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SomeTipsandTricksforUsingLaTeX
inMathTheses
byRobBenedetto
Howto Usethelessamplethesis.tex, thesis.tex, and
latextips.tex
WARNING!!!!
Thisdocument(latextips.tex)is
NOT
agoodmodeltobuild
amaththesisfrom. Themarginsarewrong,thespacingiswrong,andthestyleofwriting
isfartoocolloquial.(Forexample,youshouldavoidcontractionsandthepronouns\I"and
\you,"avoidusingquotationmarksunlessyou’reactuallyquoting something,minimizethe
useofparentheticalcommentsandtheword\so,"andgenerallyuseamoreformalwriting
stylethanyou’llndinthislatextips.texdocument.)
Instead,youshouldusethelesamplethesis.texasamodelforyourthesis.Thatle
has allthemarginsandspacingsetproperly,anditiswritteninastyleappropriatefora
maththesis. Toactuallywriteyourownthesis,startwiththele e thesis.tex,whichhas
allthecorrectstructureandformattingcommandsyouwillneedbutnowrittencontent.
Still,Ihopeyouwillndthis latextips.tex document usefulas well. . It t isintended
to givesuggestionsfor howtouse LaTeX eectively,togive awider variety of examples
of LaTeX tricks s than n appeared in samplethesis.tex, and to explain some of the inner
workingsofsamplethesis.texandthesis.tex.Thatis,youshouldusethesis.texforits
structure,samplethesis.texandsamplethesis.pdf asanexample,andlatextips.tex
andlatextips.pdfforadvice.
I’drecommendyoulooknotonlyatthethreeraw.texles,butalsoattheLaTeX-edand
printeddocumentstheygenerate.Therearealotoflittletricksandtechniquesembeddedin
them,andyoushouldfamiliarizeyourselfwithboththerawLaTeXcodeandtheresulting
printeddisplay.Quiteafewofthosetricks,likehowtomakethedouble-barnormsymbols
kkthatappearlater,arenotexplicitlymentionedinthetextofthisdocument,sobeready
toscrollbackthroughthe.texletolearnhowsomesymbolwasgenerated.
Ofcourse,there’s much more toLaTeXthanwhat you’llndhere; ; so get t yourself a
goodLaTeXbook,suchasG.Gratzer,MathintoLaTeX,3rded.,Birkhauser,Boston,2000.
Thereareonlinesources,too. Forexample,theLaTeXWikibookmaybefoundat
http://en.wikibooks.org/wiki/LaTeX
MorelinkstoanumberofonlineLaTeXmanualsandtutorialsat
http://www.tug.org/interest.html#latexmanuals
1
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Chapter1
SomeLaTeXExamples
First,aquickcommentthatcanonlygohere,eventhoughitistopicallyoutofplace: ifI
putaSubsectionhere(beforetherstSectionofaChapter),Igetaweirdnumber,likethis:
1.0.1 SubsectionNumbersInvolvingZero
See, it t looks strange e to o refer implicitly to Section Zero. . The e same thing happens
1
with
Theorems(or Denitions,etc.) ) appearingbeforetherst t Section of aChapter; ; see,e.g.,
Theorem1.0.1insamplethesis.tex.Avoidnumberinginvolvingzerosinathesis.
1.1 MathCommands
Multilineequations canbegeneratedwiththealign*environment,using&foralignment
pointsandcolumnbreaks,and\\fornewlines:
i
(logr)=(p
i
+1)logkfk
(x;r)
2p
i
(logr+logkf
0
k
(x;r)
)
=(1 p
i
)logkfk
(x;r)
2p
i
log(f;(x;r))
logkfk
(x;r)
p
i
(f;(x;r)):
Ifyouwantlabelsonthatkindofequation,trythealignenvironment.
logkfk
(x;
~
R)
logkfk
(x;R00)
+
2p
p 1
[(r;(x;R
00
)) (r;(x;
~
R))]
1
p 1
plogjj+2plog logkfk
(x;R00)
:
(1.1)
NotethatsinceIonlywantedthesecondline,andnotbothlines,ofinequality(1.1)tohave
alabel,Iusedthe\notagcommandinthe.texleontherstline.
