List of mathematical abbreviations

This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology.


 * This list is limited to abbreviations of two or more letters (excluding number sets). The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.

A

 * A – adele ring or algebraic numbers.
 * AC – Axiom of Choice, or set of absolutely continuous functions.
 * a.c. – absolutely continuous.
 * acrd – inverse chord function.
 * ad – adjoint representation (or adjoint action) of a Lie group.
 * adj – adjugate of a matrix.
 * a.e. – almost everywhere.
 * AFSOC - Assume for the sake of contradiction
 * Ai – Airy function.
 * AL – Action limit.
 * Alt – alternating group (Alt(n) is also written as An.)
 * A.M. – arithmetic mean.
 * AP – arithmetic progression.
 * arccos – inverse cosine function.
 * arccosec – inverse cosecant function. (Also written as arccsc.)
 * arccot – inverse cotangent function.
 * arccsc – inverse cosecant function. (Also written as arccosec.)
 * arcexc – inverse excosecant function. (Also written as arcexcsc, arcexcosec.)
 * arcexcosec – inverse excosecant function. (Also written as arcexcsc, arcexc.)
 * arcexcsc – inverse excosecant function. (Also written as arcexcosec, arcexc.)
 * arcexs – inverse exsecant function. (Also written as arcexsec.)
 * arcexsec – inverse exsecant function. (Also written as arcexs.)
 * 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.
 * arctan2 – inverse tangent function with two arguments. (Also written as atan2.)
 * arg – argument of.
 * 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.
 * atan2 – inverse tangent function with two arguments. (Also written as arctan2.)
 * A.P. – arithmetic progression.
 * Aut – automorphism group.

B

 * bd – boundary. (Also written as fr or ∂.)
 * Bi – Airy function of the second kind.
 * BIDMAS – Brackets, Indices, Divide, Multiply, Add, Subtract.
 * Bias – bias of an estimator.
 * BWOC – by way of contradiction.

C

 * C – complex numbers.
 * Card – cardinality of a set. (Card(X) is also written #X, ♯X or |X|.)
 * cas – cos + sin function.
 * cdf – cumulative distribution function.
 * c.f. – cumulative frequency.
 * c.c. – complex conjugate.
 * char – characteristic of a ring.
 * Chi – hyperbolic cosine integral function.
 * Ci – cosine integral function.
 * cis – cos + i sin function. (Also written as expi.)
 * Cl – conjugacy class.
 * cl – topological closure.
 * CLT – central limit theorem.
 * cod, codom – codomain.
 * cok, coker – cokernel.
 * colsp – column space of a matrix.
 * conv – convex hull of a set.
 * Cor – corollary.
 * corr – correlation.
 * cos – cosine function.
 * cosec – cosecant function. (Also written as csc.)
 * cosech – hyperbolic cosecant function. (Also written as csch.)
 * cosh – hyperbolic cosine function.
 * cosiv – coversine function. (Also written as cover, covers, cvs.)
 * cot – cotangent function. (Also written as ctg.)
 * coth – hyperbolic cotangent function.
 * cov – covariance of a pair of random variables.
 * cover – coversine function. (Also written as covers, cvs, cosiv.)
 * covercos – covercosine function. (Also written as cvc.)
 * covers – coversine function. (Also written as cover, cvs, cosiv.)
 * crd – chord function.
 * CRT – Chinese remainder theorem.
 * csc – cosecant function. (Also written as cosec.)
 * csch – hyperbolic cosecant function. (Also written as cosech.)
 * ctg – cotangent function. (Also written as cot.)
 * curl – curl of a vector field. (Also written as rot.)
 * cvc – covercosine function. (Also written as covercos.)
 * cvs – coversine function. (Also written as cover, covers, cosiv.)

D

 * def – define or definition.
 * deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.)
 * del – del, a differential operator. (Also written as $$\nabla$$.)
 * det – determinant of a matrix or linear transformation.
 * DFT – discrete Fourier transform.
 * 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 – domain of a function. (Or, more generally, a relation.)

