1 KB (214 words) - 20:32, 13 March 2022
  • '''Euler's Totient Theorem''' is a theorem closely related to his [[totient function]] Let <math>\phi(n)</math> be [[Euler's totient function]]. If <math>n</math> is a positive integer, <math>\phi{(n)
    3 KB (542 words) - 17:45, 21 March 2023
  • .../math>, <math>c</math>, <math>d</math> are the four side lengths and <math>s = \frac{a+b+c+d}{2}</math>. <cmath>16[ABCD]^2=16(s-a)(s-b)(s-c)(s-d)</cmath>
    3 KB (465 words) - 18:31, 3 July 2023
  • #REDIRECT[[Ptolemy's theorem]]
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  • ...[equality condition | equality case]] of [[Ptolemy's Inequality]]. Ptolemy's theorem frequently shows up as an intermediate step in problems involving i ...ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>:
    7 KB (1,198 words) - 20:39, 9 March 2024
  • #REDIRECT[[Vieta's formulas]]
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  • '''Euler's totient function''' <math>\phi(n)</math> applied to a [[positive integer]] ...p_m^{e_m} </math> where the <math>p_i </math> are distinct [[prime number]]s. Now, we can use a [[PIE]] argument to count the number of numbers less th
    5 KB (898 words) - 19:12, 28 January 2024
  • #REDIRECT[[Stewart's theorem]]
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  • '''Jensen's Inequality''' is an inequality discovered by Danish mathematician Johan Jen One of the simplest examples of Jensen's inequality is the [[quadratic mean]] - [[arithmetic mean]] inequality. Taki
    3 KB (623 words) - 13:10, 20 February 2024
  • '''Ptolemy's Inequality''' is a famous inequality attributed to the Greek mathematician *[[Ptolemy's Theorem]]
    3 KB (602 words) - 09:01, 7 June 2023
  • '''Muirhead's Inequality''' states that if a sequence <math>p</math> [[Majorization|major ...ath> majorizes <math>(4,2)</math> (as <math>5>4, 5+1=4+2</math>), Muirhead's inequality states that for any positive <math>x,y</math>,
    8 KB (1,346 words) - 12:53, 8 October 2023
  • ...hat order) and [[diagonal]]s of length <math>p, q</math>. '''Bretschneider's formula''' states that the [[area]] [[Lagrange's Identity]] states that <math>|\vec{a}|^2|\vec{b}|^2-(\vec{a}\cdot\vec{b})^2
    3 KB (566 words) - 03:51, 12 February 2021
  • ...hur's Inequality''' is an [[inequality]] that holds for [[positive number]]s. It is named for Issai Schur. Schur's inequality states that for all non-negative <math>a,b,c \in \mathbb{R}</mat
    2 KB (398 words) - 16:57, 29 December 2021
  • #REDIRECT[[Vieta's formulas]]
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  • '''Fermat's Last Theorem''' is a recently proven [[theorem]] stating that for positive Fermat's Last Theorem was proposed by [[Pierre de Fermat]] in the <math>1600s</math>
    3 KB (453 words) - 11:13, 9 June 2023
  • '''Pascal's triangle''' is a triangle which contains the values from the [[binomial exp ...oose k}}=2^n</math>, the sum of the values on row <math>n</math> of Pascal's Triangle is <math>2^n</math>.
