List of mathematical abbreviations

• AC – Axiom of Choice, or set of absolutely continuous functions.
• a.c. – absolutely continuous.
• acrd – inverse chord function.
• ad – adjoint representation of a Lie group.
• adj – adjugate of a matrix.
• a.e. – almost everywhere.
• Ai – Airy function.
• AL – Action limit.
• Alt – alternating group
• A.M. – arithmetic mean.
• arccos – inverse cosine function.
• arccosec – inverse cosecant function.
• arccot – inverse cotangent function.
• arccsc – inverse cosecant function.
• arcexc – inverse excosecant function.
• arcexcosec – inverse excosecant function.
• arcexcsc – inverse excosecant function.
• arcexs – inverse exsecant function.
• arcexsec – inverse exsecant function.
• arcosech – inverse hyperbolic cosecant function.
• arcosh – inverse hyperbolic cosine function.
• arcoth – inverse hyperbolic cotangent function.
• arcsch – inverse hyperbolic cosecant function.
• arcsec – inverse secant function.
• arcsin – inverse sine function.
• arctan – inverse tangent function.
• arctan2 – inverse tangent function with two arguments.
• 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.
• A.P. – arithmetic progression.
• Aut – automorphism group.
• bd – boundary.
• 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.
• 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.
• Cl – conjugacy class.
• cl – topological closure.
• cod, codom – codomain.
• cok, coker – cokernel.
• conv – convex hull of a set.
• Cor – corollary.
• corr – correlation.
• cos – cosine function.
• cosec – cosecant function.
• cosech – hyperbolic cosecant function.
• cosh – hyperbolic cosine function.
• cosiv – coversine function.
• cot – cotangent function.
• coth – hyperbolic cotangent function.
• cov – covariance of a pair of random variables.
• cover – coversine function.
• covercos – covercosine function.
• covers – coversine function.
• crd – chord function.
• csc – cosecant function.
• csch – hyperbolic cosecant function.
• ctg – cotangent function.
• curl – curl of a vector field.
• cvc – covercosine function.
• cvs – coversine function.
• def – define or definition.
• deg – degree of a polynomial.
• del – del, a differential operator.
• det – determinant of a matrix or linear transformation.
• dim – dimension of a vector space.
• div – divergence of a vector field.
• dkl – decalitre
• DNE – a solution for an expression does not exist, or is undefined. Generally used with limits and integrals.
• dom – domain of a function.
• 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.
• excosec — excosecant function.
• excsc — excosecant function.
• exs — exsecant function.
• exsec — exsecant function.
• exp – exponential function.
• expi – cos + i sin function.
• expm1 – exponential minus 1 function.
• exp1m – exponential minus 1 function.
• 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.
• Frob – Frobenius endomorphism.
• Gal – Galois group.
• gcd – greatest common divisor of two numbers.
• gd – Gudermannian function.
• GF – Galois field.
• GF – Generating function.
• OBGF – ordinary bivariate generating function
• MGF - moment generating function
• GL – general linear group.
• G.M. – geometric mean.
• glb – greatest lower bound.
• G.P. – geometric progression.
• grad – gradient of a function.
• hacover – hacoversine function.
• hacovercos – hacovercosine function.
• hacovers – hacoversine function.
• hav – haversine function.
• havercos – havercosine function.
• hcc – hacovercosine function.
• hcv – hacoversine function.
• hcf – highest common factor of two numbers.
• 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.
• 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.
• im – image
• inf – infimum of a set.
• int – interior.
• I.o. – Infinitely often.
• ker – kernel.
• lb – binary logarithm.
• lcm – lowest common multiple or least common multiple of two numbers.
• LCHS - Locally Compact Hausdorff second Countable
• ld – binary logarithm.
• lerp – linear interpolation.
• lg – common logarithm or binary logarithm.
• 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.
• lnp1 – natural logarithm plus 1 function.
• ln1p – natural logarithm plus 1 function.
• log – logarithm.
• logh – natural logarithm, log_e.
• LST – language of set theory.
• lub – least upper bound.
• max – maximum of a set.
• M.I. – mathematical induction.
• min – minimum of a set.
• mod – modulo.
• Mp – metaplectic group.
• mtanh – modified hyperbolic tangent function.
• mth – modified hyperbolic tangent function.
• mx – matrix.
• NAND – not-and in logic.
• No. – number.
• NOR – not-or in logic.
• NTS – need to show.
• 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.
• 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 construction.
• ran – range of a function.
• rank – rank.
• Re – real part of a complex number.
• resp – respectively.
• RHS – right-hand side of an equation.
• rk – rank.
• RMS, rms – root mean square.
• rng – non-unital ring.
• rot – rotor of a vector field.
• RTP – required to prove.
• RV – Random Variable.
• SD - standard deviation
• SE - standard error
• sec – secant function.
• sech – hyperbolic secant function.
• seg – initial segment of.
• sem – haversine function.
• SFIP – strong finite intersection property.
• sgn – signum function.
• Shi – hyperbolic sine integral function.
• Si – sine integral function.
• sin – sine function.
• sinc – sinc function.
• sinh – hyperbolic sine function.
• siv – versine function.
• 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.
• Spec – spectrum of a ring.
• Spin – spin group.
• s.t. – such that or so that or subject to.
• st – standard part function.
• STP – sufficient to prove.
• SU – special unitary group.
• sup – supremum of a set.
• supp – support of a function.
• swish – swish function, an activation function in data analysis.
• Sym – symmetric group or symmetric algebra.
• tan – tangent function.
• tanh – hyperbolic tangent function.
• TFAE – the following are equivalent.
• tg – tangent function.
• tgn – tangent function.
• 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.
• ver – versine function.
• vercos – vercosine function.
• vers – versine function.
• 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.
• 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 of set theory.