Youcanrefertolabelledequations,likeequation(1.1)orsequence(1.2),fromanywhere
inthepaper,evenbeforetheyappear. Butmakesuretouse\eqrefratherthan\refwhen
referencingequations;\refgivesusequation1.1ratherthanthenicerequation(1.1).
1
That’sbecauseInumberedTheoremsbySectioninsamplethesis.tex.You’dalsogetzerosifforsome
reasonyouputaTheorembeforeChapter1,evenifyounumberyourTheoremsbyChapter.
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Ifyouwantjustaregularone-linedisplayedequationlabelled,usetheequationenvi-
ronment.Forexample,here’sasequenceofonesandzeros.
0;:::;0
|
{z
}
m
0
;1;:::;1
|
{z
}
M
1
;0;:::;0
|
{z
}
m
1
;1;:::;1
|
{z
}
M
2
;0;:::;0
|
{z
}
m
2
;::::
(1.2)
Formatrices,usethematrixenvironment,againusing&forcolumnbreaksand\\for
newlines. Use e \left and\right to make brackets bigenough tot aroundwhatever is
betweenthem.Use\cdots,\vdots,and\ddotstogetvariousdirectionsofdots:
A=
0
B
B
B
B
B
@
1
1

1
x
1
x
2

x
n
x
2
1
x
2
2

x
2
n
.
.
.
.
.
.
.
.
.
.
.
.
x
n 1
1
x
n 1
2
 x
n 1
n
1
C
C
C
C
C
A
; ha;bi=a
T
1 2
3 4
b; and d r
~
F =
~
i
~
j
~
k
@
@x
@
@y
@
@z
P
Q
R
:
Ifyouwant,youcanskiptyping outthe\left( and\right)parenthesescommandsfor
matricesbyreplacingthematrixenvironmentwithpmatrixforregular(round)parentheses,
bmatrixforsquarebrackets,vmatrixforverticallines,Vmatrixfordoubleverticallines,or
Bmatrixforcurlybrackets.Forexample,
Tr
0
@
1
 4
2
5
1
1  1 1 8
1
A
=1+5+8=14;
and
det
2
6
6
6
6
6
4
1
1

1
x
1
x
2
 x
n
x
2
1
x
2
2
 x
2
n
.
.
.
.
.
.
.
.
.
.
.
.
x
n 1
1
x
n 1
2
 x
n 1
n
3
7
7
7
7
7
5
=
1
1

1
x
1
x
2

x
n
x
2
1
x
2
2

x
2
n
.
.
.
.
.
.
.
.
.
.
.
.
x
n 1
1
x
n 1
2
 x
n 1
n
=
Y
1i<jn
(x
j
x
i
):
Youcanuse\left(and\right)(or\left[and\right],or\left\{and\right\},
or\left|and\right|,oreven\left(and\right]|theydon’thavetomatch)tomake
bracketsaroundanyclumpofmathsymbols.Butsometimesyoumaywantbigbutnothuge
brackets.Forexample,theparenthesesaround
0
B
@
X
1in
i6=5
i
2
1
C
A
3
and
(
X
1in
i6=5
i
2
)
3
arewaytoobigandwaytoosmall,respectively.Instead,theexpression
X
1in
i6=5
i
2
3
3
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looks much h better, , even if the subscript sticks out t the e bottom a little. . You u can make
parentheseslikethese,anywherefromonetofourspecicsizesbigger,usingthe\big,\Big,
\bigg,or\Biggcommandsjustbeforetheparentheses.
