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# Exponentiation

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: In that case, bn is called the n-th power of b, or b raised to the power n. The exponent is usually shown as a superscript to the right of the base. [1]

## ABAP

ABAP (Advanced Business Application Programming, originally Allgemeiner Berichts-Aufbereitungs-Prozessor, German for "general report creation processor") is a high-level programming language created by the German software company SAP.

## Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī

Abū al-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qalaṣādī (1412&ndash;1486) was a Muslim mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence.

## Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written (the axiom of commutativity).

## Absolute value

In mathematics, the absolute value (or modulus) of a real number is the non-negative value of without regard to its sign.

## Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

## Ackermann function

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

Ada is a structured, statically typed, imperative, wide-spectrum, and object-oriented high-level computer programming language, extended from Pascal and other languages.

Addition (often signified by the plus symbol "+") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.

In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by positive integer powers that requires a minimal number of multiplications.

## Algebra

Algebra (from Arabic and Farsi "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

## Algebraic number

An algebraic number is a possibly complex number that is a root of a finite, non-zero polynomial in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

## Algebraic structure

In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a some list of axioms.

## ALGOL

ALGOL (short for ALGOrithmic Language) is a family of imperative computer programming languages, originally developed in the mid-1950s, which greatly influenced many other languages and was the standard method for algorithm description used by the ACM in textbooks and academic sources for more than thirty years.

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## Analogy

Analogy (from Greek ἀναλογία, analogia, "proportion") is a cognitive process of transferring information or meaning from a particular subject (the analogue or source) to another (the target), or a linguistic expression corresponding to such a process.

## Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

## Analytica (software)

Analytica is a visual software package developed by Lumina Decision Systems for creating, analyzing and communicating quantitative decision models.

## APL (programming language)

APL (named after the book A Programming Language) is a programming language developed in the 1960s by Kenneth E. Iverson.

## Approximation

An approximation is anything that is similar but not exactly equal to something else.

## Archimedes

Archimedes of Syracuse (Ἀρχιμήδης; BC – BC) was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer.

## Argument (complex analysis)

In mathematics, arg is a function operating on complex numbers (visualized in a complex plane).

## Associative property

In mathematics, the associative property is a property of some binary operations.

## Atan2

In a variety of computer languages, the function atan2 is the arctangent function with two arguments.

## August Ferdinand Möbius

August Ferdinand Möbius (17 November 1790 &ndash; 26 September 1868) was a German mathematician and theoretical astronomer.

## Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 1789 – 23 May 1857) was a French mathematician reputed as a pioneer of analysis.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## Bash (Unix shell)

Bash is a Unix shell and command language written by Brian Fox for the GNU Project as a free software replacement for the Bourne shell.

## BASIC

BASIC (an acronym for Beginner's All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages whose design philosophy emphasizes ease of use.

## Bc (programming language)

bc, for basic calculator, is "an arbitrary precision calculator language" with syntax similar to the C programming language.

## Big O notation

In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system, or base-2 numeral system, which represents numeric values using two different symbols: typically 0 (zero) and 1 (one).

## Binary operation

In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set (more formally, an operation whose arity is two, and whose two domains and one codomain are (subsets of) the same set).

## Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

## Bit

A bit is the basic unit of information in computing and digital communications.

## Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

## C0-semigroup

In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function.

## Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

## Cartesian closed category

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

## Cartesian product

In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set or simply product) from multiple sets.

## Cauchy product

In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two sequences or two series.

## Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said to have characteristic zero if this sum never reaches the additive identity.

## Characterizations of the exponential function

In mathematics, the exponential function can be characterized in many ways.

## Charles Babbage

Charles Babbage, FRS (26 December 1791 –18 October 1871) was an English polymath.

## Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes.

## Christoph Rudolff

Christoff Rudolff (born 1499 in Jawor, Silesia, died 1545 in Vienna) was the author of the first German textbook on algebra.

## Circular sector

A circular sector or circle sector (symbol: ⌔), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.

## COBOL

COBOL (an acronym for common business-oriented language) is a compiled English-like computer programming language designed for business use.

## CoffeeScript

CoffeeScript is a programming language that transcompiles to JavaScript.

## College Mathematics Journal

The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years.

## Commodore BASIC

Commodore BASIC, also known as PET BASIC, is the dialect of the BASIC programming language used in Commodore International's 8-bit home computer line, stretching from the PET of 1977 to the C128 of 1985.

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

## Complex logarithm

In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the real natural logarithm ln x is the inverse of the real exponential function ex.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

## Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis.

