## 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 ...

## 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 ...

## 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.

## 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 ...

## 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 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 ...

## 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. ...

## 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 ...

## 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 ...

## Godel number

In formal number theory a Godel numbering is a function which assigns to each symbol and formula of some formal language a unique natural number called a Godel number. The concept was first used by Kurt Godel for the proof of his incompleteness t ...

## Godels incompleteness theorems

Godels incompleteness theorems is the name given to two theorems, proved by Kurt Godel in 1931. They are theorems in mathematical logic. Mathematicians once thought that everything that is true has a mathematical proof. A system that has this pro ...

## Grahams number

Grahams number is a very big natural number that was defined by a man named Ronald Graham. Graham was solving a problem in an area of mathematics called Ramsey theory. He proved that the answer to his problem was smaller than Grahams number. Grah ...

## Graph

A graph is a picture designed to express words, particularly the connection between two or more quantities. You can see a graph on the right. A simple graph usually shows the relationship between two numbers or measurements in the form of a grid. ...

## Group theory

In mathematics and abstract algebra, group theory studies a type of algebraic structure called a group. Group theory is often used in mathematics as a starting point for the study of many algebraic structures, such as a set of numbers along with ...

## Halting problem

The Halting problem is a problem in computer science. The problem is looking at a computer program and finding out if the program is going to run forever or not. We say that a program "solves the halting problem" if it can look at any other progr ...

## Heaviside Function

The Heaviside function, often written as H, is a non-continuous function whose value is zero for a negative input and one for a positive input. The function is used in the mathematics of control theory to represent a signal that switches on at a ...

## Heuristic

A heuristic is a practical way to solve a problem. It is better than chance, but does not always work. A person develops a heuristic by using intelligence, experience, and common sense. Trial and error is the simplest heuristic, but one of the we ...

## Hilberts paradox of the Grand Hotel

Hilberts paradox of the Grand Hotel is a mathematical paradox named after the German mathematician David Hilbert. Hilbert used it as an example to show how infinity does not act in the same way as regular numbers do.

## Hilberts problems

In 1900, the mathematician David Hilbert published a list of 23 unsolved mathematical problems. The list of problems turned out to be very influential. After Hilberts death, another problem was found in his writings; this is sometimes known as Hi ...