Forintegrals,try usingthe\, spacingcommandtogetjusttherightamountofspace
beforethedx(orinthiscase,d):
L
C
(r)=r
Z
2
0
f
#
(re
i
)d insteadof L
C
(r)=r
Z
2
0
f
#
(re
i
)d:
Formultipleintegrals,youcando
ZZ
S
(curl
~
F)d
~
S=
I
C
~
Fd~r
or
ZZZ
E
div
~
G(x;y;z)dV =
ZZ
S
~
Gd
~
S;
butifyouwantiteratedmultipleintegrals,justuse\intmultipletimes:
Z
1
0
Z
1 x
0
Z
1 x y
2
0
dzdydx
xsin(yz)+3
:
As you may y have e noticed, , for certainsymbols s like sums s and d products, LaTeX treats
subscriptsandsuperscriptsdierentlyindisplayedversusin-linemathematics.Forexample,
Z
b
a
f(x)dx= lim
n!1
n
X
i=1
f(x
i
)x
i
:
becomes
R
b
a
f(x)dx=lim
n!1
P
n
i=1
f(x
i
)x
i
inin-linemathmode,sothatitwilltverti-
cally. Youcanusethe\displaystylecommandtoget
Z
b
a
f(x)dx= lim
n!1
n
X
i=1
f(x
i
)x
i
in
in-linemathmode. Buteitherway,ifanin-linemathequationistoobig,itcanmakethe
paragraphhardtoread. Bigequationsshouldbedisplayed.
Thesamesizingissuecomesupwithfractions,evenindisplayedmath.Forexample,
lim
h!0
x+h+2
(x+h)2
x+2
x2
h
and f(x;y)=
(
x
2
+3xy
2
x2+y2
if(x;y)6=(0;0)
0
if(x;y)=(0;0)
havetiny,unreadablefractions.Youcanforcethosefractionstobebiggerbyusing\dfrac
insteadof\frac,toobtain
lim
h!0
x+h+2
(x+h)
2
x+2
x
2
h
and f(x;y)=
8
<
:
x
2
+3xy
2
x
2
+y
2
if(x;y)6=(0;0)
0
if(x;y)=(0;0):
HerearesomeothermiscellaneousLaTeXcommandstobeawareof:
 \varepsilongivesadierent-lookingepsilon:"insteadofthedefault.
 \varphigivesadierent-lookingphi:’insteadof.
4
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 \smallsetminusgivesasmallersetsubtractionsignthan\setminus|compareArB
withAnB.
 \varnothinggivesamorecircularnullsetsignthan\emptyset|compare?with;.
 \nmidgivesthe\doesnotdivide"sign. Ingeneral,ifyouwanttoputaslashthrough
asymbol,precedethesymbolwith\not,asinx62Aorx65. (Forexample,\neq
iseectivelyjustanabbreviationfor\not =,albeitaveryusefulone.) ) Butifyoutry
\not |or\not \mid,yougettheugly6jor6j,whereas\nmidgivesthemuchnicer-.
 \binom{n}{m}makesthe\nchoosem"binomialcoecientsymbol,giving
n+1
k+1
=
n
k
+
n
k+1
fordisplayedmathmode,and
7
5
forin-linemathmode.
Thebulletlistabovewasproducedbyanitemizeenvironment. (Togetthesymbol
byitself,use\bulletinmathmode.) LaTeXalsohastwootherbuilt-inlistenvironments:
enumerate,whichgivesnumberedlists,anddescription,whichgiveslistswhereeachitem
beginswithadierentlabel. There’salsothemuchmore exible(buthardertouse)list
environment,butyouareunlikelytoneeditforathesis.
2
1.2 SectioningCommandsandOtherComments
1.2.1 Subsections
Besideschaptersandsections,therearealsosubsections.Butdon’thaveonlyonesubsection
inasection,oronlyonesectioninachapter. Whybreaksomethingupintoonepiece?
3
1.2.2 HatsandBars
Toputahatonamathsymbol,use\hat,asin
^
h(x)or
^
f().Butsometimeswidehatlooks
better,asin
b
Gor
b
R.Similarly,\bargives
f,but\overline,like\widehat,willstretch,as
in
f,oreven
abcd.
2
IusedalistenvironmenttogetthealphabeticallyenumeratedlistinthestatementsofProposition2.1.2
andLemma3.2.2ofsamplethesis.tex.
