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.^[1]
a.c. – absolutely continuous.
adj – adjugate of a matrix.
a.e. – almost everywhere.
Ai – Airy function.
AL – Action limit.
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.)
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.^[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.
A.P. – arithmetic progression.
Aut – automorphism group.
bd – boundary.
Bi – Airy function of the second kind.
Bias – bias of an estimator
Card – cardinality of a set.^[3] (Card(X) is also written #X, ♯X or |X|.)
cdf – cumulative distribution function.
c.f. – cumulative frequency.
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 – codomain. (Also written as codom.)
codom – codomain. (Also written as cod.)
cok – cokernel. (Also written as coker.)
coker – cokernel. (Also written as cok.)
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.
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.)
def – define or definition.
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.
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.^[1] (Or, more generally, a relation.)
End – categories of endomorphisms.
Ei – exponential integral function.
Eqn – equation.
erf – error function.
erfc – complementary error function.
exp – exponential function. (exp x is also written as e^x.)
Ext – Ext functor.
ext – exterior.
FIP – finite intersection property.
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.
G.M. – geometric mean.
glb – greatest lower bound. (Also written as inf.)
G.P. – geometric progression.
grad – gradient of a scalar field.
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.
iff – if and only if.
iid – independent and identically distributed random variables.
Im – imaginary part of a complex number^[2] (which is also written $\Im$ ).
im – image
inf – infimum of a set. (Also written as glb.)
int – interior.
ker – kernel.
lcm – lowest common multiple of two numbers.
lerp – linear interpolation.^[4]
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.^[5]
LST – language of set theory.
lub – least upper bound.^[1] (Also written sup.)
max – maximum of a set.
M.I. – mathematical induction.
min – minimum of a set.
mod – modulo.
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.^[3]
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.
rank – rank. (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 – root mean square. (Also written as rms.)
rms – root mean square. (Also written as RMS.)
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.^[1]
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.
SL – special linear group.
Soln – solution.
sp – linear span of a set of vectors. (Also written with angle brackets.)
Spec – spectrum of a ring.
s.t. – such that or so that.
st – standard part function.
STP – [it is] sufficient to prove.
sup – supremum of a set.^[1] (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.
whp – with high probability.
wlog – without loss of generality.
WMA – we may assume.
WO – well-ordered set.^[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.^[3]
ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.^[3]

References

↑ 1.0 1.1 1.2 1.3 1.4 1.5 Goldrei, Derek (1996), Classic Set Theory, London: Chapman and Hall, pp. 283–287 (Index), ISBN 0-412-60610-0
↑ 2.0 2.1 2.2 Priestley, H. A. (2003), Introduction to Complex Analysis (2nd ed.), Oxford University Press, p. 321 (Notation index), ISBN 978-0-19-852562-2
↑ 3.0 3.1 3.2 3.3 Hamilton, A. G. (1982), Numbers, sets and axioms, Cambridge University Press, pp. 249–251 (Index of symbols), ISBN 0-521-24509-5
↑ Raymond, Eric (2003), "LERP", Jargon File (version 4.4.7)
↑ Jolley, L.B.W. (1961), Summation of Series, Second Revised Edition Dover Publications, INC., New York, Library of Congress: 61-65274

List of mathematical abbreviations

References

See also