List of mathematical abbreviations

This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology.

This list is limited to abbreviations of two or more letters. The capitalization of some of these abbreviations is not standardized – different authors use different capitalizations.

This list is incomplete; you can help by expanding it.

• AC – Axiom of Choice.
• adj – adjugate of a matrix.
• a.e. – almost everywhere
• Ai – Airy function.
• Alt – alternating group (Alt(n) is also written as A_n.)
• arccos – inverse cosine function.
• arccosec – inverse cosecant function. (Also written as arccsc.)
• arccot – inverse cotangent function.
• arccsc – inverse cosecant function. (Also written as arccosec.)
• arcosech – inverse hyperbolic cosecant function. (Also written as arcsch.)
• arcosh – inverse hyperbolic cosine function.
• arcoth – inverse hyperbolic cotangent function.
• arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.)
• arcsec – inverse secant function.
• arcsin – inverse sine function.
• arctan – inverse tangent function.
• arg – argument of a complex number.
• arg max – argument of the maximum.
• arg min – argument of the minimum.
• arsech – inverse hyperbolic secant function.
• arsinh – inverse hyperbolic sine function.
• artanh – inverse hyperbolic tangent function.
• a.s. – almost surely
• Aut – automorphism group.
• Bi – Airy function of the second kind.
• Card – cardinality of a set. (Card(X) is also written #X, ♯X or |X|.)
• cdf – cumulative distribution function.
• char – characteristic of a ring.
• Chi - hyperbolic cosine integral function.
• Ci - cosine integral function.
• cis - cos + i sin function.
• Cl – topological closure.
• cod – codomain. (Also written as codom.)
• codom – codomain. (Also written as cod.)
• cos – cosine function.
• cosec – cosecant function. (Also written as csc.)
• cosech – hyperbolic cosecant function. (Also written as csch.)
• cosh – hyperbolic cosine function.
• cot – cotangent function.
• coth – hyperbolic cotangent function.
• cov – covariance of a pair of random variables.
• csc – cosecant function. (Also written as cosec.)
• csch – hyperbolic cosecant function. (Also written as cosech.)
• curl – curl of a vector field. (Also written as rot.)
• deg – degree of a polynomial. (Also written as ∂.)
• del – del, a differential operator. (Also written as $\nabla$.)
• det – determinant of a matrix or linear transformation.
• dim – dimension of a vector space.
• div – divergence of a vector field.
• DNE - a solution for an expression does not exist, or is undefined. Generally used with limits and integrals.
• dom – domain of a function. (Or, more generally, a relation.)
• End – categories of endomorphisms.
• Ei – exponential integral function.
• erf – error function.
• erfc – complementary error function.
• exp – exponential function. (exp x is also written as e^x.)
• Ext – Ext functor.
• ext – exterior.
• FOL – first-order logic.
• Frob – Frobenius endomorphism.
• Gal – Galois group. (Also written as Γ.)
• gcd – greatest common divisor of two numbers. (Also written as hcf.)
• GF - Galois field.
• GL – general linear group.
• glb – greatest lower bound. (Also written as inf.)
• grad – gradient of a scalar field.
• hcf – highest common factor of two numbers. (Also written as gcd.)
• HOL – higher-order logic.
• Hom – Hom functor.
• iff – if and only if.
• Im – either image of a function or imaginary part of a complex number (which is also written $\Im$).
• inf – infimum of a set. (Also written as glb.)
• int – interior.
• Ker – kernel.
• lcm – lowest common multiple of two numbers.
• lerp – linear interpolation.
• lg – common logarithm (log₁₀) or binary logarithm (log₂).
• LHS – left-hand side of an equation.
• Li – offset logarithmic integral function.
• li – logarithmic integral function or linearly independent.
• lim – limit of a sequence, or of a function.
• lim inf – limit inferior.
• lim sup – limit superior.
• ln – natural logarithm, log_e.
• log – logarithm. (If without a subscript, this may mean either log₁₀ or log_e.)
• logh - natural logarithm, log_e.
• LST – language of set theory.
• lub – least upper bound. (Also written sup.)
• max – maximum of a set.
• min – minimum of a set.
• mod – modulo.
• mx – matrix.
• NAND - not-and in logic.
• NOR - not-or in logic.
• NTS – need to show.
• ord – ordinal number of a well-ordered set.
• pdf – probability density function.
• pf – proof.
• PGL – projective general linear group.
• pmf – probability mass function.
• Pr – probability of an event. (See Probability theory. Also written as P or $\mathbb{P}$.)
• PSL – projective special linear group.
• QED – "Quod erat demonstrandum", a Latin phrase used at the end of a definitive proof.
• QEF - "quod erat faciendum", a Latin phrase sometimes used at the end of a construction.
• ran – range of a function.
• Re – real part of a complex number. (Also written $\Re$.)
• resp – respectively.
• RHS – right-hand side of an equation.
• Rk – rank.
• rng – non-unital ring.
• rot – rotor of a vector field. (Also written as curl.)
• RTP – required to prove.
• RV – Random Variable. (or as R.V.)
• sec – secant function.
• sech – hyperbolic secant function.
• seg – initial segment of.
• sgn – signum function.
• Shi - hyperbolic sine integral function.
• Si - sine integral function.
• sin – sine function.
• sinc – sinc function.
• sinh – hyperbolic sine function.
• SL – special linear group.
• Sp – linear span of a set of vectors. (Also written with angle brackets.)
• Spec – spectrum of a ring.
• st – such that or so that.
• STP – [it is] sufficient to prove.
• sup – supremum of a set. (Also written lub.)
• supp – support of a function.
• Sym – symmetric group (Sym(n) is also written as S_n.)
• tan – tangent function.
• tanh – hyperbolic tangent function.
• TFAE – the following are equivalent.
• Thm – theorem.
• Tor – Tor functor.
• Tr – trace, either the field trace, or the trace of a matrix or linear transformation.
• undef - a function or expression is undefined
• var – variance of a random variable.
• W^5 – which was what we wanted. Synonym of Q.E.D.
• walog – without any loss of generality.
• wff – well-formed formula.
• wlog – without loss of generality.
• WMA - we may assume.
• WO – well-ordered set.
• wrt – with respect to or with regard to.
• WTP – want to prove.
• WTS – want to show.
• XOR - exclusive or in logic.
• ZF – Zermelo–Fraenkel axioms of set theory.
• ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.

See also

• Greek letters used in mathematics, science, and engineering
• ISO 31-11
• Mathematical alphanumeric symbols
• Mathematical jargon
• Mathematical notation
• Notation in probability and statistics
• Physical constants
• Roman letters used in mathematics
• Table of logic symbols
• Table of mathematical symbols
• Unicode mathematical operators