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In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
An example is the function that relates each real number x to its square x 2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
Functions differing by only a constant have the same derivative, and it can be shown that the antiderivative of a given function is a family of functions differing only by a constant. [49]: 326 Since the derivative of the function y = x 2 + C, where C is any constant, is y′ = 2x, the antiderivative of the latter is given by:
In doing so, he discovered a connection between Riemann zeta function and prime numbers, known as the Euler product formula for the Riemann zeta function. Euler proved Newton's identities , Fermat's little theorem , Fermat's theorem on sums of two squares , and made distinct contributions to the Lagrange's four-square theorem .
In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines. Prominent careers for professional mathematicians include math teacher or professor, statistician, actuary, financial analyst, economist, accountant, commodity trader, or computer consultant. [181]
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