## Compound interest

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on.

## Computer algebra system

A computer algebra system (CAS) is a software program that allows computation over mathematical expressions in a way which is similar to the traditional manual computations of mathematicians and scientists.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations Computer science is the scientific and practical approach to computation and its applications.

## Computer terminal

A computer terminal is an electronic or electromechanical hardware device that is used for entering data into, and displaying data from, a computer or a computing system.

## Concatenation

In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end.

## Concrete Mathematics

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, is a textbook that is widely used in computer-science departments.

## Conjugacy class

In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.

## Continuous function

In mathematics, a continuous function is, roughly speaking, a function for which small changes in the input result in small changes in the output.

## Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

## Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

## Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

## Cube (algebra)

In arithmetic and algebra, the cube of a number is its third power: the result of the number multiplied by itself twice: It is also the number multiplied by its square: This is also the volume formula for a geometric cube with sides of length, giving rise to the name.

## D (programming language)

The D programming language is an object-oriented, imperative, multi-paradigm system programming language created by Walter Bright of Digital Mars and released in 2001.

## Decimal

The decimal numeral system (also called base 10 or occasionally denary) has ten as its base.

## Dense set

In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A &mdash; for instance, every real number is either a rational number or has one arbitrarily close to it (see Diophantine approximation).

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable).

## Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

## Differintegral

In fractional calculus, an area of applied mathematics, the differintegral is a combined differentiation/integration operator.

## Diffie–Hellman key exchange

Diffie–Hellman key exchange (D–H) Synonyms of Diffie–Hellman key exchange include.

## Direct sum of modules

In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module.

## Direction (geometry)

Direction is the information contained in the relative position of one point with respect to another point without the distance information.

## Discrete logarithm

In mathematics, a discrete logarithm is an integer k solving the equation, where b and g are elements of a finite group.

## Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

## Dynamical system

In mathematics, a dynamical system is a set of relationships among two or more measurable quantities, in which a fixed rule describes how the quantities evolve over time in response to their own values.

## Dynamical system (definition)

The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.

## E (mathematical constant)

The number is an important mathematical constant that is the base of the natural logarithm.

## Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that does not change its direction under the associated linear transformation.

## Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

## Empty function

In mathematics, an empty function is a function whose domain is the empty set.

## Empty product

In mathematics, an empty product, or nullary product, is the result of multiplying no factors.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry".

## Euler's formula

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

## Euler's identity

In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler.

## Exclusive or

Exclusive disjunction or exclusive or is a logical operation that outputs true only when both inputs differ (one is true, the other is false).

## Exponential decay

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

## Exponential growth

Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function's current value.

## Exponential object

In mathematics, specifically in category theory, an exponential object is the categorical equivalent of a function space in set theory.

## Exponentiation by squaring

In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.

## Extended real number line

In mathematics, the affinely extended real number system is obtained from the real number system R by adding two elements: +∞ and −∞ (read as positive infinity and negative infinity respectively).

## F Sharp (programming language)

F# (pronounced eff sharp) is a strongly typed, multi-paradigm programming language that encompasses functional, imperative, and object-oriented programming techniques.

## Field (mathematics)

In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

## Floating point

In computing, floating point is the formulaic representation which approximates a real number so as to support a trade-off between range and precision.

## Fortran

Fortran (previously FORTRAN, derived from Formula Translating System) is a general-purpose, imperative programming language that is especially suited to numeric computation and scientific computing.

## Fourth power

In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together.

## FoxPro

FoxPro is a text-based procedurally oriented programming language and DBMS, and it is also an object-oriented software programming language, originally published by Fox Software and later by Microsoft, for MS-DOS, Windows, Macintosh, and UNIX.

## Fractal

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.

## Fractional calculus

Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation operator and the integration operator J. (Usually J is used instead of I to avoid confusion with other I-like glyphs and identities.) In this context, the term powers refers to iterative application of a linear operator acting on a function, in some analogy to function composition acting on a variable, e.g.,. For example, one may ask the question of meaningfully interpreting as an analog of the functional square root for the differentiation operator (an operator half iterated), i.e., an expression for some linear operator that when applied twice to any function will have the same effect as differentiation.

## Freshman's dream

The freshman's dream is a name sometimes given to the error (x + y)n.

## Frobenius endomorphism

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.

## Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

## Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

## Functional square root

In mathematics, a half iterate (sometimes called a functional square root) is a square root of a function with respect to the operation of function composition.

## Galois group

In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

## GAP (computer algebra system)

GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory.