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  • ...sums''' give us a clever and efficient way of finding the sums of [[root]]s of a [[polynomial]] raised to a power. They can also be used to derive sev Newton's sums tell us that,
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  • '''Euler's number''' is a [[constant]] that appears in a variety of mathematical conte An approximation for Euler's number is <math>e\approx 2.7182818284590452...</math>
    4 KB (764 words) - 21:09, 13 March 2022
  • ''See also: [[Hölder's inequality]]'' ...n, \dotsc, z_1, z_2, \dotsc, z_n</math> are [[nonnegative]] [[real number]]s and <math>\lambda_a, \lambda_b, \dotsc, \lambda_z</math> are nonnegative re
    4 KB (774 words) - 12:12, 29 October 2016
  • ...>F</math> denote the number of [[vertex|vertices]], [[edge]]s, and [[face]]s, respectively. Then <math>V-E+F=2</math>. Apply Euler's Polyhedral Formula on the following polyhedra:
    1,006 bytes (134 words) - 14:15, 6 March 2022
  • '''Bertrand's postulate''' states that for any [[positive integer]] <math>n</math>, there It is similar to the proof of Chebyshev's estimates in the [[Prime Number Theorem|prime number theorem]] article but
    2 KB (309 words) - 21:43, 11 January 2010
  • '''Newman's Tauberian Theorem''' is a [[tauberian theorem]] its [[Laplace transform]] <math>F(s) = \int_0^\infty f(t)e^{-st}dt</math>
    6 KB (1,034 words) - 07:55, 12 August 2019
  • '''Euler's Formula''' is <math>e^{i\theta}=\cos \theta+ i\sin\theta</math>. It is na ...ing problems involving [[complex numbers]] and/or [[trigonometry]]. Euler's formula replaces "[[cis]]", and is a superior notation, as it encapsulates
    3 KB (452 words) - 23:17, 4 January 2021
  • 33 bytes (4 words) - 14:53, 29 November 2018
  • #REDIRECT [[Hölder's Inequality]]
    34 bytes (4 words) - 13:36, 11 July 2006
  • '''Rolle's theorem''' is an important theorem among the class of results regarding the <LI>[[Lagrange's mean value theorem]]</LI>
    1 KB (270 words) - 12:13, 30 May 2019
  • '''Pick's Theorem''' expresses the [[area]] of a [[polygon]], all of whose [[vertex |
    2 KB (301 words) - 13:08, 20 February 2024
  • '''Euclid's Lemma''' is a result in [[number theory]] attributed to [[Euclid]]. It stat ...ies that <math>p \mid a</math> or <math>p\mid b</math>, for all [[integer]]s <math>a</math> and <math>b</math>.
    1 KB (188 words) - 04:18, 20 November 2023
  • ...ek mathematician [[Euclid]] that there are infinitely many [[prime number]]s.
    1 KB (179 words) - 11:57, 14 August 2022
  • '''DeMoivre's Theorem''' is a very useful theorem in the mathematical fields of [[complex This is one proof of De Moivre's theorem by [[induction]].
    2 KB (363 words) - 01:42, 11 January 2024
  • == Pascal's Triangle == Pascal's Triangle is a triangular array of numbers where each number is the sum of t
    2 KB (341 words) - 16:57, 16 June 2019
  • 44 bytes (4 words) - 13:38, 3 March 2015
  • #REDIRECT[[Vieta's formulas]]
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  • ...math> in the polynomial <math> \prod_{i=1}^{n}(t+x_i) </math> (see [[Viete's sums]]). We define the ''symmetric average'' <math>d_k </math> to be <math ...have a root between <math>x_i </math> and <math>x_{i+1} </math> by [[Rolle's theorem]] if <math>x_i \neq x_{i+1} </math>, and if <math> x_i = x_{i+1} =
    5 KB (830 words) - 04:05, 28 January 2023
  • ...ymmetric polynomial]]s. For notation and background, we refer to [[Newton's Inequality]]. By the lemma from [[Newton's Inequality]], it suffices to show that for any <math>n </math>,
    992 bytes (146 words) - 16:48, 29 December 2021
  • '''Nesbitt's [[Inequality]]''' is a theorem which, although rarely cited, has many instr If <math> a_1, \ldots a_n </math> are positive and <math> \sum_{i=1}^{n}a_i = s </math>, then
    7 KB (1,224 words) - 16:21, 24 October 2022
  • '''Pascal's Theorem''' is a result in [[projective geometry]]. It states that if a [[h Since it is a result in the projective plane, it has a dual, [[Brianchon's Theorem]], which states that the diagonals of a hexagon circumscribed about
    4 KB (712 words) - 21:57, 25 April 2020
  • The '''Russell's Paradox''', credited to Bertrand Russell, was one of those which forced the
    580 bytes (100 words) - 17:57, 12 May 2023
  • '''Green's Theorem''' is a result in [[real analysis]]. It is continuous [[partial derivative]]s mapping an open set containing
    2 KB (381 words) - 12:12, 30 May 2019
  • '''Cramer's Rule''' is a method of solving systems of equations using [[matrix|matrices Cramer's Rule employs the [http://en.wikipedia.org/wiki/Determinant matrix determina
    2 KB (352 words) - 18:22, 11 October 2023
  • #REDIRECT[[Ceva's theorem/Problems]]
    36 bytes (4 words) - 16:16, 9 May 2021
  • 530 bytes (82 words) - 16:16, 9 May 2021
  • '''L'Hopital's Rule''' is a theorem dealing with [[limit]]s that is very important to [[calculus]]. ...cdot \epsilon(h)}</math>, which would hence prove our lemma for L'Hospital's rule.
