View source for List of mathematical abbreviations

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

:''This list is limited to abbreviations of two or more letters (excluding number sets). The capitalization of some of these abbreviations is not standardized – different authors might use different capitalizations.''
:{{Expand list|date=February 2011}}

{{Compact TOC|j=|y=|seealso=yes|refs=yes}}

== A ==
* A – [[adele ring]] or [[Algebraic number|algebraic numbers]].
* a.a.s. – [[asymptotically almost surely]].
* AC – [[Axiom of Choice]],<ref name="d-goldrei-set">{{Cite book |last1=Goldrei |first1=Derek |title=Classic Set Theory |pages=283–287 (Index) |year=1996 |publisher=[[Chapman and Hall]] |isbn=0-412-60610-0 |location=London, UK}}</ref> or set of [[absolute continuity|absolutely continuous]] functions.
* a.c. – [[absolute continuity|absolutely continuous]].
* acrd – [[inverse chord (trigonometry)|inverse chord]] function.
* ad – [[adjoint representation]] (or adjoint action) of a [[Lie group]].
* adj – [[adjugate matrix|adjugate]] of a matrix.
* a.e. – [[almost everywhere]].
* AFSOC - [[Proof by contradiction|Assume for the sake of contradiction]]
* Ai – [[Airy function]].
* AL – [[Action limit]].
* Alt – [[alternating group]] (Alt(''n'') ''is also written as'' A<sub>''n''</sub>''.'')
* A.M. – [[arithmetic mean]].
* AP – [[arithmetic progression]].
* arccos – [[inverse cosine]] function.
* arccosec – [[inverse cosecant]] function. (''Also written as'' arccsc''.'')
* arccot – [[inverse cotangent]] function.
* arccsc – [[inverse cosecant]] function. (''Also written as'' arccosec''.'')
* arcexc – [[inverse excosecant]] function. (''Also written as'' arcexcsc'','' arcexcosec''.'')
* arcexcosec – [[inverse excosecant]] function. (''Also written as'' arcexcsc'','' arcexc''.'')
* arcexcsc – [[inverse excosecant]] function. (''Also written as'' arcexcosec'','' arcexc''.'')
* arcexs – [[inverse exsecant]] function. (''Also written as'' arcexsec''.'')
* arcexsec – [[inverse exsecant]] function. (''Also written as'' arcexs''.'')
* 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.
* arctan2 – [[atan2|inverse tangent function with two arguments]]. (''Also written as'' atan2''.'')
* arg – [[arg (mathematics)|argument]] of.<ref name="h-priestley">{{Cite book |last1=Priestley |first1=H. A. |title=Introduction to Complex Analysis |edition=2 |page=321 (Notation index) |year=2003 |publisher=[[Oxford University Press]] |isbn=978-0-19-852562-2}}</ref>
* arg max – [[arg max|argument of the maximum]].
* arg min – [[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 – [[atan2|inverse tangent function with two arguments]]. (''Also written as'' arctan2''.'')
* A.P. – [[arithmetic progression]].
* Aut – [[automorphism group]].

== B ==
* bd – [[boundary (topology)|boundary]]. (''Also written as'' fr ''or'' [[∂]]''.'')
* Bi – [[Airy function]] of the second kind.
* BIDMAS – Brackets, Indices, Divide, Multiply, Add, Subtract.<ref>{{Cite web|title=How to use BIDMAS to solve equations|url=https://www.bbc.co.uk/bitesize/topics/znmtsbk/articles/zj29dxs|access-date=2020-08-08|website=BBC Bitesize|language=en-GB}}</ref>
* Bias – [[bias of an estimator]] .
* BWOC – [[List of mathematical jargon#BWOC|by way of contradiction]].