## Gnuplot

gnuplot is a command-line program that can generate two- and three-dimensional plots of functions, data, and data fits.

## Greek mathematics

Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

## Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements together with an operation that combines any two elements to form a third element.

## Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing.

## Heat equation

The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.

## Henricus Grammateus

Henricus Grammateus (also known as Henricus Scriptor, Heinrich Schreyber or Heinrich Schreiber; 1495 – 1525 or 1526) was a German mathematician.

## Hyperoperation

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n.

## Identity (mathematics)

In mathematics an identity is an equality relation A.

## Identity element

In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set.

## IEEE floating point

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

## Imaginary unit

The term imaginary unit or unit imaginary number refers to a solution to the equation.

## Indeterminate form

In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form.

## Indirection

In computer programming, indirection is the ability to reference something using a name, reference, or container instead of the value itself.

## Infinite set

In set theory, an infinite set is a set that is not a finite set.

## Initial and terminal objects

In category theory, an abstract branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

## Inverse function

In mathematics, an inverse function is a function that "reverses" another function.

## Involution (mathematics)

In mathematics, an (anti-)involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## Irrational number

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers.

## Irreducible fraction

An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).

## Isaac Newton

Sir Isaac Newton (25 December 164220 March 1726/7) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution.

## Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism (or more generally a morphism) that admits an inverse.

## Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

## J (programming language)

The J programming language, developed in the early 1990s by Kenneth E. Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL function-level languages created by John Backus.

## Java (programming language)

Java is a general-purpose computer programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

## Jost Bürgi

Jost Bürgi (also Joost, Jobst; latinized surname Burgius or Byrgius; 28 February 1552 &ndash; 31 January 1632), active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.

## Kilo-

Kilo (from the Greek χίλιοι, literally a thousand) is a unit prefix in the metric system denoting multiplication by one thousand.

## Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

## Limit (mathematics)

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n sin(1/n) becomes arbitrarily close to 1.

## Limit point

In mathematics, a limit point of a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.

## Linear algebra

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces.

## Linear differential equation

In mathematics, linear differential equations are differential equations having differential equation solutions which can be added together to form other solutions.

## Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

## List of trigonometric identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables.

## Lua (programming language)

Lua (from meaning moon; explicitly not "LUA" for it is not an acronym) is a lightweight multi-paradigm programming language designed as a scripting language with extensible semantics as a primary goal.

## Macsyma

Macsyma (Project MAC’s SYmbolic MAnipulator) is a computer algebra system that was originally developed from 1968 to 1982 at MIT as part of Project MAC and later marketed commercially.

## Magma (algebra)

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.

## Magma (computer algebra system)

Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics.

## Maple (software)

Maple is a commercial computer algebra system developed and sold commercially by Maplesoft, a software company based in Waterloo, Ontario, Canada.

## Markov chain

A Markov chain (discrete-time Markov chain or DTMC), named after Andrey Markov, is a random process that undergoes transitions from one state to another on a state space.

## Mathematica

Mathematica is a computational software program used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics.

## Mathematical Association of America

The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.

## Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy.

## Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

## Mathematical structure

In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that, in some manner, attach (or relate) to the set, endowing the collection with meaning or significance.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Mathematics in medieval Islam

The history of mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, building on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta), saw important developments, such as the full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra (named for the work of scholar Al-Kwarizmi), and advances in geometry and trigonometry.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and fourth-generation programming language.

## Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is interpreted and manipulated in certain prescribed ways.

## Matrix exponential

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.

## Matrix ring

In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.

## Mercury (programming language)

Mercury is a functional logic programming language geared towards real-world applications.

## Method (computer programming)

A method (or message) in object-oriented programming (OOP) is a procedure associated with an object class.

## Metre per second

Metre per second (U.S. spelling: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector quantity which specifies both magnitude and a specific direction), defined by distance in metres divided by time in seconds.

## Metric prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit.

## Michael Stifel

Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk and mathematician.

## Microsoft Excel

Microsoft Excel is a spreadsheet application developed by Microsoft for Microsoft Windows,, and iOS.

## Modular exponentiation

Modular exponentiation is a type of exponentiation performed over a modulus.

## Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

There is some confusion in the literature on whether al-Khwārizmī's full name is or.

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "·" or by the absence of symbol) is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Multivalued function

In mathematics, a multivalued function (short form: multifunction; other names: many-valued function, set-valued function, set-valued map, point-to-set map, multi-valued map, multimap, correspondence, carrier) is a left-total relation (that is, every input is associated with at least one output) in which at least one input is associated with multiple (two or more) outputs.