3
The hierarchy y of sectioning g commands actually y continues further to o subsubsection, , paragraph, and
subparagraph. Butlet’snotgetcarriedaway. Besides,theselessercousinsofsectionsaren’tnumbered,so
youcan’trefertothemwith\labeland\ref.
Bytheway, \label assigns s tothat label-name the number of the currentstructure|chapter, , section,
subsection,theorem,equation,etc.|thatwe’redeepestinsideandthathasanumber.Ifyouuse\label
inalessercousinlikeasubsubsection,you’llgetthenumberofthesubsectionit’sinside.
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1.2.3 Quantiers
Although LaTeX provides the 9 and 8 symbols, youshould not t use e them,unless you’re
actuallywritingalogicthesisandtheyappearaspartofsymbolicsentences,orsomething
likethat.Ifyouwanttosaythatthereissomex2Rsuchthatblahblahblah,thenactually
writeout\thereissomex2Rsuchthat...,"not\9x2Rs.t....."
1.2.4 PunctuatingMathematics
Don’t forget that you need to o punctuate math. . Allof f the math h in n samplethesis.tex
andlatextips.tex,whetherin-textordisplayed,includespunctuation(period,comma,or
whatever)whenappropriate. Fordisplayedmath,makesurethepunctuationisinsidethe
mathmodedelimiters;LaTeXisprettysmartandwill(usually)doagoodjobinputtingthe
punctuationintherightplace,withtherightamountofspacing. Forin-linemath,itcan
beeither insideoroutsidemathmode;butifit’soutside,youcan’tleaveaspacebetween
theending$or\)andthepunctuation.
4
1.2.5 Spacing
LaTeXisgenerallyvery goodaboutgettingspacingcorrect. . For r example,itputs amore
spaceafteraperiodthanitdoesafteracommaorbetweenwords,regardlessofhowmany
timesyouhitthespacebar. However,ifyouonlywantaregularspaceafteraperiod(say,
becauseyou’reusinganabbreviation),putabackslashjustbeforethespace.Forexample,
Serre et t al. proved
printsas\Serreetal.proved",whereas
Serre et t al.\ proved
printsas\Serreetal.proved".
Meanwhile, to prevent t LaTeX from breaking a line between two words, , use e a tilde ~
insteadofaspace. For r example,alinebreakinthe middleofareferenceto,say,Section
1.2 just looks weird. . Instead, , I’ve been n using g tildes s whenever I make a a \ref f reference
to Chapters, Sections, , equations, , etc., so as s to force e LaTex x to o print t such h references s as
Section1.2. Notethat t thespacingbetweenwords onthelastfewlines wasalittlewider
thanusual;that’sLaTeXrearrangingthingstoavoidtheforbiddenlinebreak.
4
Note that this s paragraph contains both italicized andboldfacedtext, , producedwith\emph h (short
for\emphasis")and\textbf,respectively. Althoughyoucanalsouse\textittogetitalics,itisusually
bettertouse\emph. Forexample,using\emphinsideatheoremenvironment,wherethesurroundingtextis
alreadyitalicized,makesthefollowingtextnon-italicized,sothatitactuallystandsoutasintended;lookat
Proposition2.1.2.dofsamplethesis.tex. Otherrelatedcommandsinclude\textttfortypewriter r text
(usefulfordisplayingprogramcode)and\textslforslantedtext.
FYI,incaseyouseeitsomewhere: therearealsolegalbutolder-styleLaTeXcommands\bf,\em,\tt,
\sl,etc.,buttheyarealittleclunkierandareusedslightlydierently. Still,\textbf{hello world}and
{\bf hello world}bothproducehelloworld,forexample.
