## Currying

Currying is a technique used in mathematics and computer science that consists of changing a function that takes several arguments into a number of functions that each take one argument. Mathematicians Moses Schonfinkel and Gottlob Frege laid the ...

## Daubechies wavelet

Daubechies wavelets are a family of orthogonal wavelets named after Belgian physicist and mathematician Ingrid Daubechies. They are used in discrete wavelet transform.

## Decimal

The decimal numeral system is the most usual way of writing numbers. It has ten as a starting point, or base. It is sometimes called the base ten or denary numeral system. The word "decimal" is also used instead of the word "period" to mean the d ...

## Decimal separator

The decimal separator is a symbol used to mark the border between the integral and the fractional parts of a decimal numeral. This symbol can be a period, as is common in United States and other English-speaking countries, or a comma, as in conti ...

## Decision problem

A decision problem is a problem that can be posed as a yes-no question of the input values. It is a type of problem in mathematics. An example of a decision problem is deciding whether a given natural number is prime. Another is the problem "give ...

## Decision theory

Decision theory is a mathematical theory about how to best reach a decision. This is done using probability theory, statistics and logical reasoning. A decision can be made in different ways. Decision theory usually picks the best decision by loo ...

## Decison problem

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer. The answer is dependent on the values of the input parameters. Decision problems typically appear in math ...

## Degree (mathematics)

The degree of a polynomial p {\displaystyle p}, represented by the symbol deg ⁡) {\displaystyle \deg)}, is the highest exponent that occurs inside that polynomial. For example, if we look at the polynomial 2 x 3 − 7 x 2 + 5 x − 4 {\displaystyle 2 ...

## Dependent and independent variables

In an experiment, the variables used can be classed as either dependent or independent variables. The dependent variable is the possible outcome of the experiment; the effect. It depends on what happens to other variables in the experiment. The d ...

## Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all the units cancel ...

## Direct proof

A direct proof is a way of showing that something is true or false by using logic. This is done by combining known facts. No assumptions are made when doing a direct proof. Lemmas and theorems are used to prove direct proofs. A statement that can ...

## Discrete mathematics

Discrete mathematics is the study of mathematical structures that are discrete rather than continuous. In contrast to real numbers that vary "smoothly", discrete mathematics studies objects such as integers, graphs, and statements in logic. These ...

## Discriminant

In algebra, the discriminant, sometimes represented by the symbol Δ {\displaystyle \Delta }, is an algebraic expression used to determine the number of roots a polynomial have. For example, the discriminant of the quadratic polynomial a x 2 + b x ...

## Distance

Distance is how far one thing is from another thing. It is also a measure of the space between two things. It can be measured along any path. Thus, someone who goes around in a circle has traveled a distance, even though his position has not chan ...

## Distribution (mathematics)

This is about distribution in a mathematical sense, other meanings can be found at distribution In mathematics, a distribution is a generalisation of a function. Distributions were introduced in the middle of the 20th century by Laurent Schwartz, ...

## Dynamical systems theory

Dynamical systems theory is a field of applied mathematics. It tries to describe complex dynamical systems, often using differential equations and difference equations. When differential equations are used, the theory is called continuous dynamic ...

## EASIAM

EASIAM is the eastern Asian branch of the US-based Society for Industrial and Applied Mathematics. EASIAM is aiming to advance studies of applied mathematics in eastern Asia.

## Egyptian fraction

## Einstein field equations

The Einstein field equations, or Einstein-Hilbert equations, or simply Einstein equations are equations that describe gravity in the classical sense. They are named after Albert Einstein and David Hilbert. The basic idea is to use geometry to mod ...

## Entscheidungsproblem

The Entscheidungsproblem is a famous problem of mathematics. David Hilbert formulated the problem in 1928: Is there an algorithm that will take a formal language, and a logical statement in that language, and that will output "True" or "False", d ...

## Equality (mathematics)

In mathematics, two things are equal if and only if they are exactly the same in every way. That is, they have the same value and the same mathematical properties. Mathematicians use the equals sign to say this. This defines a binary relation, eq ...

## Equivalence relation

In mathematics, an equivalence relation R {\displaystyle R} on a set is a mathematical relation that is symmetric, transitive and reflexive. For a given element a {\displaystyle a} on that set, the set of all elements related to a {\displaystyle ...

## Estimation

Estimation is the approximation of a result that one can use even if they are using information that is not clear or is incomplete. It is like making an educated, reasonable guess based on the information given. If an estimate is more than the ac ...

## Euler characteristic

In mathematics, the Euler characteristic of a shape is a number that describes a topological space, so that anything in the space will have the same number. It is calculated by taking the number of points in the shape, the number of lines in the ...

## Eulers formula

In complex analysis, Eulers formula, also sometimes called Eulers relation, is an equation involving complex numbers and trigonometric functions. More specifically, it states that e i x = cos ⁡ x + i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} ...

## Eulers identity

Eulers identity, sometimes called Eulers equation, is this equation: e i π + 1 = 0 {\displaystyle e^{i\pi }+1=0} It features the following mathematical constants: i {\displaystyle i}, imaginary unit π {\displaystyle \pi }, pi π ≈ 3.14159 {\displa ...