E

 * End – categories of endomorphisms.
 * Ei – exponential integral function.
 * epi – epigraph of a function.
 * Eqn – equation.
 * erf – error function.
 * erfc – complementary error function.
 * erfcx – scaled complementary error function.
 * erfi – imaginary error function.
 * etr – exponent of the trace.
 * exc – excosecant function. (Also written as excsc, excosec.)
 * excosec – excosecant function. (Also written as excsc, exc.)
 * excsc – excosecant function. (Also written as excosec, exc.)
 * exs – exsecant function. (Also written as exsec.)
 * exsec – exsecant function. (Also written as exs.)
 * exp – exponential function. (exp x is also written as ex.)
 * expi – cos + i sin function. (Also written as cis.)
 * expm1 – exponential minus 1 function. (Also written as exp1m.)
 * exp1m – exponential minus 1 function. (Also written as expm1.)
 * Ext – Ext functor.
 * ext – exterior.
 * extr – a set of extreme points of a set.

F

 * FFT – fast Fourier transform.
 * FIP – finite intersection property.
 * FOC – first order condition.
 * FOL – first-order logic.
 * fr – boundary. (Also written as bd or ∂.)
 * Frob – Frobenius endomorphism.
 * FT – Fourier transform.
 * FTA – fundamental theorem of arithmetic or fundamental theorem of algebra.

G

 * Gal – Galois group. (Also written as Γ.)
 * gcd – greatest common divisor of two numbers. (Also written as hcf.)
 * gd – Gudermannian function.
 * GF – Galois field.
 * GF – generating function.
 * GL – general linear group.
 * G.M. – geometric mean.
 * glb – greatest lower bound. (Also written as inf.)
 * G.P. – geometric progression.
 * grad – gradient of a function.
 * graph – graph of a function.

H

 * H – quaternion numbers.
 * hacover – hacoversine function. (Also written as hacovers, hcv.)
 * hacovercos – hacovercosine function. (Also written as hcc.)
 * hacovers – hacoversine function. (Also written as hacover, hcv.)
 * hav – haversine function. (Also written as sem.)
 * havercos – havercosine function. (Also written as hvc.)
 * h.c. – Hermitian conjugate, often used as part of + h.c. (Also written as H.c.)
 * hcc – hacovercosine function. (Also written as hacovercos.)
 * hcv – hacoversine function. (Also written as hacover, hacovers.)
 * hcf – highest common factor of two numbers. (Also written as gcd.)
 * H.M. – harmonic mean.
 * HOL – higher-order logic.
 * Hom – Hom functor.
 * hom – hom-class.
 * hot – higher order term.
 * HOTPO – half or triple plus one.
 * hvc – havercosine function. (Also written as havercos.)
 * hyp – hypograph of a function.

I

 * iff – if and only if.
 * IH – induction hypothesis.
 * iid – independent and identically distributed random variables.
 * Im – imaginary part of a complex number. (Also written as $$\Im$$.)
 * im – image.
 * inf – infimum of a set. (Also written as glb.)
 * int – interior.
 * I.o. – Infinitely often.

K

 * ker – kernel.

L

 * lb – binary logarithm (log2). (Also written as ld.)
 * lcm – lowest common multiple (a.k.a. least common multiple) of two numbers.
 * LCHS – locally compact Hausdorff second countable.
 * ld – binary logarithm (log2). (Also written as lb.)
 * lsc – lower semi-continuity.
 * 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.
 * LLN – law of large numbers.
 * ln – natural logarithm, loge.
 * lnp1 – natural logarithm plus 1 function.
 * ln1p – natural logarithm plus 1 function.
 * log – logarithm. (If without a subscript, this may mean either log10 or loge.)
 * logh – natural logarithm, loge.
 * LST – language of set theory.
 * lub – least upper bound. (Also written sup.)

M

 * max – maximum of a set.
 * MGF – moment-generating function.
 * M.I. – mathematical induction.
 * min – minimum of a set.
 * mod – modulo.
 * Mp – metaplectic group.
 * mtanh – modified hyperbolic tangent function. (Also written as mth.)
 * mth – modified hyperbolic tangent function. (Also written as mtanh.)
 * mx – matrix.

N

 * N – natural numbers.
 * NAND – not-and in logic.
 * No. – number.
 * NOR – not-or in logic.
 * NTS – need to show.
 * Null, null – (See Kernel.)
 * Nullity, nullity – nullity.