== C ==
* C – [[Complex number|complex numbers]].
* Card – [[cardinality]] of a set.<ref name="a-hamilton">{{Cite book |last1=Hamilton |first1=A. G. |title=Numbers, sets and axioms |pages=[https://archive.org/details/numberssetsaxiom0000hami/page/249 249–251 (Index of symbols)] |year=1982 |publisher=[[Cambridge University Press]] |isbn=0-521-24509-5 |url=https://archive.org/details/numberssetsaxiom0000hami/page/249 }}</ref> (Card(''X'') ''is also written'' #''X'', ♯''X'' ''or'' |''X''|''.'')
* cas – [[cas (mathematics)|cos + sin]] function.
* cdf – [[cumulative distribution function]].
* c.f. – [[cumulative frequency analysis|cumulative frequency]].
* c.c. – [[complex conjugate]].
* char – [[characteristic (algebra)|characteristic]] of a ring.
* Chi – [[Trigonometric integral#Hyperbolic cosine integral|hyperbolic cosine integral]] function.
* Ci – [[Trigonometric integral#Cosine integral|cosine integral]] function.
* cis – [[cis (mathematics)|cos + i sin]] function. (''Also written as'' expi''.'')
* Cl – [[conjugacy class]].
* cl – [[closure (topology)|topological closure]].
* CLT – [[central limit theorem]].
* cod, codom – [[codomain]].
* cok, coker – [[cokernel]].
* colsp – [[Row and column spaces|column space]] of a matrix.
* conv – [[convex hull]] of a set.
* 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.
* cosiv – [[coversine]] function. (''Also written as'' cover'','' covers'','' cvs''.'')
* cot – [[cotangent]] function. (''Also written as'' ctg''.'')
* coth – [[hyperbolic cotangent]] function.
* cov – [[covariance]] of a pair of random variables.
* cover – [[coversine]] function. (''Also written as'' covers'','' cvs'','' cosiv''.'')
* covercos – [[covercosine]] function. (''Also written as'' cvc''.'')
* covers – [[coversine]] function. (''Also written as'' cover'','' cvs'','' cosiv''.'')
* crd – [[chord (trigonometry)|chord]] function.
* CRT – [[Chinese remainder theorem]].
* csc – [[cosecant]] function. (''Also written as'' cosec''.'')
* csch – [[hyperbolic cosecant]] function. (''Also written as'' cosech''.'')
* ctg – [[cotangent]] function. (''Also written as'' cot''.'')
* curl – [[curl (mathematics)|curl]] of a vector field. (''Also written as'' rot''.'')
* cvc – [[covercosine]] function. (''Also written as'' covercos''.'')
* cvs – [[coversine]] function. (''Also written as'' cover'','' covers'','' cosiv''.'')

== D ==
* def – [[define]] or [[definition]].
* deg – [[degree of a polynomial]], or other recursively-defined objects such as [[well-formed formula]]s. (''Also written as'' ∂''.'')
* del – [[del]], a differential operator. (''Also written as'' <math>\nabla</math>''.'')
* det – [[determinant]] of a matrix or linear transformation.
* DFT – [[discrete Fourier transform]].
* dim – [[dimension (vector space)|dimension]] of a vector space.
* div – [[divergence]] of a vector field.
* DNE – a solution for an expression does not exist, or is [[Undefined (mathematics)|undefined]]. Generally used with [[limit (mathematics)|limits]] and [[integral]]s.
* dom, domain – [[domain (function)|domain]] of a function.<ref name="d-goldrei-set" /> (''Or, more generally, a relation.'')

== E ==
* End – categories of [[endomorphism]]s.
* Ei – [[exponential integral]] function.
* epi – [[Epigraph (mathematics)|epigraph]] of a function.
* Eqn – [[equation]].
* erf – [[error function]].
* erfc – [[complementary error function]].
* erfcx – [[Error function#Complementary error function|scaled complementary error function]].
* erfi – [[Error function#Imaginary error function|imaginary error function]].
* etr – exponent of the [[trace (linear algebra)|trace]].
* exc – [[excosecant]] function. (''Also written as'' excsc'','' excosec''.'')
* excosec – [[excosecant]] function. (''Also written as'' excsc'','' exc''.'')
* excsc – [[excosecant]] function. (''Also written as'' excosec'','' exc''.'')
* exs – [[exsecant]] function. (''Also written as'' exsec''.'')
* exsec – [[exsecant]] function. (''Also written as'' exs''.'')
* exp – [[exponential function]]. (exp ''x'' ''is also written as'' ''e<sup>x</sup>.'')
* expi – [[expi (mathematics)|cos + i sin]] function. (''Also written as'' cis''.'')
* expm1 – [[exponential minus 1]] function. (''Also written as'' exp1m''.'')
* exp1m – [[exponential minus 1]] function. (''Also written as'' expm1''.'')
* Ext – [[Ext functor]].
* ext – [[exterior (topology)|exterior]].
* extr – a set of [[extreme point]]s of a set.

