List of mathematical abbreviations
This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology.
A
- A β adele ring or algebraic numbers.
- a.a.s. β asymptotically almost surely.
- AC β Axiom of Choice, or set of absolutely continuous functions.
- a.c. β absolutely continuous.
- acrd β inverse chord function.
- ad β adjoint representation of a Lie group.
- adj β adjugate of a matrix.
- a.e. β almost everywhere.
- AFSOC - Assume for the sake of contradiction
- Ai β Airy function.
- AL β Action limit.
- Alt β alternating group
- A.M. β arithmetic mean.
- AP β arithmetic progression.
- arccos β inverse cosine function.
- arccosec β inverse cosecant function.
- arccot β inverse cotangent function.
- arccsc β inverse cosecant function.
- arcexc β inverse excosecant function.
- arcexcosec β inverse excosecant function.
- arcexcsc β inverse excosecant function.
- arcexs β inverse exsecant function.
- arcexsec β inverse exsecant function.
- arcosech β inverse hyperbolic cosecant function.
- arcosh β inverse hyperbolic cosine function.
- arcoth β inverse hyperbolic cotangent function.
- arcsch β inverse hyperbolic cosecant function.
- arcsec β inverse secant function.
- arcsin β inverse sine function.
- arctan β inverse tangent function.
- arctan2 β [atan2|inverse tangent (trigonometry)|tangent function with two arguments].
- arg β argument of.
- arg max β argument of the maximum.
- arg min β argument of the minimum.
- arsech β inverse hyperbolic secant function.
- arsinh β inverse hyperbolic sine function.
- artanh β inverse hyperbolic tangent function.
- a.s. β almost surely.
- atan2 β inverse tangent function with two arguments.
- A.P. β arithmetic progression.
- Aut β automorphism group.
B
- bd β boundary.
- Bi β Airy function of the second kind.
- BIDMAS β Brackets, Indices, Divide, Multiply, Add, Subtract.
- Bias β bias of an estimator.
- BWOC β by way of contradiction.
C
- C β complex numbers.
- Card β cardinality of a set.
- cas β cos + sin function.
- cdf β cumulative distribution function.
- c.f. β cumulative frequency.
- c.c. β complex conjugate.
- char β characteristic of a ring.
- Chi β hyperbolic cosine integral function.
- Ci β cosine integral function.
- cis β cos + i sin function.
- Cl β conjugacy class.
- cl β topological closure.
- CLT β central limit theorem.
- cod, codom β codomain.
- cok, coker β cokernel.
- colsp β column space of a matrix.
- conv β convex hull of a set.
- Cor β corollary.
- corr β correlation.
- cos β cosine function.
- cosec β cosecant function.
- cosech β hyperbolic cosecant function.
- cosh β hyperbolic cosine function.
- cosiv β coversine function.
- cot β cotangent function.
- coth β hyperbolic cotangent function.
- cov β covariance of a pair of random variables.
- cover β coversine function.
- covercos β covercosine function.
- covers β coversine function.
- crd β chord function.
- CRT β Chinese remainder theorem.
- csc β cosecant function.
- csch β hyperbolic cosecant function.
- ctg β cotangent function.
- curl β curl of a vector field.
- cvc β covercosine function.
- cvs β coversine function.
D
- def β define or definition.
- deg β degree of a polynomial, or other recursively defined objects such as well-formed formulas.
- del β del, a differential operator.
- det β determinant of a matrix or linear transformation.
- DFT β discrete Fourier transform.
- dim β dimension of a vector space.
- div β divergence of a vector field.
- DNE β a solution for an expression does not exist, or is undefined. Generally used with limits and integrals.
- dom, domain β domain of a function.
E
- End β categories of endomorphisms.
- Ei β exponential integral function.
- epi β epigraph of a function.
- Eqn β equation.
- erf β error function.
- erfc β complementary error function.
- erfcx β scaled complementary error function.
- erfi β imaginary error function.
- etr β exponent of the trace.
- exc β excosecant function.
- excosec β excosecant function.
- excsc β excosecant function.
- exs β exsecant function.
- exsec β exsecant function.
- exp β exponential function.
- expi β cos + i sin function.
- expm1 β exponential minus 1 function.
- exp1m β exponential minus 1 function.
- Ext β Ext functor.
- ext β exterior.
- extr β a set of extreme points of a set.
F
- FFT β fast Fourier transform.
- FIP β finite intersection property.
- FOC β first order condition.
- FOL β first-order logic.
- fr β boundary.
- Frob β Frobenius endomorphism.
- FT β Fourier transform.
- FTA β fundamental theorem of arithmetic or fundamental theorem of algebra.
G
- Gal β Galois group.
- gcd β greatest common divisor of two numbers.
- gd β Gudermannian function.
- GF β Galois field.
- GF β generating function.
- GL β general linear group.
- G.M. β geometric mean.
- glb β greatest lower bound.
- G.P. β geometric progression.
- grad β gradient of a function.
- graph β graph of a function.
H
- H β quaternion numbers.
- hacover β hacoversine function.
- hacovercos β hacovercosine function.
- hacovers β hacoversine function.
- hav β haversine function.
- havercos β havercosine function.
- h.c. β Hermitian conjugate, often used as part of + h.c.
- hcc β hacovercosine function.
- hcv β hacoversine function.
- hcf β highest common factor of two numbers.
- H.M. β harmonic mean.