6
Weekof
Sections
TopicsandComments
Feb2
13.5,13.6,14.1
Lines,Planes,Quadrics,Vector-valuedFunctions
Feb9
14.2{14.4
CalculusforVector-valuedFunctions
Feb16
15.1,15.2
MultivariableFunctions,Limits
FIRSTMIDTERM:Wednesday,Feb18
Feb23
15.3{15.5
PartialDerivatives,ChainRule
Mar2
15.6,15.7
Gradient,ExtremeValues
Mar9
15.8,16.1,16.2
LagrangeMultipliers,DoubleIntegrals
Mar16
|
(SpringBreak;noclasses)
Table1.1:AportionofaMath13syllabus
1.2.6 Tables
Ifyouneedatableinyour thesis,you canmakeonewiththetabular environment. . I’ll
put one right here. . (Well,I’m m typing g ithere,but t LaTeX decidedto put it at thetopof
thispage;moreonthatinasecond.) Thelettersl,c,andrinsidethebracketsrightafter
\begin{tabular}specifywhethereachparticularcolumnoftextisleft-justied,centered,
orright-justied.Thejsymbols,ofcourse,saywheretheverticallinesgo.
Note that because Iput Table 1.1insidea table environment, , LaTeX automatically
gaveitatablenumber,soitwouldshowupinthelistoftables(ifIhada\listoftables
commandinthefront matter;see Section B.2),andIcanreferto itwith \ref, , as s Idid
earlierinthissentence. Inaddition,Iwasabletogiveitacaption.Thetableenvironment
alsoturnsthetableintoa\ oatingobject",meaningthatLaTeXwillputitwhereitthinks
best,whichwillprobablybeinadierentplaceorevenonadierentpage. Forexample,
Table1.1 appears atthetopofthe page,eventhoughItypedthe code that createdthe
tableimmediatelyafterthesecondsentenceofthissection. Youcan(tryto)forceLaTeX
toputthetableinaparticularplacebyputtinganoptionrightafterthat\begin{table}
command:[h]toputitrighthere,[b]toputitatthebottomofthepage,[t]toputitat
thetopofthepage,or[p]toputitonadierentpage. (Butifthetablesimplywon’tt
whereyouwantit,LaTeXwilljustdothebestitcan.)
Ifyouusethetabularenvironmentwithoutthetableenvironment,thetablewillappear
justwhereyouputit,butwithnolabel,caption,orappearanceinalistoftables,likethis:
x
( 1; 1)
( 1;1=
3
p
2)
(1=
3
p
2;1)
f
0
(x)
+
+
f(x)
%
%
&
1.2.7 Figures
Ifyouneedguresinyourthesis,usethefigureenvironmentandthe\includegraphics
command. You’llalsoneedtohavethecommand\usepackage{graphicx} } somewherein
yourpreamble,sothatLaTeXactuallyknowsthe\includegraphicscommand. (SeeSec-
tionB.1).Thegraphicxpackageknowsalotofleformats,including.pngand.pdf.(Some
7
graphicsutilitiesproduce.epsles(EncapsulatedPostScript);dependingonyourlatexim-
plementation,youmayneedtoconvertthoseto.pdfwithautilitylikeepstopdf.) Figure1.1
givesanexample.
Z
3
1
3
+Z
3
2
3
+Z
3
Figure1.1:AnExampleofaFigure.
Figures,liketables,arealso oatingobjects. As s withthe tableenvironment,youcan
usethe[h],[b],[t],and[p]optionswiththefigureenvironment,ifyouwant. Iused
the[h]optiononFigure1.1,toprodLaTeXintoputtingitjustwhereItypedit.
IalsoputFigureA.1laterinthisdocument. FigureA.1usesthesamegraphicsleas
Figure1.1(namely,sample
fig.pdf).However,forthesakeofvariety,IhadLaTeXrescale
thesizeofFigureA.1withthe\scaleboxcommand;specically,Iused\scalebox{0.8},
tomakethegure80%ofitsactualsize.
8
AppendixA
Otherlittlethings
A.1 Howtomakeappendices
Justput\appendixinthe.texle,andpresto,all\chapters"thatfollowareAppendices!