    2 KB (475 words) - 15:04, 24 March 2022

Page text matches

  • ...theorems in [[geometry]], and is one of the many tools in a good geometer's arsenal. A very large number of geometry problems can be solved by building label("$G$", G, S);
    5 KB (886 words) - 21:12, 22 January 2024
  • ...tangent to both axes and to the second and third circles. What is <math>r/s</math>? label("$s$",(-1.5,4));
    2 KB (307 words) - 15:30, 30 March 2024
  • ...ers and Emilio adds his numbers. How much larger is Star's sum than Emilio's?
    967 bytes (143 words) - 03:18, 27 June 2023
  • ...lish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays <math>40</math> coins in toll to Rabbit after ea
    1 KB (169 words) - 14:59, 8 August 2021
  • The second line's equation can be found in a similar fashion. Its slope is <math>m = \frac{0-
    8 KB (1,016 words) - 00:17, 31 December 2023
  • * [[Math Kangaroo]] may be the world's largest [[mathematics competition]]. [http://www.mathkangaroo.org/mk/defau
    4 KB (473 words) - 16:14, 1 May 2024
  • ...tions in the United States. These exams lead up to the selection of the U.S. team for the [[International Mathematical Olympiad]]. ([http://www.maa.org * [https://simiode.org/scudem SIMIODE SCUDEM] -- SIMIODE's (Systemic Initiative for Modeling Investigations and Opportunities using Di
    5 KB (583 words) - 17:26, 21 February 2024
  • There's also some exams with the part of mathematics being as hard as an olympiad,
    4 KB (406 words) - 11:20, 26 February 2021
  • Alabama's math competition community is fairly large and active and there are a numbe ...Math Tournament]]-- Grades 7-12. The VHHS tournament is one of the nation's largest local math tournaments, drawing around 1700 students annually.
    3 KB (411 words) - 21:32, 8 December 2014
  • * [[Women's Technology Program]] at [[MIT]], [http://wtp.mit.edu/ Website]
    14 KB (1,851 words) - 23:51, 13 May 2024
  • ...shift, six days a week. The lead instructors are mathematicians with Ph.D.s and the apprentice instructors are graduate or undergraduate math students. Here's what the {MathILy, MathILy-Er} application process looks like:
    5 KB (706 words) - 23:49, 29 January 2024
  • * [[Moody's Mega Math Challenge]] [http://m3challenge.siam.org/ website]
    3 KB (409 words) - 15:02, 28 January 2022
  • * National Science Foundation's Robert Noyce Scholarship. <dollar/>10,000 for undergraduate or graduate stu * American Meteorological Society's undergraduate scholarships and graduate fellowships for students in STEM ma
    7 KB (851 words) - 10:54, 29 January 2022
  • * Current high school senior enrolled in a U.S. high school * U.S Citizen or permanent resident
    894 bytes (123 words) - 15:48, 13 June 2022
  • * [[Mathematical Kangaroo]] is perhaps the world's largest [[mathematics competition]]. * [[Mathematical Kangaroo]] is perhaps the world's largest [[mathematics competition]].
