linguistics Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds ...

and

semiotics Semiotics ( ) is the systematic study of sign processes and the communication of meaning. In semiotics, a sign is defined as anything that communicates intentional and unintentional meaning or feelings to the sign's interpreter. Semiosis is a ...

, a notation system is a

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...

of graphics or

symbol A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...

s, characters and abbreviated expressions, used (for example) in

artistic Art is a diverse range of culture, cultural activity centered around works of art, ''works'' utilizing Creativity, creative or imagination, imaginative talents, which are expected to evoke a worthwhile experience, generally through an express ...

and

scientific discipline The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups: * Formal sciences: the study of formal systems, such as those under the branches of logic and mat ...

s to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an

arbitrary Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle". It is also used to refer to a choice made without any specific criterion or restraint. Arbitrary decisions are not necess ...

meaning, created to facilitate structured communication within a

domain knowledge Domain knowledge is knowledge of a specific discipline or field in contrast to general (or domain-independent) knowledge. The term is often used in reference to a more general discipline—for example, in describing a software engineer who has ge ...

field of study An academic discipline or academic field is a subdivision of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part) and recognized by the academic journals in which research is published, a ...

. Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

and

biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...

, but can also be seen in areas like

business Business is the practice of making one's living or making money by producing or Trade, buying and selling Product (business), products (such as goods and Service (economics), services). It is also "any activity or enterprise entered into for ...

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

and

music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

Written communication

Writing systems

* Phonographic

writing systems A writing system comprises a set of symbols, called a ''script'', as well as the rules by which the script represents a particular language. The earliest writing appeared during the late 4th millennium BC. Throughout history, each independe ...

, by definition, use symbols to represent components of auditory language, i.e.

speech Speech is the use of the human voice as a medium for language. Spoken language combines vowel and consonant sounds to form units of meaning like words, which belong to a language's lexicon. There are many different intentional speech acts, suc ...

, which in turn refers to things or ideas. The two main kinds of phonographic notational system are the

alphabet An alphabet is a standard set of letter (alphabet), letters written to represent particular sounds in a spoken language. Specifically, letters largely correspond to phonemes as the smallest sound segments that can distinguish one word from a ...

and the

syllabary In the Linguistics, linguistic study of Written language, written languages, a syllabary is a set of grapheme, written symbols that represent the syllables or (more frequently) mora (linguistics), morae which make up words. A symbol in a syllaba ...

. Some written languages are more consistent in their correlation of written symbols (or

grapheme In linguistics, a grapheme is the smallest functional unit of a writing system. The word ''grapheme'' is derived from Ancient Greek ('write'), and the suffix ''-eme'' by analogy with ''phoneme'' and other emic units. The study of graphemes ...

s) with sound (or

phoneme A phoneme () is any set of similar Phone (phonetics), speech sounds that are perceptually regarded by the speakers of a language as a single basic sound—a smallest possible Phonetics, phonetic unit—that helps distinguish one word fr ...

s), and are therefore considered to have better

phonemic orthography A phonemic orthography is an orthography (system for writing a language) in which the graphemes (written symbols) correspond consistently to the language's phonemes (the smallest units of speech that can differentiate words), or more generally ...

. * Ideographic writing, by definition, refers to things or ideas independently of their pronunciation in any language. Some ideographic systems are also

pictogram A pictogram (also pictogramme, pictograph, or simply picto) is a graphical symbol that conveys meaning through its visual resemblance to a physical object. Pictograms are used in systems of writing and visual communication. A pictography is a wri ...

s that convey meaning through their pictorial resemblance to a physical object.

Linguistics

* Various brackets, parentheses, slashes, and lines are used around words and letters in

to distinguish written from spoken forms, etc. See .

Biology and medicine

Nucleic acid notation The nucleic acid notation currently in use was first formalized by the International Union of Pure and Applied Chemistry (IUPAC) in 1970. This universally accepted notation uses the Roman characters G, C, A, and T, to represent the four nucleotides ...

* Systems Biology Graphical Notation (SBGN) * Sequence motif pattern-description notations * Cytogenetic notation * Energy Systems Language

Chemistry

* A

chemical formula A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as pare ...

describes a chemical compound using element symbols and subscripts, e.g. for water or for glucose * SMILES is a notation for describing the structure of a molecule with a

plain text In computing, plain text is a loose term for data (e.g. file contents) that represent only characters of readable material but not its graphical representation nor other objects ( floating-point numbers, images, etc.). It may also include a lim ...

string, e.g. N=N for nitrogen or CCO for ethanol

Computing

* BNF (Backus normal form, or

Backus–Naur form In computer science, Backus–Naur form (BNF, pronounced ), also known as Backus normal form, is a notation system for defining the Syntax (programming languages), syntax of Programming language, programming languages and other Formal language, for ...