O

 * O – octonion numbers.
 * OBGF – ordinary bivariate generating function.
 * ob – object class.
 * ord – ordinal number of a well-ordered set.

P

 * pdf – probability density function.
 * pf – proof.
 * PGL – projective general linear group.
 * Pin – pin group.
 * pmf – probability mass function.
 * Pn – previous number.
 * Pr – probability of an event. (See Probability theory. Also written as P or $$\mathbb{P}$$.)
 * probit – probit function.
 * PRNG – pseudorandom number generator.
 * PSL – projective special linear group.
 * PNT – prime number theorem.
 * PRP – probable prime.
 * PSO – projective orthogonal group.
 * PSU – projective special unitary group.
 * PU – projective unitary group.

Q

 * Q – rational numbers.
 * 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 geometrical construction.

R

 * R – real numbers.
 * ran – range of a function.
 * rank – rank of a matrix. (Also written as rk.)
 * Re – real part of a complex number. (Also written $$\Re$$.)
 * resp – respectively.
 * RHS – right-hand side of an equation.
 * rk – rank. (Also written as rank.)
 * RMS, rms – root mean square.
 * rng – non-unital ring.
 * rot – rotor of a vector field. (Also written as curl.)
 * rowsp – row space of a matrix.
 * RTP – required to prove.
 * RV – random variable. (Also written as R.V.)

S

 * S – sedenion numbers.
 * SD – standard deviation.
 * SE – standard error.
 * sec – secant function.
 * sech – hyperbolic secant function.
 * seg – initial segment of.
 * sem – haversine function. (Also written as hav.)
 * SFIP – strong finite intersection property.
 * sgn – sign function.
 * Shi – hyperbolic sine integral function.
 * Si – sine integral function.
 * sigmoid – sigmoid function.
 * sin – sine function.
 * sinc – sinc function.
 * sinh – hyperbolic sine function.
 * siv – versine function. (Also written as ver, vers.)
 * SL – special linear group.
 * SO – special orthogonal group.
 * SOC – second order condition.
 * Soln – solution.
 * Sp – symplectic group.
 * Sp – trace of a matrix, from the German "spur" used for the trace.
 * sp, span – linear span of a set of vectors. (Also written with angle brackets.)
 * Spec – spectrum of a ring.
 * Spin – spin group.
 * sqrt – square root.
 * s.t. – such that or so that or subject to.
 * st – standard part function.
 * STP – [it is] sufficient to prove.
 * SU – special unitary group.
 * sup – supremum of a set. (Also written as lub, which stands for least upper bound.)
 * supp – support of a function.
 * swish – swish function, an activation function in data analysis.
 * Sym – symmetric group (Sym(n) is also written as Sn) or symmetric algebra.

T

 * tan – tangent function. (Also written as tgn, tg.)
 * tanh – hyperbolic tangent function.
 * TFAE – the following are equivalent.
 * tg – tangent function. (Also written as tan, tgn.)
 * tgn – tangent function. (Also written as tan, tg.)
 * Thm – theorem.
 * Tor – Tor functor.
 * Tr – field trace.
 * tr – trace of a matrix or linear transformation. (Also written as Sp.)

U

 * undef – a function or expression is undefined.
 * usc – upper semi-continuity.

V

 * V – volume.
 * var – variance of a random variable.
 * vcs – vercosine function. (Also written as vercos.)
 * ver – versine function. (Also written as vers, siv.)
 * vercos – vercosine function. (Also written as vcs.)
 * vers – versine function. (Also written as ver, siv.)

W

 * W^5 – which was what we wanted. Synonym of Q.E.D.
 * walog – without any loss of generality.
 * wff – well-formed formula.
 * whp – with high probability.
 * wlog – without loss of generality.
 * WMA – we may assume.
 * WO – well-ordered set.
 * WOP – well-ordered principle.
 * w.p. – with probability.
 * wp1 – with probability 1.
 * wrt – with respect to or with regard to.
 * WTP – want to prove.
 * WTS – want to show.

X

 * XOR – exclusive or in logic.

Z

 * Z – integer numbers.
 * ZF – Zermelo–Fraenkel axioms of set theory.
 * ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.