## NaN

In computing, NaN, standing for not a number, is a numeric data type value representing an undefined or unrepresentable value, especially in floating-point calculations.

## Natural logarithm

The natural logarithm of a number is its logarithm to the base e, where ''e'' is an irrational and transcendental constant approximately equal to.

## Natural number

In mathematics, the natural numbers (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

## Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.

## Nicolas Chuquet

Nicolas Chuquet (1445, but some sources say 1455, Paris, France &ndash; 1488, some sources say 1500, Lyon, France) was a French mathematician.

## Normative

Normative means relating to an ideal standard or model, or being based on what is considered to be the normal or correct way of doing something.

## Nth root

In mathematics, the nth root of a number x, where n is a positive integer, is a number r which, when raised to the power n yields x where n is the degree of the root.

## Number

A number is a mathematical object used to count, measure and label.

## Number theory

Number theory (or arithmeticEspecially in older sources; see two following notes.) is a branch of pure mathematics devoted primarily to the study of the integers.

## OCaml

OCaml, originally known as Objective Caml, is the main implementation of the Caml programming language, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez and others in 1996.

## One half

One half is the irreducible fraction resulting from dividing one by two (½), or the fraction resulting from dividing any number by its double.

## One-sided limit

In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.

## Operation (mathematics)

The general operation as explained on this page should not be confused with the more specific operators on vector spaces.

## Ordinal number

In set theory, an ordinal number, or ordinal, is the order type of a well-ordered set.

## Oren Patashnik

Oren Patashnik (born 1954) is a computer scientist.

## PARI/GP

PARI/GP is a computer algebra system with the main aim of facilitating number theory computations.

## Parity (mathematics)

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd.

## Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

## Perl

Perl is a family of high-level, general-purpose, interpreted, dynamic programming languages.

## PHP

PHP is a server-side scripting language designed for web development but also used as a general-purpose programming language.

## PL/I

PL/I ("Programming Language One", pronounced) is a procedural, imperative computer programming language designed for scientific, engineering, business and systems programming applications.

## Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

## Polynomial ring

In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.

## Population growth

In biology, population growth is the increase in the number of individuals in a population.

## Positive real numbers

In mathematics, the set of positive real numbers, \mathbb_.

## Power associativity

In abstract algebra, power associativity is a property of a binary operation which is a weak form of associativity.

## Power of two

In mathematics, a power of two means a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

## Power rule

In calculus, the power rule is one of the most important differentiation rules.

## Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term, c is a constant, and x varies around c (for this reason one sometimes speaks of the series as being centered at c).

## Power set

In mathematics, the power set (or powerset) of any set, written, ℘(),, or 2''S'', is the set of all subsets of, including the empty set and itself.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

## Principal branch

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.

## Principal value

In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.

## Processor register

In computer architecture, a processor register is a small amount of storage available as part of a digital processor, such as a central processing unit (CPU).

## Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

## Product topology

In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.

## Programming language

A programming language is a formal constructed language designed to communicate instructions to a machine, particularly a computer.

## Public-key cryptography

Public-key cryptography, also known as asymmetric cryptography, is a class of cryptographic protocols based on algorithms that require two separate keys, one of which is secret (or private) and one of which is public.

## Python (programming language)

Python is a widely used general-purpose, high-level programming language.

## R (programming language)

R is a programming language and software environment for statistical computing and graphics.

## Racks and quandles

In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams.

The radian is the standard unit of angular measure, used in many areas of mathematics.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero.

## Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

## Recurrence relation

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.

## René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 159611 February 1650) was a French philosopher, mathematician, and scientist who spent about 20 years of his life in the Dutch Republic.

## Rexx

Rexx (REstructured eXtended eXecutor) is an interpreted programming language developed at IBM by Mike Cowlishaw.

## Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold.

## Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

## Ring (mathematics)

In mathematics, and more specifically in algebra, a ring is an algebraic structure with operations that generalize the arithmetic operations of addition and multiplication.

## Ring homomorphism

In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.

## Robert Recorde

Robert Recorde (ca. 1512–1558) was a Welsh physician and mathematician.

## Ronald Graham

Ronald (Ron) Lewis Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years".

## Ruby (programming language)

Ruby is a dynamic, reflective, object-oriented, general-purpose programming language.

## SageMath

SageMath (previously Sage or SAGE, System for Algebra and Geometry Experimentation) is mathematical software with features covering many aspects of mathematics, including algebra, combinatorics, numerical mathematics, number theory, and calculus.

