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. The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations. * 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. * Ai – Airy function. * AL – . * Alt – alternating group (Alt(n) is also written as An.) * A.M. – arithmetic mean. * 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. * 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 * 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. * 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. * 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.) * 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 .) * 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. * epi – epigraph of a function. * Eqn – equation. * erf – error function. * erfc – complementary 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. * FIP – finite intersection property. * FOC – first order condition. * FOL – first-order logic. * fr – boundary. (Also written as bd or ∂.) * Frob – Frobenius endomorphism. * 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. * 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.) * 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. * 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 – image * inf – infimum of a set. (Also written as glb.) * int – interior. * I.o. – Infinitely often. * ker – kernel. * 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.) * 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.) * 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. * NAND – not-and in logic. * No. – number. * NOR – not-or in logic. * NTS – need to show. * OBGF – ordinary bivariate generating function. * ob – object class. * ord – ordinal number of a well-ordered set. * 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 .) * PSL – projective special linear group. * PSO – projective orthogonal group. * PSU – projective special unitary group. * PU – projective unitary 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 geometrical construction. * ran – range of a function. * rank – rank of a matrix. (Also written as rk.) * Re – real part of a complex number. (Also written .) * 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.) * RTP – required to prove. * RV – random variable. (or as R.V.) * R - Real 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. * 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 – linear span of a set of vectors. (Also written as span or written with angle brackets.) * Spec – spectrum of a ring. * Spin – spin group. * 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. * 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 – trace, either the field trace, or the trace of a matrix or linear transformation. * undef – a function or expression is undefined * 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^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. * wp1 – with probability 1. * 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. (Wikipedia).