== F ==
* FFT – [[fast Fourier transform]].
* FIP – [[finite intersection property]].
* FOC – [[first order condition]].
* FOL – [[first-order logic]].
* fr – [[boundary (topology)|boundary]]. (''Also written as'' bd ''or'' [[∂]]''.'')
* Frob – [[Frobenius endomorphism]].
* FT – [[Fourier transform]].
* FTA – [[fundamental theorem of arithmetic]] or [[fundamental theorem of algebra]].

== G ==
* Gal – [[Galois group]]. (''Also written as'' Γ''.'')
* gcd – [[greatest common divisor]] of two numbers. (''Also written as'' hcf''.'')
* gd – [[Gudermannian function]].
* GF – [[Galois field]].
* GF – [[generating function]].
* GL – [[general linear group]].
* G.M. – [[geometric mean]].
* glb – [[greatest lower bound]]. (''Also written as'' inf''.'')
* G.P. – [[geometric progression]].
* grad – [[gradient]] of a function.
* graph – [[graph of a function]].

== H ==
* H – [[quaternion]] numbers.
* hacover – [[hacoversine]] function. (''Also written as'' hacovers'','' hcv''.'')
* hacovercos – [[hacovercosine]] function. (''Also written as'' hcc''.'')
* hacovers – [[hacoversine]] function. (''Also written as'' hacover'','' hcv''.'')
* hav – [[haversine]] function. (''Also written as'' sem''.'')
* havercos – [[havercosine]] function. (''Also written as'' hvc''.'')
* h.c. – [[Hermitian adjoint|Hermitian conjugate]], often used as part of [[+ h.c.]] (''Also written as'' H.c.)
* hcc – [[hacovercosine]] function. (''Also written as'' hacovercos''.'')
* hcv – [[hacoversine]] function. (''Also written as'' hacover'','' hacovers''.'')
* hcf – [[highest common factor]] of two numbers. (''Also written as'' gcd''.'')
* H.M. – [[harmonic mean]].
* HOL – [[higher-order logic]].
* Hom – [[Hom functor]].
* hom – [[Morphism#Hom-set|hom-class]].
* hot – higher order term.
* HOTPO – [[Collatz conjecture|half or triple plus one]].
* hvc – [[havercosine]] function. (''Also written as'' havercos''.'')
* hyp – [[Hypograph (mathematics)|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.<ref name="h-priestley" /> (''Also written as'' <math>\Im</math>''.'')
* im – [[image (mathematics)|image]].
* inf – [[infimum]] of a set. (''Also written as'' glb''.'')
* int – [[interior (topology)|interior]].
* I.o. – Infinitely often.

== K ==
* ker – [[kernel (category theory)|kernel]].

