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,^[1] 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 A_n.)
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^[2]
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.^[3]
Bias – bias of an estimator
BWOC – by way of contradiction
Card – cardinality of a set.^[4] (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 $\nabla$ .)
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.^[1] (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 e^x.)
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^[2] (Also written as $\Im$ ).
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.^[5]
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, log_e.
lnp1 – natural logarithm plus 1 function.
ln1p – natural logarithm plus 1 function.
log – logarithm. (If without a subscript, this may mean either log₁₀ or log_e.)
logh – natural logarithm, log_e.^[6]
LST – language of set theory.
lub – least upper bound.^[1] (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.^[4]
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 $\mathbb {P}$ .)
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.^[2] (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.)
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.^[1]
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.^[1] (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 S_n) 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.^[1]
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.^[4]
ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.^[4]

References[]

^ ^a ^b ^c ^d ^e ^f Goldrei, Derek (1996). Classic Set Theory. London, UK: Chapman and Hall. pp. 283–287 (Index). ISBN 0-412-60610-0.
^ ^a ^b ^c Priestley, H. A. (2003). Introduction to Complex Analysis (2 ed.). Oxford University Press. p. 321 (Notation index). ISBN 978-0-19-852562-2.
^ "How to use BIDMAS to solve equations". BBC Bitesize. Retrieved 2020-08-08.
^ ^a ^b ^c ^d Hamilton, A. G. (1982). Numbers, sets and axioms. Cambridge University Press. pp. 249–251 (Index of symbols). ISBN 0-521-24509-5.
^ Raymond, Eric S. (2003), "LERP", Jargon File, 4.4.7
^ Jolley, L.B.W. (1961). Summation of Series (2 (revised) ed.). New York, USA: Dover Publications, Inc. LCCN 61-65274.

[d-goldrei-set-1] ^ ^a ^b ^c ^d ^e ^f Goldrei, Derek (1996). Classic Set Theory. London, UK: Chapman and Hall. pp. 283–287 (Index). ISBN 0-412-60610-0.

[h-priestley-2] Priestley, H. A. (2003). Introduction to Complex Analysis (2 ed.). Oxford University Press. p. 321 (Notation index). ISBN 978-0-19-852562-2.

[3] "How to use BIDMAS to solve equations". BBC Bitesize. Retrieved 2020-08-08.

[a-hamilton-4] Hamilton, A. G. (1982). Numbers, sets and axioms. Cambridge University Press. pp. 249–251 (Index of symbols). ISBN 0-521-24509-5.

[e-raymond-lerp-5] Raymond, Eric S. (2003), "LERP", Jargon File, 4.4.7

[Jolley_1961-6] Jolley, L.B.W. (1961). Summation of Series (2 (revised) ed.). New York, USA: Dover Publications, Inc. LCCN 61-65274.

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List of mathematical abbreviations

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