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Desmos
Desmos is an advanced graphing calculator implemented as a web application and a mobile application written in TypeScript and JavaScript. History Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, and was launched as a startup at TechCrunch's Disrupt New York conference in 2011. , it had received around 1 million US dollars of funding from Kapor Capital, Learn Capital, Kindler Capital, Elm Street Ventures and Google Ventures. The name ''Desmos'' came from the Greek word which means a bond or a tie. In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. In May 2023, Desmos released a beta for a remade Geometry Tool. In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. In September 2 ...
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Amplify (company)
Amplify (formerly Wireless Generation) is a curriculum and assessment company founded in 2000. It provides assessment and analytics for data-driven instruction and digital curriculum based on the Common Core State Standards. History Wireless Generation was founded in 2000 by Larry Berger and Greg Gunn. The company sold its products and services to districts and states that used government funding for early reading and other programs. It also developed and maintained the New York City online warehouse of student data ARIS, and wrote the algorithm for the School of One, the New York City Department of Education's math help system. Berger served as the CEO of Wireless Generation until it was sold to News Corporation in 2010. News Corp purchased a 90% stake in Wireless Generation for $360 million in 2010. At the time of the sale, the users of Wireless Generation software included three million students and 200,000 educators. Following the acquisition, News Corp invested $540 ...
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Graphing Calculator
Graphing Calculator may refer to: * Graphing calculators, calculators that are able to display and/or analyze mathematical function graphs * NuCalc, a computer software program able to perform many graphing calculator functions * Grapher, the Mac OS X successor to NuCalc {{disambiguation ...
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Permalink
A permalink or permanent link is a URL that is intended to remain unchanged for many years into the future, yielding a hyperlink that is less susceptible to link rot. Permalinks are often rendered simply, that is, as clean URLs, to be easier to type and remember. Most modern blogging and content-syndication software systems support such links. Sometimes URL shortening is used to create them. A permalink is a type of persistent identifier and the word ''permalink'' is sometimes used as a synonym of ''persistent identifier.'' More often, though, ''permalink'' is applied to persistent identifiers which are generated by a content management system for pages served by that system. This usage is especially common in the blogosphere. Such links are not maintained by an outside authority, and their persistence is dependent on the durability of the content management system itself. History In the early years of the web, all content was static, and thus all hyperlinks pointed at a filen ...
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Chi-squared Distribution
In probability theory and statistics, the \chi^2-distribution with k Degrees of freedom (statistics), degrees of freedom is the distribution of a sum of the squares of k Independence (probability theory), independent standard normal random variables. The chi-squared distribution \chi^2_k is a special case of the gamma distribution and the univariate Wishart distribution. Specifically if X \sim \chi^2_k then X \sim \text(\alpha=\frac, \theta=2) (where \alpha is the shape parameter and \theta the scale parameter of the gamma distribution) and X \sim \text_1(1,k) . The scaled chi-squared distribution s^2 \chi^2_k is a reparametrization of the gamma distribution and the univariate Wishart distribution. Specifically if X \sim s^2 \chi^2_k then X \sim \text(\alpha=\frac, \theta=2 s^2) and X \sim \text_1(s^2,k) . The chi-squared distribution is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in constru ...
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Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ...
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Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ...
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Error Function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a function \mathrm: \mathbb \to \mathbb defined as: \operatorname z = \frac\int_0^z e^\,\mathrm dt. The integral here is a complex Contour integration, contour integral which is path-independent because \exp(-t^2) is Holomorphic function, holomorphic on the whole complex plane \mathbb. In many applications, the function argument is a real number, in which case the function value is also real. In some old texts, the error function is defined without the factor of \frac. This nonelementary integral is a sigmoid function, sigmoid function that occurs often in probability, statistics, and partial differential equations. In statistics, for non-negative real values of , the error function has the following interpretation: for a real random variable that is normal distribution, normally distributed with mean 0 and standard deviation \frac, is the probability that falls in the range . ...
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Transcendental Functions
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable that can be written using only the basic operations of addition, subtraction, multiplication, and division (without the need of taking limits). This is in contrast to an algebraic function. Examples of transcendental functions include the exponential function, the logarithm function, the hyperbolic functions, and the trigonometric functions. Equations over these expressions are called transcendental equations. Definition Formally, an analytic function f of one real or complex variable is transcendental if it is algebraically independent of that variable. This means the function does not satisfy any polynomial equation. For example, the function f given by :f(x)=\frac for all x is not transcendental, but algebraic, because it satisfies the polynomial equation :(ax+b)-(cx+d)f(x)=0. Similarly, the function f ...
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Integrals
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an '' antiderivative'', a function whose ...
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Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ...
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