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Short Math Guide for LaTeX
ShortMathGuideforL A T E X
MichaelDownes
AmericanMathematicalSociety
Version1.09(2002-03-22),currentlyavailableat
http://www.ams.org/tex/short-math-guide.html
1.IntroductionThisisaconcisesummaryofrecommendedfeaturesinL A T E Xanda
coupleofextensionpackagesforwritingmathformulas.Readersneedinggreaterdepth
ofdetailarereferredtothesourceslistedinthebibliography,especially[Lamport],[LUG],
[AMUG],[LFG],[LGG],and[LC].AcertainamountoffamiliaritywithstandardL A T E X
terminologyisassumed;ifyourmemoryneedsrefreshingontheL A T E Xmeaningofcommand,
optionalargument,environment,package,andsoforth,see[Lamport].
ThefeaturesdescribedhereareavailabletoyouifyouuseL A T E Xwithtwoextension
packagespublishedbytheAmericanMathematicalSociety: amssymb and amsmath .Thus,
thesourcefileforthisdocumentbeginswith
\documentclass{article}
\usepackage{amssymb,amsmath}
The amssymb packagemightbeomissiblefordocumentswhosemathsymbolusageisrela-
tivelymodest;theeasiestwaytotestthisistoleaveoutthe amssymb referenceandseeif
anymathsymbolsinthedocumentproduce‘Undefinedcontrolsequence’messages.
Manynoteworthyfeaturesfoundinotherpackagesarenotcoveredhere;seeSection10.
Regardingmathsymbols,pleasenoteespeciallythatthelistgivenhereisnotintendedtobe
comprehensive,buttoillustratesuchsymbolsasuserswillnormallyfindalreadypresentin
theirL A T E Xsystemandusablewithoutinstallinganyadditionalfontsordoingothersetup
work.
Ifyouhaveaneedforasymbolnotshownhere,youwillprobablywanttoconsultThe
ComprehensiveL A T E XSymbolsList(Pakin):
http://www.ctan.org/tex-archive/info/symbols/comprehensive/ .
2.Inlinemathformulasanddisplayedequations
2.1.ThefundamentalsEnteringandleavingmathmodeinL A T E Xisnormallydonewith
thefollowingcommandsandenvironments.
inlineformulas displayedequations
$ ... $
\( ... \)
\[...\] unnumbered
\begin{equation*}
...
\end{equation*}
unnumbered
\begin{equation}
...
\end{equation}
automatically
numbered
Note.Alternativeenvironments \begin{math} ... \end{math} , \begin{displaymath} ... \end{displaymath}
areseldomneededinpractice.UsingtheplainT E Xnotation $$ ... $$ fordisplayedequationsisnotrecom-
mended.AlthoughitisnotexpresslyforbiddeninL A T E X,itisnotdocumentedanywhereintheL A T E Xbook
asbeingpartoftheL A T E Xcommandset,anditinterfereswiththeproperoperationofvariousfeatures
suchasthe fleqn option.
Environmentsforhandlingequationgroupsandmulti-lineequationsareshowninTable1.
1
389516661.004.png
ShortMathGuideforL A T E X,version1.09(2002-03-22) 2
Table1:Multi-lineequationsandequationgroups(verticallinesindicatingnominalmar-
gins).
\begin{equation}\label{xx}
\begin{split}
a&=b+c-d\\
&\quad+e-f\\
&=g+h\\
&=i
\end{split}
\end{equation}
a=b+c−d
+e−f
=g+h
=i
(2.1)
\begin{multline}
a+b+c+d+e+f\\
+i+j+k+l+m+n
\end{multline}
a+b+c+d+e+f
+i+j+k+l+m+n (2.2)
\begin{gather}
a_1=b_1+c_1\\
a_2=b_2+c_2-d_2+e_2
\end{gather}
a 1 =b 1 +c 1 (2.3)
a 2 =b 2 +c 2 −d 2 +e 2 (2.4)
\begin{align}
a_1&=b_1+c_1\\
a_2&=b_2+c_2-d_2+e_2
\end{align}
a 1 =b 1 +c 1 (2.5)
a 2 =b 2 +c 2 −d 2 +e 2 (2.6)
\begin{align}
a_{11}&=b_{11}&
a_{12}&=b_{12}\\
a_{21}&=b_{21}&
a_{22}&=b_{22}+c_{22}
\end{align}
a 11 =b 11 a 12 =b 12 (2.7)
a 21 =b 21 a 22 =b 22 +c 22 (2.8)
\begin{flalign*}
a_{11}&=b_{11}&
a_{12}&=b_{12}\\
a_{21}&=b_{21}&
a_{22}&=b_{22}+c_{22}
\end{flalign*}
a 11 =b 11 a 12 =b 12
a 21 =b 21 a 22 =b 22 +c 22
Note1.The split environmentissomethingofaspecialcase.Itisasubordinateenvironmentthatcan
beusedasthecontentsofan equation environmentorthecontentsofone“line”inamultiple-equation
structuresuchas align or gather .
