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On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences, also known as Sloanes, is a large searchable database. It is on the Web, and it contains number sequences, like the Fibonacci numbers or the powers of two. It contains over 270.000 sequences. This ma ...

                                               

Optimal control

Optimal control theory is a theory from mathematics. It looks at how to find a good solution in a dynamic system. The system is described by a function, and the problem often is to find values that minimize or maximize this function over an inter ...

                                               

Order of magnitude

If two numbers have the same order of magnitude, they are about the same size. But if one would compare the surface of an orange with that of the earth, one would say the surface of the earth is many orders of magnitude larger than that of the or ...

                                               

Order theory

Order theory is a field of mathematics. It concerns itself with being able to compare different elements of a set. Given a binary relation it is then possible to put all the elements of the set in a certain order. It is also possible to say that ...

                                               

Ordered pair

In mathematics, an ordered pair is a collection of two objects, where one of the objects is first, and the other is second. An ordered pair where the first coordinate is a {\displaystyle a} and the second coordinate is b {\displaystyle b} is usua ...

                                               

Parameter

In some non-technical contexts or in jargon, parameter may simply be a synonym for criterion. In mathematics, statistics, and the mathematical sciences, parameters L: auxiliary measure are quantities that define certain relatively constant charac ...

                                               

Pascals Triangle

Pascals Triangle is a mathematical triangular array. It is named after French mathematician Blaise Pascal, but it was used in China 3 centuries before his time. Pascals triangle can be made as follows. On the first row, write only the number 1. T ...

                                               

Pearson product-moment correlation coefficient

Pearsons correlation is a mathematical formula used to calculate correlation coefficients between two datasets. Most computer programs have a command to calculate this such as CORREL. You would calculate this your self by. Step 4: Sum up ab, sum ...

                                               

Percentage

Percent means out of one hundred. It is often shown with the symbol "%". It is used even if there are not a hundred items. The number is then scaled so it can be compared to one hundred. Percent is also used to indicate changes in numerical quant ...

                                               

Perfect information

Perfect information has different definitions depending on the field. In economics, the term perfect information refers to an element of competition in a market which is perfect and idealized. This is commonly known as perfect competition. In the ...

                                               

Permutation

A permutation is a single way of arranging a group of objects. It is useful in mathematics. A permutation can be changed into another permutation by simply switching two or more of the objects. For example, the way four people can sit in a car is ...

                                               

Philosophy of mathematics

The philosophy of mathematics is a kind of philosophy that tries to study what mathematics really is. Philosophers of math ask themselves questions like: Why some people think math is "beautiful"? Is mathematics really true, or just something tha ...

                                               

Pi Day

Pi Day or Pie Approximation Day is a day when people around the world celebrate the number pi. They also eat pie to celebrate the pun as both words sound the same. Pi Day is held on March 14.

                                               

Pigeonhole principle

The pigeonhole principle explains that when there are pigeon-sized holes in a pigeon container, then its impossible to fit more than pigeons in that container, without having at least one hole containing more than one. The pigeons are used here a ...

                                               

Polynomial

In mathematics, a polynomial is a kind of mathematical expression. It is a sum of several mathematical terms called monomials. That is, a number, a variable, or a product of a number and several variables. When an algebraic expression contains le ...

                                               

Population genetics

Population genetics is the branch of genetics which studies the genetic composition of populations. It brings together genetics, evolution, natural selection, breeding, statistics and mathematics. Mathematical and computer models are produced, an ...

                                               

Power series

In mathematics, a power series is an infinite series of the form f x = ∑ n = 0 ∞ a n x − c n = a 0 + a 1 x − c + a 2 x − c 2 + a 3 x − c 3 + ⋯ {\displaystyle fx=\sum _{n=0}^{\infty }a_{n}\leftx-c\right^{n}=a_{0}+a_{1}x-c+a_{2}x-c^{2}+a_{3}x-c^{3} ...

                                               

Predator-prey equations

The predator-prey equations is a system of two linked equations that models two species that depend on each other: One is the prey, which provides food for the other, the predator. Both prey and predator populations grow if conditions are right. ...

                                               

Predicate logic

In logic and philosophy, predicate logic is a system of mathematical logic. It uses predicates to express the state of certain things, which are "incomplete propositions" with a placeholder for objects or subjects that must be inserted in order t ...

                                               

Probability space

Probability space is a mathematical model used to describe scientific experiments. A probability space consists of three parts: A function that assigns probabilities to each event A set of events. Each event associates zero or more outcomes A sam ...

                                               

Problem

A problem is a situation preventing something from being achieved. The word comes from a Greek word meaning an "obstacle". Someone who has a problem must find a way of solving it. The means of solving a problem is called a "solution".

                                               

Proportions

In mathematics, the word proportions means two ratios put into an equation. Some examples of proportions are: + x ⁄ 100 = 3 ⁄ 4, where x = 75. 75 ⁄ 100 = 3 ⁄ 4 50 ⁄ 100 = 1 ⁄ 2 In algebra, proportions can be used to solve many common problems abo ...

                                               

Pure mathematics

Pure mathematics is a field of mathematics. Other fields of mathematics are driven and motivated by applications, they can be used to solve real-world problems, for example in physics or engineering. In contrast, pure mathematics studies abstract ...

                                               

Pythagorean triple

In mathematics, a Pythagorean triple is a set of three positive integers which satisfy the equation: x 2 + y 2 = z 2 {\displaystyle x^{2}+y^{2}=z^{2}} This equation is known as the Diophantine equation, and is related to Pythagoras theorem. The l ...

