\documentclass[a4paper,oneside]{book}\usepackage{longtable,tabu,float,hyperref,color,amsmath,amsxtra,amssymb,latexsym,amscd,amsthm,amsfonts,graphicx}\numberwithin{equation}{chapter}\usepackage{fancyhdr}\pagestyle{fancy}\fancyhf{}\fancyhead[RE,LO]{\footnotesize \textsc \leftmark}\cfoot{\thepage}\renewcommand{\headrulewidth}{0.5pt}\setcounter{tocdepth}{3}\setcounter{secnumdepth}{3}\usepackage{imakeidx}\makeindex[columns=2, title=Alphabetical Index, options= -s index.ist]\title{\Huge My notes in \LaTeX}\author{\textsc{Nguyen Quan Ba Hong}\\{\small Students at Faculty of Math and Computer Science,}\\ {\small Ho Chi Minh University of Science, Vietnam} \\{\small \texttt{email. nguyenquanbahong@gmail.com}}\\{\small \texttt{blog. \url{http://hongnguyenquanba.wordpress.com}} \footnote{Copyright \copyright\ 2016 by Nguyen Quan Ba Hong, Student at Ho Chi Minh University of Science, Vietnam. This document may be copied freely for the purposes of education and non-commercial research. Visit my site \texttt{\url{http://hongnguyenquanba.wordpress.com}} to get more.}}}\begin{document}\frontmatter\maketitle\tableofcontents\cleardoublepage\phantomsection\addcontentsline{toc}{chapter}{List of Tables}\listoftables\mainmatter\chapter{Basic \LaTeX}\section{The Fast First Step}\subsection{Structure}The structure of a common \LaTeX\ document looks like the following\begin{verbatim}\documentclass[options]{<Document_class>}Preamble %for LaTeX commands only\begin{document}<Document_text> %text with embedded LaTeX commands.\end{document}\end{verbatim}\textsc{Document class.} \texttt{article} (common used, journal articles and short report), \texttt{report} (for longer documents with chapters, e.g. PhD theses), \texttt{thesis}, \texttt{book}, \texttt{letter}, \texttt{slides}, \texttt{proc} (conference proceedings).\subsection{The Preamble Of The \LaTeX\ Input File}The syntax of the \verb|\documentclass| command is as follows. The command begins with \verb|\documentclass| and ends with the names of one of the available styles, enclosed in curly brackets. The available styles are \texttt{article, report, book} and \texttt{letter}.

Between the \verb|\documentclass| and the name of the document style, one may place a list of options. These options are separated by commas and the list of options is enclosed in square brackets (as in the above example). The options available (which are usually the names of certain \lq style files\rq) include the following\begin{description}\item[11pt] Specifies a size of type known as eleven-point, which is ten percent larger than the ten-point type normally used. \item[12pt] if you want twenty percent larger size, etc,...\item[twocolumn] Produces two-column output.\item[a4paper] This ensures that the page is appropriately positioned on A4 size paper.\\\end{description}

Typing simply\begin{verbatim}\documentclass{article}\end{verbatim}will produce a document in ten-point type size. However the printed output will not be nicely positioned on A4 paper, since the default size is intended for a different (American) paper size. Pages will be automatically numbered at the bottom of the page, unless you specify otherwise. This can be done using the \verb|\pagestyle| command. This command should come after the \verb|documentclass| command and before the \verb|\begin{document}| command. This command has the syntax \verb|\pagestyle{option}|, where the \textit{option} is one of the following\begin{description}\item[plain] The page number is at the center of the foot of the page. Provide no headings. This is the default page style for the \textit{article} and \textit{report} document styles.\item[empty] No page number is printed. Provides neither page numbers nor headings.\item[headings] The page number (and any other information determined by the document style) is put at the top of the page. Will provide page numbers and headings from any \verb|\section|'s that you are using.\item[myheadings] Similar to the \texttt{headings} pagestyle, except that the material to go at the top of the page is determined by \verb|\markboth| and \verb|\markright| commands. Will provide page numbers and custom headings.\end{description}