Note2.The eqnarray and eqnarray* environmentsdescribedin[Lamport]arenotrecommendedbecause
theyproduceinconsistentspacingoftheequalsignsandmakenoattempttopreventoverprintingofthe
equationbodyandequationnumber.
389516661.005.png 389516661.006.png 389516661.007.png 389516661.001.png 389516661.002.png 389516661.003.png
ShortMathGuideforL A T E X,version1.09(2002-03-22) 3
2.2.Automaticnumberingandcross-referencingTogetanauto-numberedequa-
tion,usethe equation environment;toassignalabelforcross-referencing,usethe \label
command:
\begin{equation}\label{reio}
...
\end{equation}
Togetacross-referencetoanauto-numberedequation,usethe \eqref command:
...usingequations\eqref{ax1}and\eqref{bz2},we
canderive...
Theaboveexamplewouldproducesomethinglike
usingequations(3.2)and(3.5),wecanderive
Inotherwords, \eqref{ax1} isequivalentto (\ref{ax1}) .
Togiveyourequationnumberstheformm.n(section-number.equation-number),use
the \numberwithin commandinthepreambleofyourdocument:
\numberwithin{equation}{section}
Formoredetailsoncustomnumberingschemessee[Lamport,§6.3,§C.8.4].
The subequations environmentprovidesaconvenientwaytonumberequationsina
groupwithasubordinatenumberingscheme.Forexample,supposingthatthecurrent
equationnumberis2.1,write
\begin{equation}\label{first}
a=b+c
\end{equation}
someinterveningtext
\begin{subequations}\label{grp}
\begin{align}
a&=b+c\label{second}\\
d&=e+f+g\label{third}\\
h&=i+j\label{fourth}
\end{align}
\end{subequations}
toget
a=b+c (2.9)
someinterveningtext
a=b+c (2.10a)
d=e+f+g (2.10b)
h=i+j (2.10c)
Byputtinga \label commandimmediatelyafter \begin{subequations} youcangeta
referencetotheparentnumber; \eqref{grp} fromtheaboveexamplewouldproduce(2.10)
while \eqref{second} wouldproduce(2.10a).
3.Mathsymbolsandmathfonts
3.1.ClassesofmathsymbolsThesymbolsinamathformulafallintodierentclasses
thatcorrespondmoreorlesstothepartofspeecheachsymbolwouldhaveiftheformula
wereexpressedinwords.Certainspacingandpositioningcuesaretraditionallyusedfor
thedierentsymbolclassestoincreasethereadabilityofformulas.
ShortMathGuideforL A T E X,version1.09(2002-03-22) 4
Class
numberMnemonic
P Q R
2 Bin binaryoperator(conjunction)+[^
3 Rel relation/comparison(verb) =<
4 Open left/openingdelimiter ([{h
5 Close right/closingdelimiter )]}i
6 Pun postfix/punctuation . ,;!
Note1.ThedistinctioninT E Xbetweenclass0andanadditionalclass7hastodoonlywithfontselection
issuesandisimmaterialhere.
Note2.SymbolsofclassBin,notablytheminussign−,areautomaticallycoercedtoclass0(nospace)if
theydonothaveasuitableleftoperand.
Thespacingforafewsymbolsfollowstraditioninsteadofthegeneralrule:although/
is(semanticallyspeaking)ofclass2,wewritek/2withnospacearoundtheslashrather
thank /2.Andcompare p|q p|q(nospace)with p\midq p | q(class-3spacing).
TheproperwaytodefineanewmathsymbolisdiscussedinL A T E X2 " fontselection
[LFG].Itisnotreallypossibletogiveausefulsynopsisherebecauseoneneedsfirstto
understandtheramificationsoffontspecifications.
3.2.SomesymbolsintentionallyomittedhereThefollowingmathsymbolsthat
arementionedintheL A T E Xbook[Lamport]areintentionallyomittedfromthisdiscussion
becausetheyaresupersededbyequivalentsymbolswhenthe amssymb packageisloaded.
