Using the Penn Biostat LaTeXTemplates

January 4 2018

Sarah J RatcliffeProfessor of Biostatistics

Why LaTeX Itrsquos is a document preparation system for high-quality

typesetting Controls all the page layout fonts formatting for you through

a style file Control over large documents containing sectioning cross-

references tables and figures Typesetting of complex mathematical formulas Advanced typesetting of mathematics with AMS-LaTeX Automatic generation of bibliographies and indexes

Penn Biostat LaTeX Templates Available from Biostat Research Website

bull httpsdbemedupennedubiostat-researchresources-educational Separate zipped bundles for

bull MS Thesisbull PhD Dissertation

Templates created to ensure your submission meets Pennrsquos formatting requirementsbull httpwwwupenneduprovostdissertation_resourcesbull Check requirements havenrsquot changed since last date template updatedbull Word template available from Provostrsquos office

Why LaTeX Itrsquos is a document preparation system for high-quality

typesetting Controls all the page layout fonts formatting for you through

a style file Control over large documents containing sectioning cross-

references tables and figures Typesetting of complex mathematical formulas Advanced typesetting of mathematics with AMS-LaTeX Automatic generation of bibliographies and indexes

Penn Biostat LaTeX Templates Available from Biostat Research Website

bull httpsdbemedupennedubiostat-researchresources-educational Separate zipped bundles for

bull MS Thesisbull PhD Dissertation

Templates created to ensure your submission meets Pennrsquos formatting requirementsbull httpwwwupenneduprovostdissertation_resourcesbull Check requirements havenrsquot changed since last date template updatedbull Word template available from Provostrsquos office

Penn Biostat LaTeX Templates Available from Biostat Research Website

bull httpsdbemedupennedubiostat-researchresources-educational Separate zipped bundles for

bull MS Thesisbull PhD Dissertation

Templates created to ensure your submission meets Pennrsquos formatting requirementsbull httpwwwupenneduprovostdissertation_resourcesbull Check requirements havenrsquot changed since last date template updatedbull Word template available from Provostrsquos office

Penn Biostat LaTeX Templates MS bundle contains

bull pennbiostatmssty - style file that controls formattingbull thesisex_2017tex - example LaTeX file to work frombull thesisex_2017pdf - compiled LaTeX documentbull dissertationexbib - example LaTeX bibliography filebull anviljpg - figure used by the example file

PhD bundle containsbull pennbiostat_biblatexsty - style file that controls formattingbull dissertationex2017tex - example LaTeX file to work frombull dissertationex2017pdf - compiled LaTeX documentbull dissertationexbib - example LaTeX bibliography filebull RR1jpg - figure used by the example file

Penn Biostat LaTeX Templates

PhD Dissertation Template ndash ltdissertationex2017texgt

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

Penn Biostat LaTeX Templates

PhD Dissertation Template ndash ltdissertationex2017texgt

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash ltdissertationex2017texgt

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash Preamble

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash Main Text

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash Main Text Can split document into multiple tex files

beginmainf

includeintroduction - links in file ltintroductiontexgtincludechapter1 - links in file ltchapter1texgtincludechapter2includechapter3includediscussion

endmainf

Allows compiling by file to check for errorsincludeonlychapter1chapter2begindocument

- only include chapters 1 amp 2 when compiling

- must come directly before begindocument

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

PhD Dissertation Template ndash Appendices

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

Labels Cross References LaTeX uses cross-references and labels to ensure all

numbering is correctbull Never type a number of a chapter section figure table equation etc

Use label to name parts to cross-referencechptIntroduction labelchptintrocaptionMy figure of the datalabelfigdata

Use ref to cross-reference the number in the textSee chapter refchptintro for more informationshown in Figure reffigdataFigure~reffig1