== L ==
* lb – [[binary logarithm]] (log<sub>2</sub>). (''Also written as'' ld''.'')
* lcm – [[lowest common multiple]] (a.k.a. least common multiple) of two numbers.
* LCHS – locally compact Hausdorff second countable.
* ld – [[binary logarithm]] (log<sub>2</sub>). (''Also written as'' lb''.'')
* lsc – lower [[semi-continuity]].
* lerp – [[linear interpolation]].<ref name="e-raymond-lerp">{{citation |first1=Eric S. |last1=Raymond |author1-link=Eric S. Raymond |date=2003 |title=Jargon File |title-link=Jargon File |version=4.4.7 |entry=LERP |contribution-url=http://www.catb.org/jargon/html/L/LERP.html}}</ref>
* lg – [[common logarithm]] (log<sub>10</sub>) or [[binary logarithm]] (log<sub>2</sub>).
* LHS – [[left-hand side]] of an equation.
* Li – [[offset logarithmic integral]] function.
* li – [[logarithmic integral]] function or [[linearly independent]].
* lim – [[limit (mathematics)|limit]] of [[limit of a sequence|a sequence]], or of [[limit of a function|a function]].
* lim inf – [[limit inferior]].
* lim sup – [[limit superior]].
* LLN – [[law of large numbers]].
* ln – [[natural logarithm]], log<sub>''e''</sub>.
* lnp1 – [[natural logarithm plus 1]] function.
* ln1p – [[natural logarithm plus 1]] function.
* log – [[logarithm]]. (''If without a subscript, this may mean either'' [[common logarithm|log<sub>10</sub>]] ''or'' [[natural logarithm|log<sub>''e''</sub>]]''.'')
* logh – [[natural logarithm]], log<sub>''e''</sub>.<ref name="Jolley_1961">{{cite book |first=L.B.W. |last=Jolley |date=1961 |title=Summation of Series |url=https://archive.org/details/summationofserie00joll |url-access=registration |edition=2 (revised) |publisher=[[Dover Publications, Inc.]] |location=New York, USA |lccn=61-65274}}</ref>
* LST – [[first-order language|language]] of [[set theory]].
* lub – [[least upper bound]].<ref name="d-goldrei-set" /> (''Also written'' sup''.'')

== M ==
* max – [[maximum]] of a set.
* MGF – [[moment-generating function]].
* M.I. – [[mathematical induction]].
* min – [[minimum]] of a set.
* mod – [[modular arithmetic|modulo]].
* Mp – [[metaplectic group]].
* mtanh – [[modified hyperbolic tangent]] function. (''Also written as'' mth''.'')
* mth – [[modified hyperbolic tangent]] function. (''Also written as'' mtanh''.'')
* mx – [[matrix (mathematics)|matrix]].

== N ==
* N – [[Natural number|natural numbers]].
* NAND – [[Sheffer stroke|not-and]] in logic.
* No. – [[number]].
* NOR – [[Logical NOR|not-or]] in logic.
* NTS – need to show.
* Null, null – (''See [[Kernel (linear algebra)#Representation as matrix multiplication|Kernel]].'')
* Nullity, nullity – [[Kernel (linear algebra)#nullity|nullity]].

== O ==
* O – [[octonion]] numbers.
* OBGF – ordinary bivariate generating function.
* ob – object class.
* ord – [[ordinal number]] of a well-ordered set.<ref name="a-hamilton" />
* O/W - otherwise.

== P ==
* pdf – [[probability density function]].
* pf – [[mathematical proof|proof]].
* PGL – [[projective general linear group]].
* Pin – [[pin group]].
* pmf – [[probability mass function]].
*Pn – previous number.
* Pr – probability of an event. (''See [[Probability theory]]. Also written as'' P ''or'' <math>\mathbb{P}</math>''.'')
* probit – [[probit]] function.
* PRNG – [[pseudorandom number generator]].
* PSL – [[projective special linear group]].
* PNT – [[prime number theorem]].
* PRP – [[probable prime]].
* PSO – [[projective orthogonal group]].
* PSU – [[projective special unitary group]].
* PU – [[projective unitary group]].

== Q ==
* Q – [[Rational number|rational numbers]].
* QED – [[Q.E.D.|"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 number|real numbers]].
* ran – [[range of a function]].
* rank – [[rank (linear algebra)|rank]] of a [[Matrix (mathematics)|matrix]]. (''Also written as'' rk''.'')
* Re – [[real part]] of a complex number.<ref name="h-priestley" /> (''Also written'' <math>\Re</math>''.'')
* resp – respectively.
* RHS – [[right-hand side]] of an equation.
* rk – [[rank (linear algebra)|rank]]. (''Also written as'' rank''.'')
* RMS, rms – [[root mean square]].
* rng – [[non-unital ring]].
* rot – [[rot (mathematics)|rotor]] of a vector field. (''Also written as'' curl''.'')
* rowsp – [[Row and column spaces|row space]] of a matrix.
* RTP – required to prove.
* RV – [[Random Variable|random variable]]. (''Also written as'' R.V''.'')