- HOL β higher-order logic.
- Hom β Hom functor.
- hom β hom-class.
- hot β higher order term.
- HOTPO β half or triple plus one.
- hvc β havercosine function.
- hyp β hypograph of a function.
I
- iff β if and only if.
- IH β induction hypothesis.
- iid β independent and identically distributed random variables.
- Im β imaginary part of a complex number.
- im β image.
- inf β infimum of a set.
- int β interior.
- I.o. β Infinitely often.
K
- ker β kernel.
L
- lb β binary logarithm.
- lcm β lowest common multiple of two numbers.
- LCHS β locally compact Hausdorff second countable.
- ld β binary logarithm.
- lsc β lower semi-continuity.
- lerp β linear interpolation.
- lg β common logarithm or binary logarithm.
- LHS β left-hand side of an equation.
- Li β offset logarithmic integral function.
- li β logarithmic integral function or linearly independent.
- lim β limit of a sequence, or of a function.
- lim inf β limit inferior.
- lim sup β limit superior.
- LLN β law of large numbers.
- ln β natural logarithm, loge.
- lnp1 β natural logarithm plus 1 function.
- ln1p β natural logarithm plus 1 function.
- log β logarithm.
- logh β natural logarithm, loge.
- LST β language of set theory.
- lub β least upper bound.
M
- max β maximum of a set.
- MGF β moment-generating function.
- M.I. β mathematical induction.
- min β minimum of a set.
- mod β modulo.
- Mp β metaplectic group.
- mtanh β modified hyperbolic tangent function.
- mth β modified hyperbolic tangent function.
- mx β matrix.
N
- N β natural numbers.
- NAND β not-and in logic.
- No. β number.
- NOR β not-or in logic.
- NTS β need to show.
- Null, null β
- Nullity, nullity β nullity.
O
- O β octonion numbers.
- OBGF β ordinary bivariate generating function.
- ob β object class.
- ODE - ordinary differential equation
- ord β ordinal number of a well-ordered set.
- O/W - otherwise.
P
- pdf β probability density function.
- pf β proof.
- PGL β projective general linear group.
- Pin β pin group.
- pmf β probability mass function.
- Pn β previous number.
- Pr β probability of an event.
- probit β probit function.
- PRNG β pseudorandom number generator.
- PSL β projective special linear group.
- PNT β prime number theorem.
- PRP β probable prime.
- PSO β projective orthogonal group.
- PSU β projective special unitary group.
- PU β projective unitary group.
Q
- Q β rational numbers.
- QED β "Quod erat demonstrandum", a Latin phrase used at the end of a definitive proof.
- QEF β "Quod erat faciendum", a Latin phrase sometimes used at the end of a geometrical construction.
R
- R β real numbers.
- ran β range of a function.
- rank β rank of a matrix.
- Re β real part of a complex number.
- resp β respectively.
- RHS β right-hand side of an equation.
- rk β rank.
- RMS, rms β root mean square.
- rng β non-unital ring.
- rot β rotor of a vector field.
- rowsp β row space of a matrix.
- RTP β required to prove.
- RV β random variable.
S
- S β sedenion numbers.
- SD β standard deviation.
- SE β standard error.
- sec β secant function.
- sech β hyperbolic secant function.
- seg β initial segment of.
- sem β haversine function.
- SFIP β strong finite intersection property.
- sgn β sign function.
- Shi β hyperbolic sine integral function.
- Si β sine integral function.
- sigmoid β sigmoid function.
- sin β sine function.
- sinc β sinc function.
- sinh β hyperbolic sine function.
- siv β versine function.
- SL β special linear group.
- SO β special orthogonal group.
- SOC β second order condition.
- Soln β solution.
- Sp β symplectic group.
- Sp β trace of a matrix, from the German "spur" used for the trace.
- sp, span β linear span of a set of vectors.
- Spec β spectrum of a ring.
- Spin β spin group.
- sqrt β square root.
- s.t. β such that or so that or subject to.
- st β standard part function.
- STP β sufficient to prove.
- SU β special unitary group.
- sup β supremum of a set.
- supp β support of a function.
- swish β swish function, an activation function in data analysis.
- Sym β symmetric group or symmetric algebra.
T
- T β trigintaduonion numbers.
- tan β tangent function.
- tanh β hyperbolic tangent function.
- TFAE β the following are equivalent.
- tg β tangent function.
- tgn β tangent function.
- Thm β theorem.
- Tor β Tor functor.
- Tr β field trace.
- tr β trace of a matrix or linear transformation.
U
- undef β a function or expression is undefined.
- usc β upper semi-continuity.
V
- V β volume.
- var β variance of a random variable.
- vcs β vercosine function.
- ver β versine function.
- vercos β vercosine function.
- vers β versine function.
W
- W^5 β which was what we wanted. Synonym of Q.E.D.
- walog β without any loss of generality.
- wff β well-formed formula.
- whp β with high probability.
- wlog β without loss of generality.
- WMA β we may assume.
- WO β well-ordered set.
- WOP β well-ordered principle.
- w.p. β with probability.
- wp1 β with probability 1.
- wrt β with respect to or with regard to.
- WTP β want to prove.
- WTS β want to show.
X
- XOR β exclusive or in logic.
Z
- Z β integer numbers.
- ZF β ZermeloβFraenkel axioms of set theory.
- ZFC β ZermeloβFraenkel axioms of set theory.