    3 KB (362 words) - 17:06, 2 April 2024
  • An individual's score is their total number of correct sprint round answers plus 2 times th ...ided by 4 plus 2 points for every correct team round answer, making a team's maximum possible score 66 points. Therefore, it is possible to win with a r
    10 KB (1,497 words) - 11:42, 10 March 2024
  • * [[St. Mary's Academy Math Team Challenge]] -- Contests for middle school students. [http
    2 KB (224 words) - 00:51, 29 January 2019
  • *[[Soli Deo Gloria Fall Tournament, aka Billy's Math Meet]] [[User:Solafidefarms/MathMeet]]
    4 KB (565 words) - 13:24, 13 September 2019
  • * [[K-State S. Thomas Parker Mathematics Competition]] [http://www.math.ksu.edu/~zlin/mat
    3 KB (473 words) - 16:11, 16 June 2020
  • * Governor's Cup [http://www.kaac.com/governors-cup/] * Governor's Cup [http://www.kaac.com/governors-cup/]
    1 KB (129 words) - 14:36, 25 October 2018
  • ...he top 5 (alternate national participant included) students from that year's MathCounts state competition will compete as a mixed team. Oklahoma does n
    2 KB (279 words) - 19:41, 23 March 2017
  • ...a/intermountain/index.html] is an college proof based math competition. It's format is similar to the Putnam, but the problems are much more approachabl
    2 KB (231 words) - 13:07, 14 December 2019
  • Ritvik Rustagi's [https://www.tmasacademy.com/ace-the-amc10-12-free-book ACE The AMC 10 and * Elias Saab's [[MathCounts]] [http://mathcounts.saab.org/ Drills page].
    16 KB (2,152 words) - 21:46, 6 May 2024
  • * [http://www.geometer.org/mathcircles/ Tom Davis's] site for [[math circles]] topics. * [[AoPS]] -- That's where you are now! [http://www.artofproblemsolving.com Home].
    4 KB (516 words) - 03:01, 13 April 2023
  • ...publishes [[Richard Rusczyk]]'s, [[David Patrick]]'s, and [[Ravi Boppana]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=prealgebra Prea * [[AoPS]] publishes [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Store/viewitem.php?item=intro:algebra I
    24 KB (3,177 words) - 12:53, 20 February 2024
  • MOEMS Executive Director [[Richard Kalman]] and many talented MOEMS PICO's run online [[Math Jams]] at [[Art of Problem Solving]]. These Math Jams ar
    2 KB (215 words) - 02:54, 18 November 2020
  • This '''Math textbooks''' page is for compiling a list of [[textbook]]s for mathematics -- not problem books, contest books, or general interest bo * [[AoPS]] publishes Dr. [[Richard Rusczyk]]'s [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?item_id=200 Intro
    7 KB (901 words) - 14:11, 6 January 2022
  • ...may have as many students as are interested sit for the exam. Each school's team score is determined by adding the ranks (not the scores) of its top th
    4 KB (623 words) - 13:11, 20 February 2024
  • ...ms are administered annually in March and students are nominated for the U.S. National Chemistry Olympiad competition based on their performance. The U.S. National Chemistry Olympiad national exam (USNCO) is a 3-part, 4 hour and
    2 KB (258 words) - 19:31, 8 March 2023
  • ...os/ASIN/0387948600/artofproblems-20 The Algorithm Design Manual] by Steve S. Skiena.
    2 KB (251 words) - 00:45, 17 November 2023
  • * [https://www.amazon.com/s?k=conceptual+physics&ref=nb_sb_noss Conceptual Physics] by Paul Hewitt ...artofproblems-20 Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions] by Lisa Randall.
    10 KB (1,410 words) - 13:07, 20 February 2024
  • What is now considered Newton's most famous achievement is the formal statement of three basic, almost triv #If the net force on any amount of matter is [[Zero]], then the object's velocity will not change if viewing from a constant reference point.