## Even number

An even number is an integer that can be divided by two and remain an integer or has no remainder. Examples of even numbers are 2, 4, 6, 8. Also, all numbers which end in 2.4.6.8 and 0 are also even numbers. An integer that is not an even number ...

## Exponent

In mathematics, an exponent indicates how many copies of a number is multiplied together. For example, in the number 5 4 {\displaystyle 5^{4}}, 5 is the base and 4 is the exponent. This can be read as "5 to the power of 4". Therefore, in this exa ...

## Exponential function

In mathematics, the exponential function is a function that grows quicker and quicker. More precisely, it is the function exp ⁡ = e x {\displaystyle \exp=e^{x}}, where e is Eulers constant, an irrational number that is approximately 2.71828.

## Exponentiation

In mathematics, exponentiation is an arithmetic operation on numbers. It can be thought of as repeated multiplication, just as multiplication can be thought of as repeated addition. In general, given two numbers x {\displaystyle x} and y {\displa ...

## Eye of Horus

The Eye of Horus was an important symbol in ancient Egypt. It was the symbol of protection and Royal Power from Ra or Horus. Horus was an ancient Egyptian sky god in the form of a falcon. The right eye represents a peregrine falcons eye and the m ...

## Factorial

The factorial of a whole number n, written as n!, is found by multiplying n by all the whole numbers less than it. For example, the factorial of 4 is 24, because 4 × 3 × 2 × 1 = 24. Hence one can write 4! = 24. For some technical reasons, 0! is e ...

## Field (mathematics)

In mathematics, a field is a certain kind of algebraic structure. In a field, one can add, subtract, multiply and divide two numbers. A field is a special ring in which division is possible. Both the set of rational numbers and the set of real nu ...

## Fixed point

1 is a fixed point of x 2 {\displaystyle x^{2}} because 1 2 = 1 {\displaystyle 1^{2}=1}. Some functions do not have fixed points. For example x + 1 {\displaystyle x+1} does not have one because x + 1 {\displaystyle x+1} is never equal to x.

## Fixed-point theorem

In mathematics, a fixed-point theorem is a theorem that a mathematical function has a fixed point. At that fixed point, the functions input and output are equal. This concept is not one theorem itself; it is a way to describe many other theorems.

## Floating point

Real numbers in binary have to be stored in a special way in a computer. Computers represent numbers as binary integers, so there is no direct way for them to represent non-integer numbers like decimals as there is no radix point. One way compute ...

## Flux

Flux is a term in physics and mathematics. It is broadly defined as "How much stuff goes through a thing". The word "flux" is similar to "flow". For instance, imagine a butterfly net. The amount of air passing through the net is the flux.

## Formal language

In mathematics, computer science and linguistics, a formal language is one that has a particular set of symbols, and whose expressions are made according to a particular set of rules. The symbol L {\displaystyle {\mathcal {L}}} is often used as a ...

## Formal verification

Formal verification is the process used to prove that a piece of software or hardware works according to its specification. Formal verification uses a mathematical proof. Systems such as those used in robots, or airplanes need to be proved correc ...

## Formula

In mathematics and science, a formula is a rule or statement written in algebraic symbols. The plural of formula can be written in two ways: formulae or formulas - the choice is based on personal preference. Formulas use letters instead of words. ...

## Fourier inversion theorem

In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information ...

## Fraction (mathematics)

A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above another number. For example, 1 4 {\displaystyle {\tfrac {1}{4}}}, 1 ⁄ 4 and 1/4.are different ways of writing the same ...

## Frequency probability

Frequency probability or Frequentism is one of the interpretations of probability theory. Repeating a scientific experiment very often gives a number of results. It is then possible, to count the number of times that a given event happened and co ...

## Function composition

In mathematics, function composition is a way of making a new function from two other functions through a chain-like process. More specifically, given a function f from X to Y and a function g from Y to Z, then the function g composed with f ", w ...

## Function space

In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. For example: In set theory, the set of functions from X to Y may be written X → Y or YX.

## Functional analysis

Functional analysis is a branch of mathematical analysis. This area emerged from the studies of differential equations. It has many applications in various fields. One of the famous use is numerical analysis.

## Fundamental theorem of algebra

The fundamental theorem of algebra is a proven fact about polynomials, sums of multiples of integer powers of one variable. It is based on mathematical analysis, the study of real numbers and limits. It was first proven by German mathematician Ca ...

## Gamblers fallacy

The term Gamblers fallacy refers to a misconception about statistics. It is also known Monte Carlo fallacy or fallacy of the maturity of chances. In statistics, a random event has a certain probability of occurring. The fallacy is that if the eve ...

## Gamma function

In mathematics, the gamma function) is a key topic in the field of special functions. Γ is an extension of the factorial function to all complex numbers except negative integers. For positive integers, it is defined as Γ =! {\displaystyle \Gamma ...

## Gauss-Bonnet theorem

The Gauss-Bonnet theorem is a theorem that connects the geometry of a shape with its topology. It is named after the two mathematicians Carl Friedrich GauS and Pierre Ossian Bonnet who both found it, independently of one another. The Curvature of ...