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2016 AMC 10A Problems/Problem 12
...Which of the following is a correct statement about the probability <math>p</math> that the product of the three integers is odd? ...{1}{8}<p<\dfrac{1}{3}\qquad\textbf{(D)}\ p=\dfrac{1}{3}\qquad\textbf{(E)}\ p>\dfrac{1}{3}</math>

2 KB (302 words) - 00:57, 18 October 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 (3,182 words) - 10:10, 31 August 2024
Physics books
.../www.amazon.com/exec/obidos/ASIN/0756613647/artofproblems-20 Chaos: Making a New Science] by James Gleick ...le.amazon.com/Dreams-Final-Theory-Steven-Weinberg/dp/0679419233/ Dreams of a Final Theory] by Weinberg

10 KB (1,410 words) - 12:07, 20 February 2024
Physics
<strong>Physics</strong> is a branch of [[science]] that studies the properties of matter, energy, and ma Modern Physics is also a group of different subjects in physics:

9 KB (1,355 words) - 06:29, 29 September 2021
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 (709 words) - 14:00, 1 June 2024
Joining an ARML team
The SD team is entering just its third year of participation, so a permanent process of selecting team members has yet to be decided upon. The A student who wishes to attend practice should try to take the SDMO. If a student wishes to speak with one of the coaches for the team, they may do s

22 KB (3,532 words) - 10:25, 27 September 2024
Wilson's Theorem
...math>(p-1)! + 1</math> is divisible by <math>p</math> if and only if <math>p</math> is prime. It was stated by John Wilson. The French mathematician Lag ...<math>(p-1)! + 1</math>. Therefore <math>p</math> does not divide <math>(p-1)! + 1</math>.

4 KB (639 words) - 00:53, 2 February 2023
Trivial Inequality
<cmath>ax^2+bx+c = a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})+c-\frac{b^2}{4a} = a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}.</cmath> .../math> is positive and <math>ax^2+bx+c\le c-\frac{b^2}{4a}</math> if <math>a</math> is negative.

3 KB (583 words) - 20:20, 2 August 2024
Polynomial
...algebra]] often an arbitrary [[field]]). Note that a [[constant]] is also a polynomial. ===A More Precise Definition===

6 KB (1,100 words) - 14:57, 30 August 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 (1,986 words) - 18:13, 19 June 2024
Relatively prime
...their difference <math>(n+1)-n = 1</math>, which is impossible since <math>p > 1</math>. ...exist some <math>x,y\in \mathbb{Z}</math> such that <math>ax+by=1</math> (a special case of [[Bezout's Lemma]]). The [[Euclidean Algorithm]] can be use

2 KB (245 words) - 17:45, 14 October 2024
1965 AHSME Problems/Problem 40
...n</math> be the number of integer values of <math>x</math> such that <math>P = x^4 + 6x^3 + 11x^2 + 3x + 31</math> is the square of an integer. Then <ma <math>\textbf{(A)}\ 4 \qquad

3 KB (571 words) - 23:42, 21 October 2021
Combination
...'binomial coefficient''', is a way of choosing <math>r</math> objects from a set of <math>n</math> where the order in which the objects are chosen is ir ...ons are, their various types, and how to calculate each type! It serves as a great introductory video to combinations, permutations, and counting proble

4 KB (615 words) - 10:43, 21 May 2021
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) - 14:28, 22 February 2024
Factorial
...!=n \cdot (n-1) \cdots 2 \cdot 1 = \prod_{i=1}^n i</math>. Alternatively, a [[recursion|recursive definition]] for the factorial is <math>n!=n \cdot (n ...</math> (remember! this is 1, not 0! (the '!' was an exclamation mark, not a factorial sign))

10 KB (809 words) - 15:40, 17 March 2024
Discriminant
...has two [[nonreal]] roots; and if the discriminant is 0, the equation has a real [[double root]]. ...nant can tell us something about the roots of a given [[polynomial]] <math>p(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0</math> of degree <math>n</math> with all t

4 KB (768 words) - 16:56, 24 June 2024
Menelaus' theorem
...earity]] of points on each of the three sides (extended when necessary) of a [[triangle]]. ...h> intersecting <math>AB</math> on <math>\triangle ABC</math>, where <math>P</math> is on <math>BC</math>, <math>Q</math> is on the extension of <math>A

5 KB (804 words) - 02:01, 12 June 2023
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 ...ibility|divisible]] by <math>{p}</math>, then <math>a^{p-1}\equiv 1 \pmod {p}</math>.

16 KB (2,660 words) - 22:42, 28 August 2024
Parabola
...[[locus]] of points that are equidistant from a point (the [[focus]]) and a line (the [[directrix]]). ...la. The first is [[polynomial]] form: <math>y = a{x}^2+b{x}+c</math> where a, b, and c are [[constant]]s. This is useful for manipulating the polynomial

3 KB (551 words) - 15:22, 13 September 2023
Geometric inequality
A '''geometric inequality''' is an [[inequality]] involving various measures ...level geometry problems. It also provides the basis for the definition of a [[metric space]] in [[analysis]].

7 KB (1,300 words) - 00:11, 28 October 2024

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