These commands can also be applied to a single page using \verb|\thispagestyle| instead of \verb|pagestyle|.\subsection{Using Package}\begin{sloppypar}\textsc{Common-Used Packages.} \texttt{amsmath} (greatly enhanced capabilities for mathematical typesetting), \texttt{amstext, amsgen, amsbsy, amsopn, amsfonts, graphicx, overcite, theorem, amssymb} (additional fonts and symbols), \texttt{amsthm} (allows the creation of environments for typesetting lemmas, theorems, examples, remarks, etc, with exible styles and numbering systems; also provides a proof environment).\end{sloppypar}\noindent\textsc{Optional.} \texttt{amscd} (commutative diagrams), \texttt{eucal} (more readable calligraphic letters).\subsection{Creating A Title}To make title, author's name and day created document, type the following commands directly after the \verb|\begin{document}| command

\begin{verbatim}\title{My_Title}\author{My_name}\date{\today}\maketitle\end{verbatim}

You can change \verb|\today| to your favorite one.\subsection{Table Of Contents}Type \texttt{\textbackslash tableofcontents} where you want the table of contents to appear in document. You may also want to change the page numbering so that roman numerals(i, ii, iii) are used for pages before the main document starts. This will alsoensure that the main document starts on page 1. Page numbering can beswitched between arabic and roman using\begin{verbatim}\pagenumbering{}\end{verbatim}Type the following on a new line below\begin{verbatim}\maketitle\end{verbatim}\begin{verbatim}\pagenumbering{roman}\tableofcontents\newpage\pagenumbering{arabic}\end{verbatim}\subsection{Sectioning}\textsc{Dividing document.} Divide document into parts, chapters, sections, subsections,...\\\textbf{Numbering.} \begin{verbatim}\part{•}, \chapter{•}, \section{•}, \subsection{•}, \subsubsection{•},\paragraph{•}, \subparagraph{•}\end{verbatim}\textbf{Non-numbering.}\begin{verbatim}\part*{•}, \chapter*{•}, \section*{•}, \subsection*{•}, \subsubsection*{•}, \paragraph*{•}, \subparagraph*{•}\end{verbatim}\textsc{Labelling.} You can label any of the sectioning commands so they can be referred to in other parts of the document. Label the section with \begin{verbatim}\label{label name}\end{verbatim}Then type\begin{verbatim}\ref{label name}\end{verbatim}or\begin{verbatim}\pageref{label name}\end{verbatim}when you want to refer to the section or page number of the label.\subsection{Files Created}

More than just the *.dvi file may be produced. Don't worry about them - exceptperhaps for the log file you won't need to look at them.\begin{itemize}\item *.aux - cross references, etc.\item *.toc - created by \verb|\tableofcontents|.\item *.lof - created by \verb|\listoffigures|.\item *.lot - created by \verb|\listoftables|.\item *.log - a copy of the diagnostic output that usually comes out on the screen.\end{itemize}Some common errors can be found using the lacheck program on the \LaTeX\file.\subsection{Document And Page Organisation}\textsc{Document classes.} The standard classes are\begin{verbatim}article, book, letter, report, slides\end{verbatim}

The differences between these are often minor. A \texttt{book} can have chapters. In a \texttt{report} sections begin at 0 whereas in an \texttt{article} they begin at 1.\\\\\textsc{Big Documents.} It's best to split your document into smaller files and havea master file looking like this\begin{verbatim}\documentclass[dvips,12pt]{book}\usepackage{a4,color,graphics,palatino,fancyhdr}\begin{document}\pagestyle{empty}\tableofcontents\listoffigures\pagestyle{fancy}\input{chapter1}\input{chapter2}\input{fig2}\input{chapter3}\input{chapter4}\appendix\input{appendices}\end{document}\end{verbatim}on which you can run \LaTeX\ just as if the master file contained all the text of \texttt{chapter1.tex} etc. The advantage of this is that once you have a chapter correct, you can comment out the corresponding \lq input\rq\ line and avoid unnecessary processing. Remember to take out the \verb|\begin{document}| and\verb|\end{document}| lines from the component files.\\\\\textsc{Page Size.} You can choose the margin sizes yourself by changing the following dimensions before the \verb|\begin{document}| line.\begin{verbatim}\setlength{\topmargin}{-0.4in}\setlength{\topskip}{0.3in} % between header and text\setlength{\textheight}{9.5in} % height of main text\setlength{\textwidth}{6in} % width of text\setlength{\oddsidemargin}{0.75in} % odd page left margin

