Written communication

• Phonographic writing systems, by definition, use symbols to represent components of auditory language, i.e. speech
  Speech
  Speech is the human faculty of speaking.It may also refer to:* Public speaking, the process of speaking to a group of people* Manner of articulation, how the body parts involved in making speech are manipulated...
  
  , which in turn refers to things or ideas. The two main kinds of phonographic notational system are the alphabet
  Alphabet
  An alphabet is a standard set of letters—basic written symbols or graphemes—each of which represents a phoneme in a spoken language, either as it exists now or as it was in the past. There are other systems, such as logographies, in which each character represents a word, morpheme, or semantic...
  
   and syllabary
  Syllabary
  A syllabary is a set of written symbols that represent syllables, which make up words. In a syllabary, there is no systematic similarity between the symbols which represent syllables with the same consonant or vowel...
  
  . Some written languages are more consistent in their correlation of written symbol or grapheme and sound or phoneme
  Phoneme
  In a language or dialect, a phoneme is the smallest segmental unit of sound employed to form meaningful contrasts between utterances....
  
  , and are therefore considered to have better Phonemic orthography
  Phonemic orthography
  A phonemic orthography is a writing system where the written graphemes correspond to phonemes, the spoken sounds of the language. In terms of orthographic depth, these are termed shallow orthographies, contrasting with deep orthographies...
  
  .
• Ideographic writing, by definition, refers to things or ideas independently of their pronunciation in any language. All of the notational systems listed below are ideographic. Some ideographic systems are also Pictogram
  Pictogram
  A pictograph, also called pictogram or pictogramme is an ideogram that conveys its meaning through its pictorial resemblance to a physical object. Pictographs are often used in writing and graphic systems in which the characters are to considerable extent pictorial in appearance.Pictography is a...
  
  s that convey meaning through their pictorial resemblance to a physical object.

Biology and Medicine

• Nucleic acid notation
  Nucleic acid notation
  The nucleic acid notation currently in use was first formalized by the International Union of Pure and Applied Chemistry in 1970. This universally accepted notation uses the Roman characters G, C, A, and T, to represent the four nucleotides commonly found in deoxyribonucleic acids...
  
  
• Systems Biology Graphical Notation
  Systems Biology Graphical Notation
  The Systems Biology Graphical Notation is a standard graphical representation crafted over several years by a community of biochemists, modelers and computer scientists....
  
   (SBGN) — orthogonal notations for Process Descriptions, Entity Relationships, and Activity Flows
• Pattern description notations used to describe sequence motif
  Sequence motif
  In genetics, a sequence motif is a nucleotide or amino-acid sequence pattern that is widespread and has, or is conjectured to have, a biological significance...
  
  s
• Cytogenetic notation
  Cytogenetic notation
  The following table summarizes symbols and abbreviations used in cytogenetics:...
  
  

Chemistry

• Chemical formula
  Chemical formula
  A chemical formula or molecular formula is a way of expressing information about the atoms that constitute a particular chemical compound....
  
  s are a way of expressing information about the atoms that constitute a particular chemical compound, e.g. H2O or C6H12O6
• Structural formula
  Structural formula
  The structural formula of a chemical compound is a graphical representation of the molecular structure, showing how the atoms are arranged. The chemical bonding within the molecule is also shown, either explicitly or implicitly...
  
  s are graphical representations of the molecular structure, showing how the atoms are arranged
• Nuclear notation
  Nuclear notation
  Nuclear notation is a common notation used in chemistry and physics to indicate the atomic number and mass number of an isotope.Nuclear notation is formed by writing an elemental symbol preceded by a subscript indicating its atomic number and a superscript indicating its mass number...
  
   provides a convention in chemistry and physics to indicate the atomic number and mass number of an isotope.

Dance and movement

• Benesh Movement Notation
  Benesh movement notation
  Benesh Movement Notation is a system of dance notation that can document any form of dance or human movement...
  
   permits a graphical representation of human bodily movements
• Laban Movement Analysis
  Laban Movement Analysis
  Laban is a way and language for interpreting, describing, visualizing and notating all ways of human movement. Created by Rudolf Laban, LMA draws on his theories of effort and shape to describe, interpret and document human movement...
  
   or Labanotation permits a graphical representation of human bodily movements
• Eshkol-Wachman Movement Notation
  Eshkol-Wachman Movement Notation
  Eshkol-Wachman Movement Notation is a notation system for recording movement on paper or computer screen. The system was created in Israel by dance theorist Noa Eshkol and Avraham Wachman, a professor of architecture at the Technion.The system is used in many fields, including dance, physical...
  
   permits a graphical representation of bodily movements of other species in addition to humans, and indeed any kind of movement (e.g. aircraft aerobatics)
• Aresti aerobatic symbols
  Aresti Catalog
  The Aresti Catalog is the Fédération Aéronautique Internationale standards document enumerating the aerobatic manoeuvers permitted in aerobatic competition...
  
   provides a way to represent flight maneuvers in aerobatics

Logic

Mathematics

• Mathematical notation
  Mathematical notation
  Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...
  
   is used to represent various kinds of mathematical ideas.
  • All types of notation in probability
    Notation in probability
    Probability theory and statistics has some commonly used conventions of its own, in addition to standard mathematical notation and mathematical symbols.-Probability theory:* Random variables are usually written in upper case roman letters: X, Y, etc....
    