== S ==
* S – [[sedenion]] numbers.
* SD – [[standard deviation]].
* SE – [[standard error]].
* sec – [[Trigonometric functions#Reciprocal functions|secant]]{{Broken anchor|date=2024-09-29|bot=User:Cewbot/log/20201008/configuration|target_link=Trigonometric functions#Reciprocal functions|reason= The anchor (Reciprocal functions) [[Special:Diff/779343428|has been deleted]].}} function.
* sech – [[hyperbolic secant]] function.
* seg – [[initial segment]] of.<ref name="d-goldrei-set" />
* sem – [[haversine]] function. (''Also written as'' hav''.'')
* SFIP – [[strong finite intersection property]].
* sgn – [[sign function|sign]] function.
* Shi – [[Trigonometric integral#Hyperbolic sine integral|hyperbolic sine integral]] function.
* Si – [[sine integral]] function.
* sigmoid – [[sigmoid function]].
* sin – [[sine]] function.
* sinc – [[Sinc function|sinc]] function.
* sinh – [[hyperbolic sine]] function.
* siv – [[versine]] function. (''Also written as'' ver'','' vers''.'')
* SL – [[special linear group]].
* SO – [[special orthogonal group]].
* SOC – [[second order condition]].
* Soln – [[Solution (mathematics)|solution]].
* Sp – [[symplectic group]].
* Sp – [[trace (linear algebra)|trace]] of a matrix, from the German "spur" used for the trace.
* sp, span – [[linear span]] of a set of vectors. (''Also'' ''written with angle brackets.'')
* 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.
* SU – [[special unitary group]].
* sup – [[supremum]] of a set.<ref name="d-goldrei-set" /> (''Also written as'' lub'', which stands for least upper bound.'')
* supp – [[support (mathematics)|support]] of a function.
* swish – [[swish function]], an activation function in data analysis.
* Sym – [[symmetric group]] (Sym(''n'') ''is also written as'' S<sub>''n''</sub>) or [[symmetric algebra]].

== T ==
* T – [[trigintaduonion]] numbers.
* tan – [[tangent (trigonometry)|tangent]] function. (''Also written as'' tgn'','' tg''.'')
* tanh – [[hyperbolic tangent]] function.
* TFAE – the following are equivalent.
* tg – [[tangent (trigonometry)|tangent]] function. (''Also written as'' tan'','' tgn''.'')
* tgn – [[tangent (trigonometry)|tangent]] function. (''Also written as'' tan'','' tg''.'')
* Thm – [[theorem]].
* Tor – [[Tor functor]].
* Tr – [[field trace]].
* tr – [[trace (linear algebra)|trace of a matrix or linear transformation]]. (''Also written as'' Sp''.'')

== U ==
* undef – a function or expression is [[Undefined (mathematics)|undefined]].
* usc – upper [[semi-continuity]].

== V ==
* V – [[volume]].
* var – [[variance]] of a random variable.
* vcs – [[vercosine]] function. (''Also written as'' vercos''.'')
* ver – [[versine]] function. (''Also written as'' vers'','' siv''.'')
* vercos – [[vercosine]] function. (''Also written as'' vcs''.'')
* vers – [[versine]] function. (''Also written as'' ver'','' siv''.'')

== 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.<ref name="d-goldrei-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.<ref name="a-hamilton" />
* ZFC – [[Zermelo–Fraenkel axioms]] (with the [[Axiom of Choice]]) of set theory.<ref name="a-hamilton" />

==See also==

* [[List of letters used in mathematics, science, and engineering]]
* [[ISO 31-11]]
* [[Language of mathematics]]
* [[List of mathematical jargon]]
* [[Mathematical notation]]
* [[Notation in probability and statistics]]
* [[Physical constant]]s
* [[List of logic symbols]]
* [[Glossary of mathematical symbols]]
* [[Mathematical operators and symbols in Unicode]]
* [[List of mathematical functions]]

==References==
{{reflist}}

{{Mathematical symbols notation language}}

{{DEFAULTSORT:Mathematical Abbreviations}}
[[Category:Mathematical notation|Abbreviations]]
[[Category:Mathematics-related lists|Abbreviations]]
[[Category:Mathematical symbols|Abbreviations]]
[[Category:Mathematical tables|Abbreviations]]