~ prevents LaTeX wrapping a line between Figure and the number No spaces

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

References Are controlled using biblatex a bibliography file and citation

commands in the tex file Never manually type a reference in your document BibLaTeX help

bull httpswwwsharelatexcomblog20130731getting-started-with-biblatexhtml

All citations should be placed in a bibliography file (bib) In your tex file use

bull Inline citation citeten2000mix Ten Have et al 2000bull Parenthesized citation

citep[eg][]pin2006eff (eg Pinheiro and Chao 2006)bull Multiple parenthesized citations citepten2000mixpin2006eff

Bibliography File Contains all details for each reference

ARTICLEli2010modauthor = LiY and WileytoE P and HeitjanDtitle = Modeling smoking cessation data with alternating states and

a cure fraction using frailty modelsjournal = Statistics in Medicinevolume = 29pages = 627-638year = 2010

Can contain references you donrsquot use in the tex file bull If not cited they wonrsquot be included in your reference list

Use to maintain capitals in titles Eg HIV

key used in cite commands to link to reference

Bibliography FileCreation of BibTex entries OttoBib - search for books by ISBN Google Scholar - click the ldquoScholar preferencesrdquo link Under

Bibliography Manager select ldquoShow links to import citations into BibTeXrdquo Save preferences

TeXMed ndash converts PubMed Medline entries into BibTex formathttpwwwbioinformaticsorgtexmed

Bibliography FileCreation of BibTex entries OttoBib - search for books by ISBN Google Scholar - click the ldquoScholar preferencesrdquo link Under

Bibliography Manager select ldquoShow links to import citations into BibTeXrdquo Save preferences

TeXMed ndash converts PubMed Medline entries into BibTex formathttpwwwbioinformaticsorgtexmed

Bibliography FileManaging BibTex entries JabRef

bull httpjabrefsourceforgenetbull Java based graphical front end to manage BibTeX databasesbull Can directly import references from online

Compiling the Dissertation Multiple steps needed to ldquoBuildrdquo1 Run LaTeX -gt PDF2 Run BibTeX - Needed to find references3 Run LaTeX -gt PDF4 Run LaTeX -gt PDF

Depending on build set-up may be able to just run LateX -gt PDF twice

Must run LaTeX at least twice at end to get all numbering correct

LaTeX Overfull hbox Warnings

Your dissertation will be rejected if you dont fix these 1 Formulae LaTeX will not wrap if they go into the margins

bull You will get a warning message but LaTeX will compile normally with the formula even running off the side of the page

2 Long Words Manually help LaTeX hyphenatebull If a long word will just end into the margin and LaTeX is not sure

where to hyphenate to split the word over two lines it may let it run into the margin

bull Control the hyphenation manually to keep within the margins using the hyphenation hints command at the top of the template Example hyphenationrep-re-sent-a-tivematlaber-go-nom-ic

3 Verbatim Use of the verbatim environment removes all of LaTeXs formating controls for that section

bull You must manually add line returns to prevent overflow

Some Useful Packages verbatim

bull Allows you to type exact text bull Great for software output

Matlab

beginboxedverbatim

gtgt A = 4ones(3)

A =

04000 04000 04000

04000 04000 04000

04000 04000 04000

endboxedverbatim

Some useful packages - Tables longtable

bull allows table that extends over multiple pages to be split multirow

bull allows table columns to span multiple rows columns

usepackagemultirow

begintabularcc|c|c|c|c|l

cline3-6

amp amp multicolumn4|c|Primes cline3-6

amp amp 2 amp 3 amp 5 amp 7 cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|504 amp 3 amp 2 amp 0 amp 1 amp cline2-6

multicolumn1|c| amp

multicolumn1|c|540 amp 2 amp 3 amp 1 amp 0 amp cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|gcd amp 2 amp 2 amp 0 amp 0 amp min cline2-6

multicolumn1|c| amp

multicolumn1|c|lcm amp 3 amp 3 amp 1 amp 1 amp max cline1-6

endtabular

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

LaTeX Overfull hbox Warnings

Your dissertation will be rejected if you dont fix these 1 Formulae LaTeX will not wrap if they go into the margins

bull You will get a warning message but LaTeX will compile normally with the formula even running off the side of the page

