Mathematical abbreviations

Common Mathematical Abbreviations

A

Abbreviation

Meaning

AC

Axiom of Choice

a.c.

Absolutely continuous

abs

Absolute value

ad

Adjoint representation (or adjoint action) of a Lie group

adj

Adjugate of a matrix

a.e.

Almost everywhere

Ai

Airy function

alg

Algebraic

AL

Action limit

Alt

Alternating group

A.M.

Arithmetic mean

amt

Amount

ang

Angle

approx

Approximately

arc

Arc length or arc cosine (acos)

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 a complex number)

arg max

Argument of the maximum

arg min

Argument of the minimum

arsinh

Inverse hyperbolic sine function

artanh

Inverse hyperbolic tangent function

asc

Ascending

assoc

Associative

asympt

Asymptotic

Aut

Automorphism group

ave

Average

B

bd

Boundary

Bi

Airy function of the second kind

BIDMAS

Brackets, Indices, Divide, Multiply, Add, Subtract

Bias

Bias of an estimator

bijective

Bijective function

binom

Binomial

BWOC

By way of contradiction

C

Card

Cardinality of a set

card

Cardinality

cas

Cos + sin function

canc

Cancellation

cdf

Cumulative distribution function

c.f.

Cumulative frequency

c.c.

Complex conjugate

ceil

Ceiling function

cf

Continued fraction

Chi

Hyperbolic cosine integral function

ci

Cosine integral function

circ

Circle, circumference, circular

cis

Cos + i sin function

Cl

Conjugacy class

cl

Topological closure

coeff

Coefficient

cod, codom

Codomain

cok, coker

Cokernel

comp

Complement, composite

conc

Concentric

conj

Conjugate

const

Constant

cont

Continuous

conv

Convolution, convergent

corr

Correlation

cos

Cosine

cosec

Cosecant function

cosech

Hyperbolic cosecant function

cosh

Hyperbolic cosine function

cosiv

Coversine function

cot

Cotangent

coth

Hyperbolic cotangent function

cov

Covariance of a pair of random variables

covar

Covariance

cover

Coversine function

covercos

Covercosine function

covers

Coversine function

crd

Chord function

csc

Cosecant

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 (angle measurement or polynomial degree)

del

Del, a differential operator

denom

Denominator

det

Determinant

diff

Differentiation, derivative

dim

Dimension of a vector space

discr

Discrete, discriminant

div

Division, divisor, divergent

dkl

Decalitre

DNE

Does not exist

dom

Domain of a function

dot

Dot product

E

eigen

Eigenvalue, eigenvector

Ei

Exponential integral function

elem

Element

End

Categories of endomorphisms

epi

Epigraph of a function

eqn

Equation

equiv

Equivalent

erf

Error function

erfc

Complementary error function

etr

Exponent of the trace

exc

Excosecant function

excosec

Excosecant function

exi

Existential quantifier

exp

Exponential function

expi

Exponential integral function

expm1

Exponential minus 1 function

Ext

Ext functor

ext

Exterior

extr

Set of extreme points of a set

F

fac

Factorial

finite

Finite

floor

Floor function

FOC

First order condition

FOL

First-order logic

frac

Fraction

fr

Boundary

Frob

Frobenius endomorphism

func

Function

G

Gal

Galois group

gcd

Greatest common divisor

gd

Gudermannian function

geom

Geometry, geometric

GF

Galois field

GF

Generating function

G.M.

Geometric mean

glb

Greatest lower bound

GL

General linear group

grad

Gradient of a function

H

hacover

Hacoversine function

hacovercos

Hacovercosine function

hav

Haversine function

havercos

Havercosine function

hcc

Hacovercosine function

hcf

Highest common factor of two numbers

hcv

Hacoversine function

H.M.

Harmonic mean

hom

Hom-class

Hom

Hom functor

homo

Homogeneous

hot

Higher Order Term

HOTPO

Half Or Triple Plus One

hvc

Havercosine function

hyp

Hypograph of a function

hyp

Hypotenuse, hyperbolic

I

id

Identity

IH

Induction Hypothesis

iid

Independent and identically distributed random variables

imag

Imaginary

im

Image

incl

Inclusion

ind

Index, indicator

inf

Infinite, infimum

inf

Infimum of a set

int

Integer, integral, interior

int

Interior

iso

Isomorphism, isosceles

Im

Imaginary part of a complex number

I.o.

Infinitely often

K

ker

Kernel

L

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

lin

Linear, line

ln

Natural logarithm

lnp1

Natural logarithm plus 1 function

log

Logarithm

logh

Natural logarithm

lub

Least upper bound

M

max

Maximum

MGF

Moment generating function

min

Minimum

mod

Modulo

Mp

Metaplectic group

mtanh

Modified hyperbolic tangent function

mth

Modified hyperbolic tangent function

mx

Matrix

N

NAND

Not-and in logic

neg

Negative

No.

Number

nondec

Nondecreasing

nonneg

Nonnegative

noninc

Nonincreasing

NOR

Not-or in logic

NTS

Need to show

num

Numerator

O

ob

Object class

OBGF

Ordinary bivariate generating function

ord

Ordinal number

orthog

Orthogonal

P

par

Parallel, parabola

pdf

Probability density function

pf

Proof

Pin

Pin group

pmf

Probability mass function

Pn

Previous number

poly

Polynomial, polygon

pos

Positive

pow

Power

Pr

Probability of an event

prod

Product

PSL

Projective special linear group

PSO

Projective orthogonal group

PSU

Projective special unitary group

PU

Projective unitary group

prop

Property, proportion

Q

QED

Quod erat demonstrandum

QEF

Quod erat faciendum

R

rad

Radius, radical

rand

Random

ran

Range of a function

rank

Rank

Re

Real part of a complex number

recip

Reciprocal

refl

Reflexive

rel

Relation

rem

Remainder

resp

Respectively

rev

Reversible

rhs

Right-hand side

RHS

Right-hand side of an equation

rk

Rank

ring

Ring

rng

Non-unital ring

rot

Rotor of a vector field

RTP

Required to prove

RV

Random Variable

S

scal

Scalar

SD

Standard deviation

sec

Secant

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

sim

Similar, similarity

sin

Sine

sin

Sine function

sinc

Sinc function

sinh

Hyperbolic sine function

siv

Versine function

skew

Skew

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

sqrt

Square root

s.t.

Such that or so that or subject to

st

Standard part function

STP

[It is] sufficient to prove

sub

Subtraction, subset

SU

Special unitary group

sup

Supremum of a set

supp

Support of a function

Sym

Symmetric group

symm

Symmetric

T

tan

Tangent

tan

Tangent function

tanh

Hyperbolic tangent function

TFAE

The following are equivalent

tg

Tangent function

theo, thm

Theorem

Tor

Tor functor

Tr

Trace

trig

Trigonometry, trigonometric

U

undef

Undefined

unimod

Unimodal

univ

Universal

V

var

Variable

var

Variance of a random variable

vec

Vector

v

Volume

vcs

Vercosine function

ver

Versine function

vercos

Vercosine function

vers

Versine function

vol

Volume

W

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

X

XOR

Exclusive or in logic

x-intercept

x-intercept

Y

y-intercept

y-intercept

Z

ZF

Zermelo–Fraenkel axioms of set theory

ZFC

Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory

z-intercept

z-intercept