                                               

Random

Random is a term used in mathematics to mean that there is no way to reliably predict an outcome or sense a pattern. Something that is chosen at random is not chosen for any conscious reason, and therefore thought to be purely by chance. An examp ...

                                               

Random sample

A random sample is a sample taken at random from a population of data. In a random sample every element in the population has an equal chance of being selected. For instance, to do an election poll, calling people randomly out of the phone book w ...

                                               

Random variable

A random variable is used in mathematics to study probability theory. It was developed to model the chance of events happening in all kinds of real-life scenarios.

                                               

Range (mathematics)

In mathematics, the range is a concept which has various meanings in different topics: In statistics, the range is the difference between the lowest and highest values. For example. in {4, 6, 9, 3, 7}, the lowest value is 3, and the highest is 9, ...

                                               

Ratio

A ratio between two or more quantities is a way of measuring their sizes compared to each other. A ratio can be indicated using colon as a separator, or It can be simply expressed as a fraction. For example, if a school has 20 teachers and 500 pu ...

                                               

Reciprocal

In mathematics, the reciprocal of a number is 1 divided by the number, or equivalently, the number raised to the power of -1. All numbers have a reciprocal except zero, since no number times 0 is 1. Two numbers are reciprocal of each other if and ...

                                               

Reductio ad absurdum

Reductio ad absurdum is a Latin phrase which means "reduction to the absurd". The phrase describes a kind of indirect proof. It is a proof by contradiction, and is a common form of argument. It shows that a statement is true because its denial le ...

                                               

Reed–Solomon error correction

Reed-Solomon error correction is a forward error correction code. It works by oversampling a polynomial constructed from the data. The polynomial is evaluated at several points, and these values are sent or recorded. Sampling the polynomial more ...

                                               

Relation (mathematics)

In mathematics, an n-ary relation on n sets, is any subset of Cartesian product of the n sets, with the most common one being a binary relation, a collection of order pairs from two sets containing an object from each set. The relation is homogen ...

                                               

Riemann sphere

The Riemann sphere is a mathematical model of the extended complex plane. The model is named after Bernhard Riemann. The extended complex plane is the plane of the complex numbers, plus a point at infinity. With this model, this point at infinity ...

                                               

Right-hand rule

The right-hand rule is a convention in vector math. It helps you remember direction when vectors get cross multiplied. If you point your "gun" straight ahead, stick out your middle finger so that it points left and all your fingers are at right a ...

                                               

Rounding

The word rounding for a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit form. For example, US.74 could be rounded to US, the fraction 312/937 could be rounded to 1/3, an ...

                                               

Sequence

A sequence is a word meaning "a set of related events, movements or items that follow each other in a particular order". It is used in mathematics and other disciplines. In ordinary use, it means a series of events, one following another. In math ...

                                               

Series

A series is a group of similar things that are all related to the same topic. In mathematics, a series is the adding of a list of usually never-ending mathematical objects such as numbers. It is sometimes written as ∑ n = i k a n {\displaystyle \ ...

                                               

Series acceleration

In numerical analysis, series acceleration is the name for algorithms that transforms slowly convergent series to rapidly convergent series.

                                               

Signed number representations

Signed Number representations are used to solve the problem of representing negative integers in binary. The problem of trying to store the negative sign of a binary number is that there are no states left to use with which to represent the negat ...

                                               

SIR model

The SIR model is a simple mathematical model of epidemics. An epidemic is when the number of people infected with a disease is increasing in a population. S, I, and R stand for: Below is a graph of a solved SIR model. The bottom x axis is time, a ...

                                               

Society for Industrial and Applied Mathematics

Society for Industrial and Applied Mathematics is an US-based professional non-profit organization of applied mathematicians who are working in the field of education and research of applied mathematics. They do so with publishing textbooks and a ...

                                               

Spearmans rank correlation coefficient

In mathematics and statistics, Spearmans rank correlation coefficient is a measure of correlation, named after its maker, Charles Spearman. It is written in short as the Greek letter rho or sometimes as r s {\displaystyle r_{s}}. It is a number t ...

                                               

Spiral

A spiral is a special curve in mathematics. This curve starts at a point, and then goes around the point, but gets farther and farther away from it. This is different from a circle (which is always at the same distance or an ellipse. A spiral is ...

                                               

Square root

In mathematics, a square root of a number x is another number that, when multiplied by itself, becomes x. When it is non-negative, it is represented by the symbol x {\displaystyle {\sqrt {x}}}, and called the principal square root of x. For examp ...

                                               

Stability

Stability is a property of many systems. It means being at rest, not liable to change. In mechanics and dynamics, a system is stable if it will not change motion of its own accord, and will resist small efforts to change its direction or position ...

                                               

Strict weak ordering

Strict weak ordering is a binary relation on a set. Such relations define a strict ordering, but they contain several elements of the same type. An example might be the relation "costs less than", or "is cheaper than". For any two elements that a ...

                                               

Superpermutation

In combinatorial math, a superpermutation is a list of numbers that contains each different arrangement of symbols it is made up of inside of it. While superpermutations can simply be made up of every arrangement listed side by side, it can also ...

                                               

Surface area

Surface area the measure of the total area that the surface of the object occupies object. The surface area of a polyhedron is found by finding the sum of the area of all of the faces. The surface area is found between many three-dimensional shap ...

                                               

Ternary numeral system

A ternary /ˈtɜːrnəri/ numeral system has three as its base. This means that you can only count with 0, 1, and 2. The first ten numbers in ternary are 00, 01, 02, 10, 11, 20, 21, 22, 100, 101. When all the digits in the number reach 2, you add a 1 ...

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