) and EBNF (extended Backus-Naur form) are the two main notation techniques for context-free grammars. * Drakon-charts are a graphical notation of algorithms and procedural knowledge. *

Hungarian notation Hungarian notation is an identifier naming convention in computer programming in which the name of a variable or function indicates its intention or kind, or in some dialects, its type. The original Hungarian notation uses only intention or kin ...

is an identifier naming convention in

computer programming Computer programming or coding is the composition of sequences of instructions, called computer program, programs, that computers can follow to perform tasks. It involves designing and implementing algorithms, step-by-step specifications of proc ...

, that represents the

type Type may refer to: Science and technology Computing * Typing, producing text via a keyboard, typewriter, etc. * Data type, collection of values used for computations. * File type * TYPE (DOS command), a command to display contents of a file. * ...

or intended use of a variable with a specific pattern within its name. *

Mathematical markup languages A mathematical markup language is a computer notation for representing mathematical formulae, based on mathematical notation. Specialized markup languages are necessary because computers normally deal with linear text and more limited character s ...

are computer notations for representing mathematical formulae. * Various notations have been developed to specify

regular expression A regular expression (shortened as regex or regexp), sometimes referred to as rational expression, is a sequence of characters that specifies a match pattern in text. Usually such patterns are used by string-searching algorithms for "find" ...

s. * The APL programming language provided a rich set of very concise new notations

Logic

A variety of symbols are used to express logical ideas; see the

List of logic symbols In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the sub ...

Management

* Time and motion study symbols such as

therblig Therbligs are elemental motions used in the study of workplace motion economy. A workplace task is analyzed by recording each of the therblig units for a process, with the results used for optimization of manual labour by eliminating unneeded movem ...

Mathematics

Mathematical notation Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling ...

is used to represent various kinds of mathematical ideas. ** All types of notation in probability **

Cartesian coordinate system In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative number ...

, for representing position and other spatial concepts in analytic geometry **

Notation for differentiation In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a Function (mathematics), function or a dependent variable have been proposed by various mathematicians, includin ...

, common representations of the

derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

Big O notation Big ''O'' notation is a mathematical notation that describes the asymptotic analysis, limiting behavior of a function (mathematics), function when the Argument of a function, argument tends towards a particular value or infinity. Big O is a memb ...

, used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected **

Z notation The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general. History In 1974, Jean-Raymond Abria ...

, a formal notation for specifying objects using

Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes suc ...

and first-order predicate logic ** Ordinal notation **

Set-builder notation In mathematics and more specifically in set theory, set-builder notation is a notation for specifying a set by a property that characterizes its members. Specifying sets by member properties is allowed by the axiom schema of specification. Th ...

, a formal notation for defining sets in

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

* Systems to represent very large numbers **

Conway chained arrow notation Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6. As wi ...

, an arrow system **

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. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperatio ...

, an arrow system ** Steinhaus–Moser notation, Polygon Numbers **

Schläfli symbol In geometry, the Schläfli symbol is a notation of the form \ that defines List of regular polytopes and compounds, regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, wh ...

in geometry ** Symbol Levelled notation, The Ultimate Leveller *

Numeral system A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent differe ...

s, notation for writing numbers, including **

Arabic numeral The ten Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are the most commonly used symbols for writing numbers. The term often also implies a positional notation number with a decimal base, in particular when contrasted with Roman numerals. ...

s **

Roman numeral Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, ea ...

s **

Scientific notation Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientif ...

for expressing large and small numbers **

Engineering notation Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes, i.e. scientific notation that al ...

Sign-value notation A sign-value notation represents numbers using a sequence of numerals which each represent a distinct quantity, regardless of their position in the sequence. Sign-value notations are typically additive, subtractive, or multiplicative depending on ...

, using signs or symbols to represent numbers **

Positional notation Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a posit ...

also known as place-value notation, in which each position is related to the next by a multiplier which is called the ''base'' of that numeral system ***

Binary notation A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may also ...

, a positional notation in base two ***

Octal Octal (base 8) is a numeral system with eight as the base. In the decimal system, each place is a power of ten. For example: : \mathbf_ = \mathbf \times 10^1 + \mathbf \times 10^0 In the octal system, each place is a power of eight. For ex ...

notation, a positional notation in base eight, used in some computers ***

Decimal notation The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the ...