Ifyouareusingthe amssymb packageanyway,theonlythingthatyouarelikelytogainby
usingthealternatenameisanunnecessaryincreaseinthenumberoffontsusedbyyour
document.
\Box ,see \square
\Diamond ,see \lozenge
\leadsto ,see \rightsquigarrow
\Join ,see \bowtie ./
\lhd ,see \vartriangleleft C
\unlhd ,see \trianglelefteq E
\rhd ,see \vartriangleright B
\unrhd ,see \trianglerighteq D
Furthermore,therearemany,manyadditionalsymbolsavailableforL A T E Xuseabove
andbeyondtheonesincludedhere.Thislistisnotintendedtobecomprehensive.Fora
muchmorecomprehensivelistofsymbols,includingnonmathematicallyorientedonessuch
asphoneticalphabeticordingbats,seeTheComprehensiveL A T E XSymbolsList(Pakin):
http://www.ctan.org/tex-archive/info/symbols/comprehensive/ .
3.3.LatinlettersandArabicnumeralsTheLatinlettersaresimplesymbols,class0.
Thedefaultfontfortheminmathformulasisitalic.
AB C DE F GH I J K LM N OP QRS T U V W X Y Z
abcdef ghij klmnopqrstuvwxyz
Whenaddinganaccenttoaniorjinmath,dotlessvariantscanbeobtainedwith \imath
and \jmath :
ı \imath | \jmath ˆ| \hat{\jmath}
Arabicnumerals0–9arealsoofclass0.Theirdefaultfontisupright/roman.
0123456789
Description
(partofspeech) Examples
0 Ord simple/ordinary(“noun”) A01
1 Op prefixoperator
ShortMathGuideforL A T E X,version1.09(2002-03-22) 5
3.4.GreeklettersLiketheLatinletters,theGreeklettersaresimplesymbols,class0.
Forobscurehistoricalreasons,thedefaultfontforlowercaseGreeklettersinmathformu-
lasisitalicwhilethedefaultfontforcapitalGreeklettersisupright/roman.(Inother
fieldssuchasphysicsandchemistry,however,thetypographicaltraditionsaresomewhat
dierent.)ThecapitalGreeklettersnotpresentinthislistarethelettersthathavethe
sameappearanceassomeLatinletter:AforAlpha,BforBeta,andsoon.Inthelistof
lowercaselettersthereisnoomicronbecauseitwouldbeidenticalinappearancetoLatino.
Inpractice,theGreeklettersthathaveLatinlook-alikesareseldomusedinmathformulas,
toavoidconfusion.
\Gamma
\Delta
\Lambda
\Phi
\Pi
\Psi
\Sigma
\Theta
\Upsilon
\Xi
\Omega
\alpha
\beta
\gamma
\delta
\epsilon
\zeta
\eta
\theta
\iota
\kappa
\lambda
µ \mu
\nu
\xi
\pi
\rho
\sigma
\tau
\upsilon
\phi
\chi
\psi
! \omega
z \digamma
" \varepsilon
{ \varkappa
' \varphi
$ \varpi
% \varrho
& \varsigma
# \vartheta
3.5.OtheralphabeticsymbolsThesearealsoclass0.
@ \aleph
i \beth
k \daleth
j \gimel
{ \complement
` \ell
ð \eth
~ \hbar
} \hslash
f \mho
@ \partial
} \wp
s \circledS
k \Bbbk
` \Finv
a \Game
= \Im
< \Re
3.6.MiscellaneoussimplesymbolsThesesymbolsarealsoofclass0(ordinary)which
meanstheydonothaveanybuilt-inspacing.
# \#
& \&
\ \angle
8 \backprime
F \bigstar
\blacklozenge
\blacksquare
N \blacktriangle
H \blacktriangledown
? \bot
| \clubsuit
\diagdown
\diagup
} \diamondsuit
; \emptyset
9 \exists
[ \flat
8 \forall
~ \heartsuit
1 \infty
\lozenge
] \measuredangle
r \nabla
\ \natural
¬ \neg
@ \nexists
0 \prime
] \sharp
\spadesuit
^ \sphericalangle
p \surd
> \top
4 \triangle
O \triangledown
? \varnothing
Note1.Acommonmistakeintheuseofthesymbolsand#istotrytomakethemserveasbinary
operatorsorrelationsymbolswithoutusingaproperlydefinedmathsymbolcommand.Ifyoumerelyuse
theexistingcommands \square or \# theinter-symbolspacingwillbeincorrectbecausethosecommands
produceaclass-0symbol.
Note2.Synonyms:¬ \lnot
\square

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