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• Resources for mathematics competitions
  ...itions]] leads to links for many of these competition homepages. Here are a few examples: * [https://brilliant.org/ Brilliant] is a website where one can solve problems to gain points and go to higher levels
  16 KB (2,152 words) - 21:46, 6 May 2024
• Math books
  ...https://artofproblemsolving.com/community/user/243060 cargeek9], currently a junior in high school. It covers the basics of algebra, geometry, combinato ...3265/ref=sr_1_1?ie=UTF8&s=books&qid=1204029652&sr=1-1 Complex Numbers from A to... Z] by [[Titu Andreescu]]
  24 KB (3,177 words) - 12:53, 20 February 2024
• Chemistry competitions
  This is a resources page for students interested in '''Chemistry competitions'''. Pl The U.S. National Chemistry Olympiad national exam (USNCO) is a 3-part, 4 hour and 45 minute exam administered in mid or late April by ACS
  2 KB (258 words) - 19:31, 8 March 2023
• Inequality
  Inequalities are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. For two [[number]]s <math>a</math> and <math>b</math>:
  12 KB (1,798 words) - 16:20, 14 March 2023
• 2015 IMO Problems
  We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> if, for 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
• Proof writing
  ...ance, when a mathematician uses the word "trivial" in a proof, they intend a different meaning to how the word is understood by the wider population. St ...n, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible.
  3 KB (502 words) - 18:16, 18 January 2016
• 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 (1,107 words) - 07:35, 26 March 2024
• 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
• 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
• Fermat's Little Theorem
  ...] (which students should study more at the introductory level if they have a hard time following the rest of this article). This theorem is credited to ...}</math> is not [[divisibility|divisible]] by <math>{p}</math>, then <math>a^{p-1}\equiv 1 \pmod {p}</math>.
  16 KB (2,658 words) - 16:02, 8 May 2024
• Brute forcing
  ...e, through bashing calculations, and can actually sometimes be faster than a more creative approach, and is thus an important tool to have. ...te force would be to list all 91 possibilities (although this would not be a smart time to use brute force).
  1 KB (190 words) - 13:22, 5 May 2023
• Real number
  A '''real number''' is a number that falls on the real number line. It can have any value. Some exam ...rrational number]]s (sometimes, but not universally, denoted <math>\mathbb{J}</math>). In addition <math>\mathbb{Z}^{+}</math> means positive integers a
  3 KB (496 words) - 23:22, 5 January 2022
• Pi
  Pi is the [[ratio]] of the [[circumference]] ([[perimeter]]) of a given [[circle]] to its [[diameter]]. It is approximately equal to 3.14159 ...i</math> is to inscribe a unit circle in a square of side length 2. Using a computer, random points are placed inside the square. Because the area of
  8 KB (1,469 words) - 21:11, 16 September 2022
• Chain Rule
  ...h> be an [[open interval]], and suppose <math>g:I \to J</math> and <math>f:J \to \mathbb{R}</math>. Let <math>h:I \to \mathbb{R}</math> such that <math> ...<math>h'(x_0)</math>,<math>f'(g(x_0))</math>, and <math>g'(x_0)</math> is a matrix.)
  12 KB (2,377 words) - 11:48, 22 July 2009
• Muirhead's Inequality
  ...>p</math> [[Majorization|majorizes]] a sequence <math>q</math>, then given a set of positive reals <math>x_1,x_2,\cdots,x_n</math>: A common [[Brute forcing|bruteforce]] technique with inequalities is to clear
  8 KB (1,346 words) - 12:53, 8 October 2023
• Vector
  ...y, but also most abstractly, a vector is any object which is an element of a given vector space. ...(x\,\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].
  7 KB (1,265 words) - 13:22, 14 July 2021
• Area
  ...size of the region that a two-[[dimension]]al figure occupies. The size of a region in higher dimensions is referred to as [[volume]]. It is often possible to find the area of a region bounded by parts of [[circle]]s and [[line segment]]s through elemen
  6 KB (1,181 words) - 22:37, 22 January 2023
• Improper fractional base
  An '''improper fractional base''' is a type of [[number base]]. Instead of using an [[integer]] for the base in o ...ntation in an improper fractional base. (Note that this means there is not a unique representation for each number in an improper fractional base.)
  787 bytes (118 words) - 19:20, 23 October 2010
• Newton's Sums
  ...ficient way of finding the sums of [[root]]s of a [[polynomial]] raised to a power. They can also be used to derive several [[factoring]] [[identity|id Consider a polynomial <math>P(x)</math> of degree <math>n</math>,
  4 KB (690 words) - 13:11, 20 February 2024
• Fundamental Theorem of Algebra
  ...tant]] [[polynomial]] with [[complex number|complex]] [[coefficient]]s has a complex [[root]]. In fact, every known proof of this theorem involves some Suppose that <math>P(z)</math> is a complex polynomial of degree <math>n</math> with no complex roots; without
  5 KB (832 words) - 14:22, 11 January 2024

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