* Ai ( x ), the Airy function, a special function in mathematics

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y ( x ) of Bessel's differential equation:

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

In mathematics, the exponential function is the function e < sup > x </ sup >, where e is the number ( approximately 2. 718281828 ) such that the function e < sup > x </ sup > is its own derivative.

In mathematics, an inverse function is a function that undoes another function: If an input x into the function ƒ produces an output y, then putting y into the inverse function g produces the output x, and vice versa.

) In modern mathematics, this formula can be derived using integral calculus, i. e. disk integration to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked centered side by side along the x axis from where the disk has radius r ( i. e. ) to where the disk has radius 0 ( i. e. ).

In mathematics, a function f from a set X to a set Y is surjective ( or onto ), or a surjection, if every element y in Y has a corresponding element x in X so that f ( x ) = y.

In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f ( x ) and f ( y ) be as close to each other as we please by requiring only that x and y are sufficiently close to each other ; unlike ordinary continuity, the maximum distance between x and y cannot depend on x and y themselves.

In mathematics, x is commonly used as the name for an independent variable or unknown value.

In mathematics, the logarithmic integral function or integral logarithm li ( x ) is a special function.

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of union is one of the axioms of Zermelo – Fraenkel set theory, stating that, for any set x there is a set y whose elements are precisely the elements of the elements of x.

* Multiplicative inverse, in mathematics, the number 1 / x, which multiplied by x gives the product 1, also known as a reciprocal

In mathematics, a Boolean ring R is a ring for which x < sup > 2 </ sup > = x for all x in R ; that is, R consists only of idempotent elements.

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results ( e. g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants ).

He was the first to use the word " group " () as a technical term in mathematics to represent a group of permutations.

In mathematics and the arts, two quantities are in the golden ratio () if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

In mathematics, the Klein bottle () is a non-orientable surface, informally, a surface ( a two-dimensional manifold ) in which notions of left and right cannot be consistently defined.

In mathematics, a Lie group () is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

The Nine Chapters on the Mathematical Art () is a Chinese mathematics book, composed by several generations of scholars from the 10th – 2nd century BCE, its latest stage being from the 1st century CE.

ETH Zürich () is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland.

In combinatorics, a branch of mathematics, a matroid () or independence structure is a structure that captures and generalizes the notion of linear independence in vector spaces.

In mathematics, a zero, also sometimes called a root, of a real -, complex-or generally vector-valued function ƒ is a member of the domain of ƒ such that ƒ () vanishes at, that is,

In mathematics the spin group Spin ()

In mathematics, the Littlewood conjecture is an open problem () in Diophantine approximation, proposed by John Edensor Littlewood around 1930.

The Keldysh Institute of Applied Mathematics () of the Russian Academy of Sciences is a research institute specializing in computational mathematics.

Steklov Institute of Mathematics or Steklov Mathematical Institute () is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences.

His father, Billy Tao () is a pediatrician, and his mother is a physics and mathematics graduate from the University of Hong Kong, formerly a secondary school teacher of mathematics in Hong Kong.

Mu Alpha Theta () is a United States mathematics honor society for high schools and two-year colleges.

He divided mathematics into two parts Mental () and Observable (), ( or in other words, Pure and Applied.

Lie theory () is an area of mathematics, developed initially by Sophus Lie.

In mathematics, a Cauchy boundary condition () imposed on an ordinary differential equation or a partial differential equation specifies both the values a solution of a differential equation is to take on the boundary of the domain and the normal derivative at the boundary.

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.