A.2 Comments
Asyou’veprobablynoticed,linesinthe.texlebeginningwith%arecomments. LaTeX
ignoreseverythingfromthe% symboluntiltheendoftheline. . Soforonething,youcan
leaveyourselfnotesexplainingwhatvarioustechnicaldeclarationsdo,ortohighlightwhere
various chapters orsections start. . For r anotherthing,ifyoudecideto cut somechunk of
yourthesisthatyou’vealreadywritten,it’sprobablysafertocommentitout(i.e.,precede
eachlineofitwitha%symbol)ratherthandeleteit.Thatway,ifyoudecidelaterthatyou
actuallywanttokeepsomeorallofwhatyoucut,it’seasytorecover.
A.3 Linebreaks
LaTeXtreatsalinebreak(i.e.,hittingtheEnterkey)essentiallythesameasaspace. The
onlyrealexceptionisthattwoormoreconsecutivelinebreaks(i.e.,leavingatleastoneblank
lineinthe.tex le)tellsLaTeXtomakeaparagraphbreak. . Ithinkit’s s agoodthingto
havealotoflinebreaksinyour.texle.Linebreaksmaketheleitselfmucheasiertoread
andtoedit,withoutchangingtheappearanceoftheprintedversion.
However,aclumpoftwo,orseven,orsevenhundredconsecutiveblanklinesistreatedthe
sameasone.Ifyouwantextraverticalspaceforsomereason,usethe\vspacecommand.For
example,Igotthebigspacejustabovebyputting\vspace{0.3in}betweentwoparagraphs.
Incidentally, paragraph breaks (i.e., double e linebreaks) ) are e not allowed in the middle
ofmathmode; they y willgive youanerror message. . Single e linebreaksinmathmode are
perfectlyne,though|asnotedabove,theyaretreatedjustlikespaces.
Oh,bytheway,I’mgoingtoputFigureA.1,whichIpromisedbackinSubsection1.2.7,
righthere. Recallthatit’sa oatingobject;LaTeXdecidedtoputitonthenextpage.
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Z
3
1
3
+Z
3
2
3
+Z
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FigureA.1: Anotherrandomgure.
A.4 Dashes,Ellipsis,andQuotes
LaTeXhandlesthesepunctuationmarksalittledierentlythanyoumightexpect.
Therearethreekindsofdashes: thehyphen-,forintra-worddashes;theendash{,for
numberorletterranges,like\pages55{70"or\parts(b){(f)";andtheemdash|,whichis,
ofcourse,apunctuationmark|thekindthat’susedinmuchthesamewayasasemicolon.
CodetheminLaTeXwith-,with--,andwith---,respectively.
An ellipsis s is the e \dot-dot-dot" punctuation ..., , used for partialquotatations. . (For
example,youwillprobablyneeditwhenwritingthe\Corrections"portionofyourthesis.)
Three periods like this... . gives s the e screwy spacing found in the middle of this s sentence.
Instead,usethe\ldotscommand,toget...,asdesired.
For double quotes, , donot t usethe "symbol. . (Aboutthe e onlyLaTeXuse of " isfor
umlauts;H\"{o}lderproducesHolder.) Instead,openwithtwoleftsingle-quotes(found
totheleftofthe1keyonmostkeyboards)andclosewithtworightsingle-quotes .Similarly,
forsinglequotes,usetheleftandrightquotesasappropriate.Forexample,
Cohen notes, , These G\"{o}del l numbers    are large.
gives:Cohennotes,\These‘Godelnumbers’arelarge." However,both
Cohen notes, ,  These  G\"{o}del l numbers    are large.
and
Cohen notes, , "These  G\"{o}del numbers  are large."
givetheugly:Cohennotes,"These’Godelnumbers’arelarge."
I’d recommend you edityour.tex x le usingthe emacs text-editor. . Amongits s many
advantages,emacsautomaticallydoeswhatyouwantwhenyouhitthe"key;itguresit
out whetheryouneedtheumlautsymbol,two left quotes, , ortworight t quotes,basedon
whetherthepreviouscharacterwasabackslash,space,orsomethingelse. Soyouactually
endupusingthe"key afterall,evenifyoudon’tendupusingthe"symbol.
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