2 Long Words Manually help LaTeX hyphenatebull If a long word will just end into the margin and LaTeX is not sure

where to hyphenate to split the word over two lines it may let it run into the margin

bull Control the hyphenation manually to keep within the margins using the hyphenation hints command at the top of the template Example hyphenationrep-re-sent-a-tivematlaber-go-nom-ic

3 Verbatim Use of the verbatim environment removes all of LaTeXs formating controls for that section

bull You must manually add line returns to prevent overflow

Some Useful Packages verbatim

bull Allows you to type exact text bull Great for software output

Matlab

beginboxedverbatim

gtgt A = 4ones(3)

A =

04000 04000 04000

04000 04000 04000

04000 04000 04000

endboxedverbatim

Some useful packages - Tables longtable

bull allows table that extends over multiple pages to be split multirow

bull allows table columns to span multiple rows columns

usepackagemultirow

begintabularcc|c|c|c|c|l

cline3-6

amp amp multicolumn4|c|Primes cline3-6

amp amp 2 amp 3 amp 5 amp 7 cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|504 amp 3 amp 2 amp 0 amp 1 amp cline2-6

multicolumn1|c| amp

multicolumn1|c|540 amp 2 amp 3 amp 1 amp 0 amp cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|gcd amp 2 amp 2 amp 0 amp 0 amp min cline2-6

multicolumn1|c| amp

multicolumn1|c|lcm amp 3 amp 3 amp 1 amp 1 amp max cline1-6

endtabular

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Some Useful Packages verbatim

bull Allows you to type exact text bull Great for software output

Matlab

beginboxedverbatim

gtgt A = 4ones(3)

A =

04000 04000 04000

04000 04000 04000

04000 04000 04000

endboxedverbatim

Some useful packages - Tables longtable

bull allows table that extends over multiple pages to be split multirow

bull allows table columns to span multiple rows columns

usepackagemultirow

begintabularcc|c|c|c|c|l

cline3-6

amp amp multicolumn4|c|Primes cline3-6

amp amp 2 amp 3 amp 5 amp 7 cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|504 amp 3 amp 2 amp 0 amp 1 amp cline2-6

multicolumn1|c| amp

multicolumn1|c|540 amp 2 amp 3 amp 1 amp 0 amp cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|gcd amp 2 amp 2 amp 0 amp 0 amp min cline2-6

multicolumn1|c| amp

multicolumn1|c|lcm amp 3 amp 3 amp 1 amp 1 amp max cline1-6

endtabular

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Some useful packages - Tables longtable

bull allows table that extends over multiple pages to be split multirow

bull allows table columns to span multiple rows columns

usepackagemultirow

begintabularcc|c|c|c|c|l

cline3-6

amp amp multicolumn4|c|Primes cline3-6

amp amp 2 amp 3 amp 5 amp 7 cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|504 amp 3 amp 2 amp 0 amp 1 amp cline2-6

multicolumn1|c| amp

multicolumn1|c|540 amp 2 amp 3 amp 1 amp 0 amp cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|gcd amp 2 amp 2 amp 0 amp 0 amp min cline2-6

multicolumn1|c| amp

multicolumn1|c|lcm amp 3 amp 3 amp 1 amp 1 amp max cline1-6

endtabular

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

usepackagemultirow

begintabularcc|c|c|c|c|l

cline3-6

amp amp multicolumn4|c|Primes cline3-6

amp amp 2 amp 3 amp 5 amp 7 cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|504 amp 3 amp 2 amp 0 amp 1 amp cline2-6

multicolumn1|c| amp

multicolumn1|c|540 amp 2 amp 3 amp 1 amp 0 amp cline1-6

multicolumn1|c|multirow2Powers amp

multicolumn1|c|gcd amp 2 amp 2 amp 0 amp 0 amp min cline2-6

multicolumn1|c| amp

multicolumn1|c|lcm amp 3 amp 3 amp 1 amp 1 amp max cline1-6

endtabular

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Some useful packages - Figures wrapfig

bull allows text to wrap around the figure instead of the figure taking up an entire line

subfigbull place several figures (or tables) into one figure (table) with separate

