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  • ...' are recommended by [[Art of Problem Solving]] administrators and members of the [{{SERVER}}/community AoPS Community]. Levels of reading and math ability are loosely defined as follows:
    23 KB (3,038 words) - 18:33, 15 February 2025
  • ...raft. Mathematics provides a kind of "quality control" for the development of trustworthy theories and equations which are important to people in most mo ...matics which are given to be true. Mathematicians then use various methods of formal [[proof]] to extend the axioms to come up with surprising and elegan
    6 KB (846 words) - 19:30, 13 February 2025
  • [[AoPSWiki]] includes one of the internet's most comprehensive guides to '''academic scholarships'''. G ...ted under a category rather than a list, please create a new page for that category and list it here.
    3 KB (337 words) - 02:35, 7 September 2020
  • ...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, sinc
    22 KB (3,532 words) - 10:25, 27 September 2024
  • ...he four individual tests (algebra, combinatorics, geometry, number theory) of their choice. Each individual test is 60 minutes long. Books, calculators In the Team Test, members of a team work together to solve problems, usually within 30 minutes.
    2 KB (295 words) - 22:19, 5 January 2019
  • ...ifferent topic themes. High School students are often organized into three groups- Mu, Alpha and Theta. Theta is the lowest level, Alpha is higher and Mu is ...w school curriculum subjects; however they are far more advanced. The main groups in the regional and invitational levels are:
    4 KB (632 words) - 17:21, 21 December 2024
  • ...more at the introductory level if they have a hard time following the rest of this article). This theorem is credited to [[Pierre de Fermat]]. ...a \pmod{p}</math>. As you can see, it is derived by multiplying both sides of the theorem by <math>a</math>. This form is useful because we no longer ne
    15 KB (2,618 words) - 11:03, 19 February 2025
  • ...nd other [[mathematical expression]]s. Algebra revolves around the concept of the [[variable]], an unknown quantity given a name and usually denoted by a Algebra can be used to solve different types of equations, but algebra is also many other things.
    3 KB (360 words) - 08:31, 21 February 2025
  • 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 [[relatio
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...e <math>k-1</math> things from <math>n-1</math> things added to the number of ways to choose <math>k</math> things from <math>n-1</math> things. Consider picking one fixed object out of <math>n</math> objects. Then, we can choose <math>k</math> objects includin
    12 KB (1,993 words) - 21:22, 15 January 2025
  • ...consists of four groups of approximately 15 high school students. The four groups are: ...as ranked 15th nationally. The total individual score was a 61 (an average of 4.07/10 per person).
    2 KB (236 words) - 11:06, 7 June 2024
  • '''Algebraic topology''' is the study of [[topology]] using methods from [[abstract algebra]]. In general, given a [ == Fundamental Groups ==
    3 KB (479 words) - 14:35, 1 December 2015
  • How many non-[[empty set | empty]] [[subset]]s <math>S</math> of <math>\{1,2,3,\ldots ,15\}</math> have the following two properties? You want to choose <math>k</math> numbers out of <math>n</math> with no consecutive numbers. For each configuration, we can
    9 KB (1,409 words) - 02:59, 8 December 2024
  • ...dies the theory thereof. The work of a statistician is based on the theory of [[probability]]. When working with large datasets, and/or when using advanc Academic statisticians often work with mathematics groups, but tend to have a more applied focus. Some mathematical statisticians ar
    2 KB (323 words) - 19:30, 11 January 2020
  • ...<math>D</math> to be a move that is diagonal. [[Casework]] upon the number of diagonal moves: ...(<math>-D-D-</math>): by the [[Pigeonhole principle]] all of at least one of the two letters must be all together (i.e., stay in a row).
    5 KB (897 words) - 23:21, 28 July 2022
  • Let <math> S </math> be the [[set]] of [[integer]]s between <math>1</math> and <math> 2^{40} </math> whose binary ...{40}</math> has 41) with leading zeroes if necessary. Therefore the number of sets where there are exactly two 1’s in this binary representation is jus
    8 KB (1,283 words) - 18:19, 8 May 2024
  • ...t>TH</tt>, and five <tt>TT</tt> subsequences. How many different sequences of 15 coin tosses will contain exactly two <tt>HH</tt>, three <tt>HT</tt>, fou ...>H</tt> four times; hence it follows that our string will have a structure of <tt>THTHTHTH</tt>.
    4 KB (772 words) - 20:09, 7 May 2024
  • ...ll the [[proper divisor]]s (all [[divisor]]s of a number excluding itself) of <math>1000000</math>. What is the integer nearest to <math>S</math>? ...iple logarithms of the same base is equal to the logarithm of the products of the numbers.
    3 KB (487 words) - 19:52, 16 September 2020
  • ...th> differ by <math>4</math> or <math>7</math>. What is the largest number of [[element]]s <math>S</math> can have? ...<math>1989 = 180\cdot 11 + 9</math>. Because this isn't an exact multiple of <math>11</math>, we need to consider some numbers separately.
    2 KB (274 words) - 03:07, 17 December 2023
  • The graphs of the equations ...\,</math> These 63 lines cut part of the plane into equilateral triangles of side length <math>\tfrac{2}{\sqrt{3}}.\,</math> How many such triangles ar
    4 KB (721 words) - 15:14, 8 March 2021

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