    
  • Cartesian coordinate system
    Cartesian coordinate system
    A Cartesian coordinate system 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...
    
    , for representing position and other spatial concepts in analytic geometry
  • Notation for differentiation
    Notation for differentiation
    In differential calculus, there is no single uniform notation for differentiation. Instead, several different notations for the derivative of a function or variable have been proposed by different mathematicians. The usefulness of each notation varies with the context, and it is sometimes...
    
    , common representations of the derivative
    Derivative
    In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
    
     in calculus
    Calculus
    Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
    
    
  • Big O notation
    Big O notation
    In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...
    
    , used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected
  • Z notation
    Z notation
    The Z notation , named after Zermelo–Fraenkel set theory, 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:...
    
    , a formal notation for specifying objects using Zermelo-Fraenkel set theory and first-order predicate logic
  • Ordinal notation
    Ordinal notation
    In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language....
    
    
  • Set-builder notation
    Set-builder notation
    In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy...
    
    , a formal notation for defining sets in set theory
    Set theory
    Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
    
    
• Systems to represent very large numbers
  • Conway chained arrow notation
    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 → 3 → 4 → 5 → 6.As with most...
    
    
  • Knuth's up-arrow notation
    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. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated...
    
    
  • Steinhaus–Moser notation
    Steinhaus–Moser notation
    In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.- Definitions :...
    
    
• Numeral system
  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 graphemes or symbols in a consistent manner....
  
  s, notation for writing numbers, including
  • Arabic numerals
  • Roman numerals
  • Scientific notation
    Scientific notation
    Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...
    
     for expressing large and small numbers
  • Sign-value notation
    Sign-value notation
    A sign-value notation represents numbers by a series of numeric signs that added together equal the number represented. In Roman numerals for example, X means ten and L means fifty. Hence LXXX means eighty . There is no need for zero in sign-value notation...
    
    , using signs or symbols to represent numbers
  • Positional notation
    Positional notation
    Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...
    
     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 positional notation in base two
    • Octal
      Octal
      The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...
      
       notation, a positional notation in base eight, used in some computers
    • Decimal notation, a positional notation in base ten
    • Hexadecimal
      Hexadecimal
      In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
      
       notation, a positional notation in base sixteen, commonly used in computers
    • Sexagesimal notation, an ancient numeral system in base sixty
• See also Table of mathematical symbols
  Table of mathematical symbols
  This is a listing of common symbols found within all branches of mathematics. Each symbol is listed in both HTML, which depends on appropriate fonts being installed, and in , as an image.-Symbols:-Variations:...
  
   - for general tokens and their definitions...

Music

• Musical notation
  Musical notation
  Music notation or musical notation is any system that represents aurally perceived music, through the use of written symbols.-History:...
  
   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 provides by far the most widely used Modern musical symbols
  Modern musical symbols
  Modern musical symbols are the marks and symbols that are widely used in musical scores of all styles and instruments today. This is intended to be a comprehensive guide to the various symbols encountered in modern musical notation.- Lines :- Clefs :...
  
  .

Physics

• Bra-ket notation
  Bra-ket notation
  Bra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...
  
   or Dirac Notation is another representation of probability in quantum mechanics
• Tensor notation is a general way to represent a gravitational field in general relativity
• Feynman Diagrams permit a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory

Typographical conventions

• Infix notation
  Infix notation
  Infix notation is the common arithmetic and logical formula notation, in which operators are written infix-style between the operands they act on . It is not as simple to parse by computers as prefix notation or postfix notation Infix notation is the common arithmetic and logical formula notation,...
  
  , the common arithmetic and logical formula notation, such as a+b-c
• Polish notation
  Polish notation
  Polish notation, also known as prefix notation, is a form of notation for logic, arithmetic, and algebra. Its distinguishing feature is that it places operators to the left of their operands. If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that...
  
   or "prefix notation", which places the operator before the operands (arguments), such as + a b
• Reverse Polish notation
  Reverse Polish notation
  Reverse Polish notation is a mathematical notation wherein every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as Postfix notation and is parenthesis-free as long as operator arities are fixed...
  
   or "postfix notation", which places the operator after the operands, such as a b +

Other systems

• Baseball scorekeeping
  Baseball scorekeeping
  Baseball scorekeeping is the practice of recording the details of a baseball game as it unfolds. Professional baseball leagues hire official scorers to keep an official record of each game , but many fans keep score as well for their own enjoyment...
  
  , to represent a game of baseball
• Chess notation
  Chess notation
  Chess notation is the term for several systems that have developed to record either the moves made during a game of chess or the position of the pieces on a chess board. The earliest systems of notation used lengthy narratives to describe each move; these gradually evolved into terser systems of...
  
  , to represent moves in a game of chess
• New Epoch Art Notation, to represent the creation of a visual image using any physical media
• Hungarian notation
  Hungarian notation
  Hungarian notation is an identifier naming convention in computer programming, in which the name of a variable or function indicates its type or intended use...
  
  , to represent the type
  Data type
  In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
  
   or intended use of a variable within its name in computer programming
  Computer programming
  Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...
  
  
• Whyte notation
  Whyte notation
  The Whyte notation for classifying steam locomotives by wheel arrangement was devised by Frederick Methvan Whyte and came into use in the early twentieth century encouraged by an editorial in American Engineer and Railroad Journal...