caption options

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

usepackagesubfig

beginfigure

centering

subfigure[A gull]qquad

subfigure[A tiger]qquad

subfigure[A mouse]

label3figs-c

captionPictures of animalslabel3figs

endfigure

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Equations Define complex commonly used symbols at start of document

newcommandvc[1]mboxboldmath$1$

newcommandyijvcy_ij

newcommandbSbvcb^T vcSigma_u vcb

newcommandcovoperatornamecov

newcommandvaroperatornamevar

newcommandtroperatornametr

Reference equations using eqref to automatically get parentheses Egequation eqrefeqintegration equation (12)

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

EquationsEnvironments in amsmath package align

bull nicer multiline equation alignment

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

beginalignvcnu^(k+1) amp= vcnu^(k)+(vcX_1E(vcM)^(k)vcX_1)^-1vcX_1E(tildevcY)^(k)halR amp= left( sum_iXRi^TXRi right)^-1Esum_ivcX_2i^T(vcr_i-vc1_n_ivcb^Tui)hb amp= Eleft( sum_in_iuiui^T right)^-1Esum_iuivc1_n_i^T(vcr_i-vcX_2ivcalpha_2)hsigu amp= left(sum_in_iright)^-1Esum_in_iuiui^Thsigb amp= left(sum_in_iright)^-1Esum_ijvcbeta_ijvcbeta_ij^ThsigR amp= left(sum_in_iright)^-1Esum_i(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)^Tamp qquad times(vcr_i-vcX_2ivcalpha_2-vc1_nivcb^Tui)endalign

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

EquationsEnvironments alignat

bull align equations at more than one place split

bull use inside equation align etc to split an equation over multiple lines with multiline equation getting only one reference number

beginequationlabelxx

beginsplit

aamp=b+c-d

ampquad +e-f

amp=g+h

amp=i

endsplit

endequation

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

EquationsEnvironments multline

bull align first line of equation on the left last line on the right and center middle lines

beginmultline

a+b+c+d+e+f

+i+j+k+l+m+n

endmultline

gatherbull center alignment of all equations

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Equations

Useful commands in amsmathpackage intertext

bull place correctly formatted lines of text in middle of equation without affecting alignment

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

The second two simulations were performed assuming the true underlying model was the shared parameter model below with 30 and 50 censoring rates respectivelybeginalignmboxlogit(mu_jkt)=amp-34+23(I_t=2)+2(mboxiron)+01(mboxtime)amp +beta_j1+(mboxtime)beta_j2 qquad qquad t=12log(r_j)=amp12+013(mboxiron)+01(mboxlength of ESRD)amp +beta_j1+01beta_j2+err_j intertextwhere left(beginarraycc beta_j1 beta_j2 endarray right) sim amp N left(left(beginarraycc00 endarray right)left(beginarraycc08 amp0101 amp02endarray right) right) err_j sim amp N(007)endalign

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

EquationsUseful commands in amsmath package left right

bull used to let LaTeX set deliminator sizes correctly over multiple lines of equations

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

beginalign

phi(yijamp|xyuivcbeta_ijhatvcvarphi)

amp=

amp times prod_t=2^S-1left(fracmboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T

1+mboxexp(alpha_01++alpha_0t+vcx_1ijk^Tvcalpha_1+T right

amp left -fracmboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1

+T

1+mboxexp(alpha_01++alpha_0(t-1)+vcx_1ijk^Tvcalpha_1+Tright)^y_ijkt

amp

Tamp=

endalign

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

Equations

Useful commands in amsmath package shoveleft shoveright

bull aligns equation to the left right of the linebeginmultline

A

B

shoverightC

D

endmultline

AB

CD

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition

LaTeX Resources

Good intro to LaTeX atbull httpswwwlatex-projectorgbull httpsenwikibooksorgwikiLaTeX

Booksbull httpswwwlatex-projectorghelpbooksbull Frank Mittelbach Michel Goossens Johannes Braams David Carlisle

Chris Rowley (2004) The LaTeX Companion 2nd edition