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- ...' are recommended by [[Art of Problem Solving]] administrators and members of the [http://aops.com/community AoPS Community]. Levels of reading and math ability are loosely defined as follows:24 KB (3,202 words) - 14:33, 13 January 2025
- This '''Math textbooks''' page is for compiling a list of [[textbook]]s for mathematics -- not problem books, contest books, or gener Levels of reading and math ability are loosely defined as follows:7 KB (902 words) - 14:34, 13 January 2025
- ...C sets the standard in the United States for talented high school students of [[mathematics]]. The AMC curriculum is both comprehensive and modern. AMC In order of increasing difficulty, AMC competitions are5 KB (696 words) - 02:47, 24 December 2019
- ...erica Mathematical Olympiad''' ('''USAMO''') is the third test in a series of exams used to challenge bright students on the path toward choosing the tea ...Solving]] (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participants from around 250 to around 500.6 KB (874 words) - 22:02, 10 November 2024
- ...on certain math topics not commonly taught in school, as well as practices of previous years' team rounds. Please email Xinke Guo-Xue at xinkeguoxue@gmai ...s organized by and practices at the San Diego Math Circle (SDMC), and most of the students on last year's team were regular attendees at SDMC. Also, sinc22 KB (3,532 words) - 10:25, 27 September 2024
- ...size of each set, and the size of all possible [[intersection]]s among the sets. Here, we will illustrate how PIE is applied with various numbers of sets.9 KB (1,703 words) - 00:20, 7 December 2024
- ...[[relatively prime]] to <math>n</math>. <math>\phi(n)</math> is read "phi of n." Given the general [[prime factorization]] of <math>{n} = {p}_1^{e_1}{p}_2^{e_2} \cdots {p}_m^{e_m}</math>, one can compu5 KB (903 words) - 14:49, 27 July 2024
- A '''function''' is a rule that maps one set of values to another set of values, assigning to each value in the first set exactly one value in the s ...ubset]] of <math>A\times B</math>, which denotes the [[Cartesian product]] of <math>A</math> and <math>B</math>. (That is, <math>f</math> is a [[relatio10 KB (1,761 words) - 02:16, 12 May 2023
- ...consists of a single round that is taken on the same date (third Thursday of March) at a registered center. Awards are given to the top scoring student ...site that is the closest or most convenient for them despite being outside of the state.6 KB (949 words) - 21:33, 17 November 2024
- ...ity of <math>\{1, \{2, 3\}, \{1, 2, 3\}\}</math> is 3, and the cardinality of the [[empty set]] is 0. ...th> is denoted by <math>|A|</math>. In the above example, the cardinality of <math>\{3, 4\}</math> is <math>|\{3, 4\}| = 2</math>. Sometimes, the notati2 KB (263 words) - 23:54, 16 November 2019
- A '''functional equation''', roughly speaking, is an equation in which some of the unknowns to be solved for are [[function]]s. For example, the followin ===The Inverse of a Function===4 KB (743 words) - 23:28, 17 November 2024
- ...m{\ such\ that\ } f(a)=b\}</math> is called the '''range''' or '''image''' of <math>f</math>. ...> given by <math>f(x) = x^2</math>, the range of <math>f</math> is the set of [[nonnegative]] [[real number]]s.693 bytes (128 words) - 19:15, 3 February 2016
- ...(if the members of each pair are adjacent to each other). The properties of kites include: * 2 sets of consecutive, congruent sides784 bytes (122 words) - 12:09, 22 July 2024
- ...ere are <math>r!</math> (the [[factorial]] of <math>r</math>) permutations of a set with <math>r</math> distinct objects. ...o consider permutations of [[infinite]] sets. In this case, a permutation of a set <math>S</math> is simply a [[bijection]] between <math>S</math> and i3 KB (422 words) - 10:01, 25 December 2020
- ...ably infinite]]. The most common example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. We give an [[indirect proof]] here. This is one of the most famous indirect proofs and was first given by [[Georg Cantor]].2 KB (403 words) - 19:53, 13 October 2019
- ...or short). This structure gives us a useful tool for solving a wide range of number-theoretic problems, including finding solutions to [[Diophantine equ ...e, if <math>n = 3</math>, then the integers are divided into the following sets:14 KB (2,317 words) - 18:01, 29 October 2021
- ...x. Simultaneously and independently, each ant moves from its vertex to one of the four adjacent vertices, each with equal [[probability]]. What is the pr We approach this problem by counting the number of ways ants can do their desired migration, and then multiply this number by10 KB (1,840 words) - 14:01, 4 July 2024
- ...we shall present just a brief discussion of the most common properties of sets and operations related to them. ...l it an [[infinite]] set. The objects in a set are called the [[element]]s of the set. A common misconception is that a set can have multiple indistinct11 KB (2,019 words) - 16:20, 7 July 2024
- ...rds that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. Find <math> n. </math> The number of ways to draw six cards from <math>n</math> is given by the [[binomial coeff1 KB (239 words) - 10:54, 31 July 2023
- ...the (unique) [[set]] containing no elements. It is therefore a [[subset]] of every set. ...a series of [[axiom|axioms]]. Thus, in a sense, the Empty Set is the basis of all [[mathematics]] as we know it - the "nothing" from which everything is489 bytes (84 words) - 20:33, 27 February 2020