, a positional notation in base ten ***

Hexadecimal Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbo ...

notation, a positional notation in base sixteen, commonly used in computers ***

Sexagesimal Sexagesimal, also known as base 60, is a numeral system with 60 (number), sixty as its radix, base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified fo ...

notation, an ancient numeral system in base sixty * See also

Table of mathematical symbols A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula ...

- for general tokens and their definitions...

Physics

Bra–ket notation Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically de ...

, or Dirac notation, is an alternative representation of probability distributions in

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

. *

Tensor index notation In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

is used when formulating physics (particularly

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mec ...

, electromagnetism, relativistic quantum mechanics and field theory, and general relativity) in the language of

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

Typographical conventions

Infix notation Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in . Usage Binary relations are ...

, the common arithmetic and logical formula notation, such as "''a'' + ''b'' − ''c''". *

Polish notation Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation, Eastern Notation or simply prefix notation, is a mathematical notation in which Operation (mathematics), operator ...

or "prefix notation", which places the operator before the operands (arguments), such as "+ ''a'' ''b''". *

Reverse Polish notation Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators ''follow'' their operands, in contrast to prefix or Polish notation ...

or "postfix notation", which places the operator after the operands, such as "''a'' ''b'' +".

Sports and games

* Baseball scorekeeping, to represent a game of baseball * Aresti Catalogue, to represent aerobatic manoeuvres *

Chess notation Chess notation systems are used to record either the moves made or the position of the pieces in a game of chess. Chess notation is used in chess literature, and by players keeping a record of an ongoing game. The earliest systems of notation used ...

, to represent moves in a game of chess ** Algebraic notation ***

Portable Game Notation Portable Game Notation (PGN) is a standard plain text format for recording chess games (both the moves and related data), which can be read by humans and is also supported by most chess software. History PGN was devised around 1993, by Steven J ...

Descriptive notation Descriptive notation is a chess notation system based on abbreviated natural language. Its distinctive features are that it refers to files by the piece that occupies the back rank square in the starting position and that it describes each square ...

Forsyth–Edwards Notation Forsyth–Edwards Notation (FEN) is a standard Chess notation, notation for describing a particular board position of a chess game. The purpose of FEN is to provide all the necessary information to restart a game from a particular position. FEN i ...

* Siteswap notation represents a juggling pattern as a sequence of numbers * Singmaster notation, to represent Rubik's Cube moves

Graphical notations

Music

Musical notation Musical notation is any system used to visually represent music. Systems of notation generally represent the elements of a piece of music that are considered important for its performance in the context of a given musical tradition. The proce ...

permits a composer to express musical ideas in a musical composition, which can be read and interpreted during performance by a trained musician; there are many different ways to do this (hundreds have been proposed), although

staff notation In Western musical notation, the staff"staff" in the Collins English Di ...

provides by far the most widely used system of modern musical symbols.

Dance and movement

* Benesh Movement Notation permits a graphical representation of human bodily movements * Laban Movement Analysis or

Labanotation Labanotation (grammatically correct form "Labannotation" or "Laban notation" is uncommon) is a system for analyzing and recording human movement (Notation, notation system), invented by Austro-Hungarian choreographer and dancer Rudolf von Laban ...

permits a graphical representation of human bodily movements * Eshkol-Wachman Movement Notation permits a graphical representation of bodily movements of other species in addition to humans, and indeed any kind of movement (e.g. aircraft aerobatics) * Juggling diagrams represent juggling patterns * Aresti aerobatic symbols provides a way to represent flight maneuvers in aerobatics

Science

Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced ...

s permit a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory *

Structural formula The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are connected to one another. The chemical bonding within the molecule is al ...

s are graphical representations of molecules *

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between set (mathematics), sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple ...

s shows logical relations between a finite collection of sets. * Drakon-charts are a graphical representation of algorithms and procedural knowledge. *

Unified Modeling Language The Unified Modeling Language (UML) is a general-purpose visual modeling language that is intended to provide a standard way to visualize the design of a system. UML provides a standard notation for many types of diagrams which can be roughly ...

is a standard notation for many types of diagrams

Other systems

Whyte notation The Whyte notation is a classification method for steam locomotives, and some internal combustion locomotives and electric locomotives, by wheel arrangement. It was devised by Frederick Methvan Whyte, and came into use in the early twenti ...

for classifying steam locomotives by wheel arrangement