## Samuel Jeake

Samuel Jeake (1623–1690), dubbed the elder to distinguish him from his son, was an English merchant, Nonconformist, antiquary and astrologer from Rye, East Sussex, England.

## SAS language

The SAS language is a computer programming language used for statistical analysis, originated by a project at the North Carolina State University.

## Schrödinger equation

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time.

## Scientific notation

Scientific notation (also referred to as "standard form" or "standard index form") is a way of expressing numbers that are too big or too small to be conveniently written in decimal form and is commonly used by scientists, mathematicians and engineers.

## Seed7

Seed7 is an extensible general-purpose programming language designed by Thomas Mertes.

## Sequence

In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Set theory

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects.

## Sine

Sine, in mathematics, is a trigonometric function of an angle.

## Singular (software)

Singular (typeset Singular) is a computer algebra system for polynomial computations with special emphasis on the needs of commutative and non-commutative algebra, algebraic geometry, and singularity theory.

## Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

## Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

## Square matrix

In mathematics, a square matrix is a matrix with the same number of rows and columns.

## Subscript and superscript

A subscript or superscript is a number, figure, symbol, or indicator that is smaller than the normal line of type and is set slightly below or above it.

## Subset

In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

## Subset sum problem

In computer science, the subset sum problem is one of the important problems in complexity theory and cryptography.

## Symbol

A symbol is an object that represents, stands for or suggests an idea, visual image, belief, action or material entity.

## Tcl

Tcl (originally from Tool Command Language, but conventionally spelled "Tcl" rather than "TCL"; pronounced as "tickle" or "tee-see-ell") is a scripting language created by John Ousterhout.

## Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperator after exponentiation, and is defined as iterated exponentiation.

## TeX

TeX ((with the final consonant sounding like Ancient Greek's or English's) but often pronounced in English) is a typesetting system designed and mostly written by Donald Knuth and released in 1978.

## The Sand Reckoner

The Sand Reckoner (Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe.

## Thomas Clausen (mathematician)

Thomas Clausen (January 16, 1801, Snogbæk, Sottrup Municipality, Duchy of Schleswig (now Denmark) &ndash; May 23, 1885, Derpt, Imperial Russia (now Estonia)) was a Danish mathematician and astronomer.

## TI-BASIC

TI-BASIC is the unofficial name of a BASIC-like language built into Texas Instruments (TI)'s graphing calculators, including the TI-83 series, TI-84 Plus series, TI-89 series, TI-92 series (including Voyage 200), TI-73, and TI-Nspire.

## Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a non-zero polynomial equation with rational coefficients.

## Transfinite induction

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.

## Trigonometric functions

In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle.

## Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

## Tuple

A tuple is a finite ordered list of elements.

## Turing (programming language)

Turing is a Pascal-like programming language developed in 1982 by Ric Holt and James Cordy, then of University of Toronto, Canada.

## Typewriter

A typewriter is a mechanical or electromechanical machine for writing in characters similar to those produced by printer's movable type by means of keyboard-operated types striking a ribbon to transfer ink or carbon impressions onto paper.

## Unicode subscripts and superscripts

Unicode has subscripted and superscripted versions of a number of characters including a full set of arabic numerals.

## Unit circle

In mathematics, a unit circle is a circle with a radius of one.

## Up to

In mathematics, the phrase up to indicates that its grammatical object is some equivalence class, to be regarded as a single entity, or disregarded as a single entity.

## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context.

## VHDL

VHDL (VHSIC Hardware Description Language) is a hardware description language used in electronic design automation to describe digital and mixed-signal systems such as field-programmable gate arrays and integrated circuits.

## Wave

In physics, a wave is an oscillation accompanied by a transfer of energy that travels through space or mass.

## Wave equation

The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves.

## Well-defined

In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value.

## Wolfram Alpha

Wolfram Alpha (also styled WolframAlpha and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Research.

## Zenzizenzizenzic

Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of a number x is the power x8), dating from a time when powers were written out in words rather than as superscript numbers.

## (ε, δ)-definition of limit

In calculus, the (ε, δ)-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit.

## .NET Framework

.NET Framework (pronounced dot net) is a software framework developed by Microsoft that runs primarily on Microsoft Windows.

## 1 (number)

1 (one; or, also called "unit", "unity", and "(multiplicative) identity", is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1.

## 10 (number)

10 (ten) is an even natural number following 9 and preceding 11.

## 4 (number)

4 (four) is a number, numeral, and glyph.

## References

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