Mathematical abbreviations

This is a listing of Mathematical abbreviations and 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.

Care should be taken as context is important. Identical mathematical symbols and notation are used in different circumstances to convey very different ideas.

Abbreviation	Meaning
abs	Absolute value
alg	Algebraic
amt	Amount
ang	Angle
approx	Approximately
arc	Arc length or arc cosine (acos)
arg	Argument (of a complex number)
asc	Ascending
assoc	Associative
asympt	Asymptotic
ave	Average
bijective	Bijective function
binom	Binomial
canc	Cancellation
card	Cardinality
ceil	Ceiling function
cf	Continued fraction
circ	Circle, circumference, circular
coeff	Coefficient
comp	Complement, composite
conc	Concentric
conj	Conjugate
const	Constant
cont	Continuous
conv	Convolution, convergent
cor	Corollary
cos	Cosine
cot	Cotangent
covar	Covariance
csc	Cosecant
cts	Continuous
deg	Degree (angle measurement or polynomial degree)
denom	Denominator
det	Determinant
diff	Differentiation, derivative
discr	Discrete, discriminant
div	Division, divisor, divergent
dom	Domain
dot	Dot product
eigen	Eigenvalue, eigenvector
elem	Element
eqn	Equation
equiv	Equivalent
exp	Exponential, exponent
ext	Exterior
fac	Factorial
finite	Finite
floor	Floor function
frac	Fraction
func	Function
geom	Geometry, geometric
gcd	Greatest common divisor
homo	Homogeneous
hyp	Hypotenuse, hyperbolic
id	Identity
imag	Imaginary
incl	Inclusion
ind	Index, indicator
inf	Infinite, infimum
int	Integer, integral, interior
iso	Isomorphism, isosceles
lim	Limit
lin	Linear, line
log	Logarithm
max	Maximum
min	Minimum
neg	Negative
nondec	Nondecreasing
nonneg	Nonnegative
noninc	Nonincreasing
num	Numerator
Mathematical abbreviations
oblique	Oblique
orthog	Orthogonal
par	Parallel, parabola
perp	Perpendicular
poly	Polynomial, polygon
pos	Positive
pow	Power
prod	Product
prop	Property, proportion
rad	Radius, radical
rand	Random
recip	Reciprocal
refl	Reflexive
rel	Relation
rem	Remainder
resp	Respectively
rev	Reversible
rhs	Right-hand side
ring	Ring
rot	Rotation
scal	Scalar
sec	Secant, second
sim	Similar, similarity
sin	Sine
skew	Skew
sol	Solution
sqrt	Square root
sub	Subtraction, subset
sup	Supremum, superlative
symm	Symmetric
tan	Tangent
trig	Trigonometry, trigonometric
unimod	Unimodal
univ	Universal
var	Variable
vec	Vector
vol	Volume
wrt	With respect to
x-intercept	x-intercept
y-intercept	y-intercept
Mathematical abbreviations
z-intercept	z-intercept
AC	Axiom of Choice
a.c.	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	Action limit
Alt	Alternating group
A.M.	Arithmetic mean
arccos	Inverse cosine function
arccosec	Inverse cosecant function (Also written as arccsc)
arccot	Inverse 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
Bi	Airy function of the second kind
BIDMAS	Brackets, Indices, Divide, Multiply, Add, Subtract
Bias	Bias of an estimator
BWOC	By way of contradiction
Mathematical abbreviations
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
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
exs	Exsecant function
exp	Exponential function
expi	Cos + i sin function
expm1	Exponential minus 1 function
Ext	Ext functor
ext	Exterior
extr	Set of extreme points of a set
Mathematical abbreviations
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
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
Mathematical abbreviations
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 (log2)
lcm	Lowest common multiple
LCHS	Locally Compact Hausdorff second Countable
ld	Binary logarithm (log2)
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
lim inf	Limit inferior
lim sup	Limit superior
ln	Natural logarithm
lnp1	Natural logarithm plus 1 function
ln1p	Natural logarithm plus 1 function
log	Logarithm
logh	Natural logarithm
LST	Language of set theory
lub	Least upper bound
max	Maximum
min	Minimum
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
Mathematical abbreviations
ob	Object class
ord	Ordinal number
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
QEF	Quod erat faciendum
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	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	[It is] sufficient to prove
SU	Special unitary group
sup	Supremum of a set
supp	Support of a function
Sym	Symmetric group
Mathematical abbreviations
tan	Tangent function
tanh	Hyperbolic tangent function
TFAE	The following are equivalent
tg	Tangent function
theo, thm	Theorem
Tor	Tor functor
Tr	Trace
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
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
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

Please note that this table includes a wide range of mathematical abbreviations. If you have any specific additions, corrections, or questions about the abbreviations, plese correct it

Mathematical abbreviations