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- ...includes [[arithmetic]], [[algebra]], [[counting]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum ...st 20 problems are usually the easiest in the competition, and the last 10 problems can be as hard as some of the Team Round questions. No calculators are allo10 KB (1,503 words) - 22:32, 4 February 2025
- ...combinatorics, and number theory, along with sets of accompanying practice problems at the end of every section. ...88606&sprefix=after+school+maths+%2Caps%2C268&sr=8-2 100 Challenging Maths Problems]23 KB (3,038 words) - 18:33, 15 February 2025
- === Chaos Theory === === Introductory Textbooks ===10 KB (1,405 words) - 14:37, 13 January 2025
- ...guably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four signs: <ma ...are part of the solution set. This does indeed give the complete solution set.12 KB (1,806 words) - 05:07, 19 June 2024
- In [[number theory]], '''Wilson's Theorem''' states that if [[integer ]]<math>p > 1</math> , t ...a \equiv 1</math> or <math>a \equiv p-1</math>. Thus we can partition the set <math>\{ 2 ,\dotsc, p-2\}</math> into pairs <math>\{a,b\}</math> such that4 KB (639 words) - 00:53, 2 February 2023
- ...ponents in [[modular arithmetic]] (which students should study more at the introductory level if they have a hard time following the rest of this article). This th In contest problems, Fermat's Little Theorem is often used in conjunction with the [[Chinese Re15 KB (2,618 words) - 11:03, 19 February 2025
- ...1, n_2, ... n_{\phi(m)} \} \pmod{m}</math> such that the elements of the [[set]] are the numbers relatively [[prime]] to <math>m</math>. It will now be proved that this set is the same as the set <math>B = \{ an_1, an_2, ... an_{\phi(m)} \} \pmod{m}</math> where <math>\4 KB (569 words) - 21:34, 30 December 2024
- ...ntity given a name and usually denoted by a letter or symbol. Many contest problems test one's fluency with [[algebraic manipulation]]. ...a in general deals with general classes of structure. Furthermore, number theory interacts more specifically with3 KB (360 words) - 08:31, 21 February 2025
- == Introductory Probability == ...following topics, a student learning about probability should learn about introductory [[counting]] techniques.4 KB (590 words) - 10:52, 28 September 2024
- ...ptible to induction solutions, but that's not to say that there aren't any problems in other areas, such as [[Inequalities]], that can be solved with induction ...eful in any level of mathematics that has an emphasis on proof. Induction problems can be found anywhere from the Power Round of the [[American Regions Math L5 KB (768 words) - 23:59, 28 September 2024
- ...common divisors of <math>{a}</math> and <math>b</math> is the same as the set of common divisors of <math>b</math> and <math>r</math> where <math>r</math ===Introductory===6 KB (923 words) - 16:39, 30 September 2024
- ...t of values to another set of values, assigning to each value in the first set exactly one value in the second. For instance, one function may map 1 to 1 Let <math>A</math>,<math>B</math> be [[set]]s and let <math>f</math> be a [[subset]] of <math>A\times B</math>, which10 KB (1,761 words) - 02:16, 12 May 2023
- ...iophantine equation is closely tied to [[modular arithmetic]] and [[number theory]]. Often, when a Diophantine equation has infinitely many solutions, [[para A Pythagorean triple is a set of three [[integer]]s that satisfy the [[Pythagorean Theorem]], <math>a^2+b9 KB (1,434 words) - 00:15, 4 July 2024
- ...A \subset B</math>. The [[empty set]] is a subset of every set, and every set is a subset of itself. The notation <math>A \subseteq B</math> emphasizes The set of all subsets of a given set <math>S</math> is called the [[power set]] of <math>S</math> and is denoted <math>\mathcal{P}(S)</math> or <math>2^S1 KB (217 words) - 08:32, 13 August 2011
- ...satisfy. These axioms are chosen to agree with our intuitive concept of a set, on one hand, and to allow various, sometimes quite sophisticated, mathemat ...t are called the [[element]]s of the set. A common misconception is that a set can have multiple indistinct elements, such as the following: <math>\{1,4,511 KB (2,019 words) - 16:20, 7 July 2024
- Let <math>S</math> be the set of the ages of Mr. Jones' children (in other words <math>i \in S</math> if [[Category:Introductory Number Theory Problems]]5 KB (878 words) - 13:39, 3 December 2023
- ...allest positive multiples of <math>4</math>, and let <math>T</math> be the set of the <math>2005</math> smallest positive multiples of <math>6</math>. How [[Category:Introductory Number Theory Problems]]1 KB (220 words) - 11:55, 14 December 2021
- ...do this for the second case, <math>9/2 - 0.5 = 4</math>, and square it and set it as <math>n</math>, we realize that since <math>\sqrt{n}</math> must be p [[Category:Introductory Number Theory Problems]]8 KB (1,245 words) - 09:53, 4 February 2025
- Since <math>d</math> is a single digit prime number, the set of possible values of <math>d</math> is <math>\{2,3,5,7\}</math>. ...number and is the units digit of the prime number <math>10d+e</math>, the set of possible values of <math>e</math> is <math>\{3,7\}</math>.2 KB (336 words) - 14:49, 19 August 2023
- What is the probability that an integer in the set <math>\{1,2,3,...,100\}</math> is divisible by <math>2</math> and not divis There are <math>100</math> integers in the set.2 KB (261 words) - 13:34, 17 August 2023