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• Art of Problem Solving
  The accomplishments of every student are unique, and there is no way to measure that success. However, we try to record and celebrate [[AoPS Community Awa ...ofproblemsolving.com/store/item/intro-number-theory Introduction to Number Theory]
  5 KB (667 words) - 17:09, 3 July 2023
• Physics
  ...[Special Relativity]], and his [[Brownian Motion#Theory of Brownian Motion|Theory of Brownian Motion]]. [[Mass]] is one of the two most basic intrinsic properties of a body. It is a measure of its [[inertia]]. [[Momentum]] is defined as the [[product]] of the mass
  9 KB (1,355 words) - 07:29, 29 September 2021
• Probability
  ...ly ignored until one reaches an advanced undergraduate level. Once measure theory is covered, probability does become a lot easier to use and understand. ...cial kind of [[measure]]), called the probability function, or probability measure. It assigns a "volume" to each possible event.
  4 KB (588 words) - 12:47, 2 October 2022
• Geometry
  ...matics, along with [[arithmetic]] (which eventually branched into [[number theory]] and [[algebra]]). The geometry usually studied is ...tructure formed by the intersection two [[ray]]s at their endpoints. It is measure in either [[degree]]s or [[radian]]s, though the less-common [[Système int
  3 KB (393 words) - 07:59, 25 September 2020
• Birch and Swinnerton-Dyer Conjecture
  ...n the basis of somewhat tenuous trends in graphical plots; which induced a measure of scepticism in J. W. S. Cassels (Birch's Ph.D. advisor). Over time the nu [[Category:Number theory]]
  7 KB (1,102 words) - 17:23, 6 September 2008
• Integral
  *[[Measure theory]]
  5 KB (909 words) - 14:16, 31 May 2022
• Measure
  In [[mathematics]], '''measure''' can mean the amount of [[degree (geometry) | degree]]s in an [[angle]], The measure of <math>\overline{AB}</math> is indicated by <math>AB</math>, without the
  1 KB (194 words) - 10:45, 11 July 2007
• Concurrence/Problems
  ...he three segments meet at a point anyway! She notices that all three sides measure an integer number of inches, that the side lengths are all distinct, and th From here, we apply a bit of [[number theory]] to find that the answer is a <math>13-12-15</math> triangle:
  3 KB (458 words) - 15:44, 1 December 2015
• Three Greek problems of antiquity
  ...traction, multiplication, division, and taking square roots. Using [[field theory]], one can then show that <math>x</math> must be an [[algebraic number]] an ...by means of [[straight edge]] and [[compass]] only, an angle one-third its measure.
  2 KB (359 words) - 17:06, 11 June 2022
• Kernel
  In general, a '''kernel''' is a measure of the failure of a [[homomorphism]] to be [[injective]]. In [[set theory]], if <math>S</math> and <math>T</math> are [[set]]s, with <math>f</math> a
  1 KB (222 words) - 13:47, 16 June 2008
• Commutator (ring)
  ...ath>[a,b]</math>, is the quantity <math>ab-ba</math>. It can be seen as a measure of the failure of the ring to be [[commutative]]; in a commutative ring, <m [[Category:Ring theory]]
  423 bytes (68 words) - 22:27, 27 May 2008
• 2008 iTest Problems
  ...the same diameter, and the trees look equally spaced. Tony fetches a tape measure from the garage and measures a distance of almost exactly <math>12</math> f and raising chickens as he does trying to map out a <math>\textit{Theory of Everything}</math>. Dr. Lisi often poses problems to the Kubik children
  71 KB (11,749 words) - 01:31, 2 November 2023
• Radical axis
  The theory of radical axis is a priceless geometric tool that can solve formidable geo ...a few challenging problems that are exemplary examples on how radical axis theory can be used and why it pertains to that situation. I hope after you read th
  10 KB (1,797 words) - 02:05, 24 October 2023
• 2009 PUMaC Problems
  It is known that a certain mechanical balance can measure any object of integer mass anywhere between 1 and 2009 (both included). Thi '''Number Theory A'''
  25 KB (4,154 words) - 16:27, 2 September 2011
• 2018 AMC 12A Problems
  ...hedule <math>3</math> mathematics courses -- algebra, geometry, and number theory -- in a <math>6</math>-period day if no two mathematics courses can be take ...A}</math> and <math>\overline{UG},</math> respectively. What is the degree measure of the acute angle formed by lines <math>MN</math> and <math>PA?</math>
  15 KB (2,380 words) - 18:52, 7 April 2022
• 2019 AIME II Problems/Problem 10
  .../math> is a multiple of <math>3</math>, and negative otherwise. The degree measure of <math>\theta</math> is <math>\tfrac{p}{q}</math>, where <math>p</math> a [[Category:Intermediate Number Theory Problems]]
  7 KB (1,109 words) - 00:40, 28 January 2024
• Ordinal
  ...rdinal strength equal to the Bachmann-Howard ordinal. Zermelo-Fraenkel set theory itself has an unknown ordinal strength. ...Bachmann-Howard ordinal, which means it is unprovable in Kripke-Platek set theory and Peano arithmetic. As another example, consider Gabriel Nivasch's ''fusi
  5 KB (811 words) - 14:16, 7 June 2020
• Real analysis
  * [[Measure theory]]
  9 KB (1,409 words) - 02:41, 30 May 2023