List of mathematical abbreviations

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

A

A – adele ring or algebraic numbers.
a.a.s. – asymptotically almost surely.
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.
AFSOC - Assume for the sake of contradiction
Ai – Airy function.
AL – Action limit.
Alt – alternating group
A.M. – arithmetic mean.
AP – arithmetic progression.
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 – [atan2|inverse tangent (trigonometry)|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.

B

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.

C

C – complex numbers.
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.
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.
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.
CRT – Chinese remainder theorem.
csc – cosecant function.
csch – hyperbolic cosecant function.
ctg – cotangent function.
curl – curl of a vector field.
cvc – covercosine function.
cvs – coversine function.

D

def – define or definition.
deg – degree of a polynomial, or other recursively defined objects such as well-formed formulas.
del – del, a differential operator.
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.

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.
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.

F

FFT – fast Fourier transform.
FIP – finite intersection property.
FOC – first order condition.
FOL – first-order logic.
fr – boundary.
Frob – Frobenius endomorphism.
FT – Fourier transform.
FTA – fundamental theorem of arithmetic or fundamental theorem of algebra.

G

Gal – Galois group.
gcd – greatest common divisor of two numbers.
gd – Gudermannian function.
GF – Galois field.
GF – generating function.
GL – general linear group.
G.M. – geometric mean.
glb – greatest lower bound.
G.P. – geometric progression.
grad – gradient of a function.
graph – graph of a function.

H

H – quaternion numbers.
hacover – hacoversine function.
hacovercos – hacovercosine function.
hacovers – hacoversine function.
hav – haversine function.
havercos – havercosine function.
h.c. – Hermitian conjugate, often used as part of + h.c.
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.

I

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.

K

ker – kernel.

L

lb – binary logarithm.
lcm – lowest common multiple of two numbers.
LCHS – locally compact Hausdorff second countable.
ld – binary logarithm.
lsc – lower semi-continuity.
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.
LLN – law of large numbers.
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.

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.
mth – modified hyperbolic tangent function.
mx – matrix.

N

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

O

O – octonion numbers.
OBGF – ordinary bivariate generating function.
ob – object class.
ODE - ordinary differential equation
ord – ordinal number of a well-ordered set.
O/W - otherwise.

P

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.
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.
rowsp – row space of a matrix.
RTP – required to prove.
RV – random variable.

S

S – sedenion numbers.
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 – 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.
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.
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 – 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.

T

T – trigintaduonion numbers.
tan – tangent function.
tanh – hyperbolic tangent function.
TFAE – the following are equivalent.
tg – tangent function.
tgn – tangent function.
Thm – theorem.
Tor – Tor functor.
Tr – field trace.
tr – trace of a matrix or linear transformation.

U

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

V

V – volume.
var – variance of a random variable.
vcs – vercosine function.
ver – versine function.
vercos – vercosine function.
vers – versine function.

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 of set theory.