    9 KB (1,355 words) - 07:29, 29 September 2021
  • ...] squared, or <math>\mathrm{N}=\mathrm{kg}\times \frac{\mathrm{m}}{\mathrm{s}^2}</math>. This is because <math>F = ma</math>, which means force (Newtons
    665 bytes (96 words) - 23:17, 2 February 2021
  • ...asy image|<math>1\,2\,3\,4\,5\,6\,7\,8\,9\,0</math>|right|The ten [[digit]]s making up <br /> the base ten number system.}} ...ematics, as shown by the [http://www.ams.org American Mathematical Society's] [http://www.ams.org/msc/ Mathematics Subject Classification] scheme.
    6 KB (902 words) - 12:53, 3 September 2019
  • ...slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four signs: <math>>,<,\ge,\le</math>. For two [[number]]s <math>a</math> and <math>b</math>:
    12 KB (1,798 words) - 16:20, 14 March 2023
  • ...t-shirt, along with other prizes like books or software of the participant's choices (with first priority to the top scorers, and then down the ranks). ...ublished. KöMaL is a popular abbreviation of Középiskolai Matematikai és Fizikai Lapok (KMaL), which means "High School Mathematics and Physics Jour
    4 KB (613 words) - 13:08, 18 July 2023
  • [[AoPSWiki]] includes one of the internet's most comprehensive guides to '''academic scholarships'''. Get started by c * Your high school's website or those of other area high schools
    3 KB (337 words) - 03:35, 7 September 2020
  • ...AMC]] -- AoPS hosts sessions for discussion of the problems from each year's [[AMC 10]], [[AMC 12]], and [[AIME]] exams.
    989 bytes (130 words) - 16:20, 20 August 2020
  • ...d Summer Program]], where students train for possible inclusion on the [[U.S. IMO]] team. ...ed to only 25 questions, and 2 years later, the A and B version of the AMC's were introduced.
    5 KB (696 words) - 03:47, 24 December 2019
  • label("$E$",(0,0),S);
    3 KB (415 words) - 18:01, 24 May 2020
  • We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> ...any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
    4 KB (692 words) - 22:33, 15 February 2021
  • ...istered to approximately 500 of the best and brightest students from the U.S. and Canada. Qualification is based on [[AMC 10]], [[AMC 12]], and [[AIME]] ...Olympiad?" in the ''American Mathematical Monthly'' 78 (1971), the [[MAA]]'s National Contest Committee revived an Olympiad Subcommittee, which voted to
    6 KB (869 words) - 12:52, 20 February 2024
  • '''Informatics competitions''' test a student's ability to understand, organize, and work with information on computers. * [[St Mary’s University High School Programming Competition]] [http://cs.stmarys.ca/hspc
    7 KB (932 words) - 12:13, 15 January 2024
  • ...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
    21 KB (3,500 words) - 18:41, 23 April 2024
  • * Kohl's Kids Who Care Scholarship Program [http://www.kohlscorporation.com/communit
    3 KB (350 words) - 01:18, 19 June 2016
  • #10 The set S is {#, !, @, *, $, %}. How many different proper subsets are possible?
    4 KB (632 words) - 17:09, 11 October 2020
  • The Power Mean Inequality follows from [[Jensen's Inequality]]. As <math>\ln(x)</math> is concave, by [[Jensen's Inequality]], the last inequality is true, proving <math>M(t)\ge M(0)</math
    3 KB (606 words) - 23:59, 1 July 2022
  • In [[number theory]], '''Wilson's Theorem''' states that if [[integer ]]<math>p > 1</math> , then <math>(p-1) ...e. Consider the [[field]] of integers modulo <math>p</math>. By [[Fermat's Little Theorem]], every nonzero element of this field is a root of the [[po
    4 KB (639 words) - 01:53, 2 February 2023
  • For all [[real number]]s <math>x</math>, <math>x^2 \ge 0</math>. ...h> and <math>s</math> are relatively prime positive integers. Find <math>r+s</math>. (Solution [[User:Ddk001#Solution_1.28Probably_official_MAA.2C_lots_
    3 KB (560 words) - 22:51, 13 January 2024
  • '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula | formula]] for finding the [[area]] o <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math>
    4 KB (675 words) - 00:05, 22 January 2024

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