\setlength{\evensidemargin}{0.75in} % even page left margin\end{verbatim}

Note that a margin width of 0cm gives you a margin 4cm wide. Rather than set absolute sizes you can modify the default sizes using commands like the following\begin{verbatim}\addtolength{\evensidemargin}{-1cm}\addtolength{\oddsidemargin}{-1cm}\addtolength{\textwidth}{2cm}\end{verbatim}

Better support for control of page layout is provided by the geometry package.To see the current values of these dimensions, use the layout package,which defines a \verb|\layout| command.\\\\\textsc{Page numbers and headings.} These are determined by the argument givenin \verb|pagestyle{}|. \texttt{fancyhdr} is a popular package that adds useful page headers when the command \verb|\pagestyle{fancy}| is used. This handout uses it.\\\\\textsc{Sectioning.} To start a chapter called Life in a book, just use \verb|\chapter{Life}|. Similar commands to start a part, section or subsection also exist in most document classes (articles don't have chapters or parts though).

If you use the *-form of the command then the sections will not be numbered, neither will it appear in the table of contents.A title will only be numbered if its \textit{depth} isn't more than secnumdepthand will only appear in the contents page if the \textit{depth} isn't more than thevalue of tocdepth. So, for example, doing\begin{verbatim}\setcounter{tocdepth}{2}\setcounter{secnumdepth}{3}\end{verbatim}will cause section 1.4.3 to be numbered, but it won't appear in the contents.\section{Some Useful And Easy Commands}\subsection{Comments}Comments are created using \verb|%text|. \subsection{Spacing}To add blank space into document use the \verb|\vspace{10pt}| or \verb|\vspace*{10pt}|.\subsection{Special Characters}The following symbols are reserved characters which have a special meaning in \LaTeX\begin{center}\#, \$, \%, \^, \&, \_, \{, \}, \~{ }, \textbackslash\end{center}

Insert these as characters\begin{verbatim}\#,\$,\%,\^{},\&,\_,\{,\},\~{}\end{verbatim}and use \verb|\textbackslash| to produce \verb|\|. More information of these character will be discussed in the next section.

\subsection{Footnotes}Footnotes can be inserted with the command \verb|\footnote{text}|. \footnote{For example of footnotes.} \subsection{Quotation Marks}Single quotation marks are produced in \LaTeX\ using \lq and\rq. Double quotation marks are produced by typing \lq\lq and\rq\rq. (The \lq undirected\rq\ double quote character \verb|"| producesdouble right quotation marks it should never be used where left quotation marks are required.) \subsection{Dashes}\LaTeX\ allows you to produce dashes of various length, known as \lq hyphens\rq, \lq endashes\rq\ and \lq em-dashes\rq. Hyphens are obtained in \LaTeX\ by typing \verb|-|, en-dashes by typing \verb|--| and em-dashes by typing \verb|---|. One normally uses en-dashes when specifying a range of numbers. Dashes used for punctuating are often typeset as em-dashes, especially in older books. These are obtained by typing \verb|---|.\subsection{Alignment}\textsc{Center alignment.} \begin{verbatim}\begin{center}...\end{center}.\end{verbatim}\textsc{Left alignment.} \begin{verbatim}\begin{flushleft}...\end{flushleft}\end{verbatim}\textsc{Right alignment.} \begin{verbatim}\begin{flushright}...\end{flushright}\end{verbatim}\subsection{National Symbols}\textsc{National symbols.}\begin{table}\begin{center}\begin{tabular}{|l|c|}\hline \textbf{Input} & \textbf{Output}\\\hline\verb|\oe| & \oe \\ \verb|\OE| & \OE \\ \verb|\ae| & \ae \\ \verb|\AE| & \AE \\ \verb|\aa| & \aa \\ \verb|\AA| & \AA \\ \verb|\o| & \o \\ \verb|\O| & \O \\ \verb|\l| & \l \\ \verb|\L| & \L \\ \verb|\ss| & \ss \\ \verb|!'| & \!' \\\verb|\dag| & \dag \\\verb|\ddag| & \ddag \\

\verb|\S| & \S \\\verb|\P| & \P \\\verb|\copyright| & \copyright \\\verb|\pounds| & \pounds \\\verb|\i| & \i \\\verb|\j| & \j \\\hline \end{tabular} \end{center}\caption{National symbols}\end{table}

More beautiful symbols will be discussed later.\subsection{Table Of Contents}You can easily control the table of contents depth\begin{verbatim}\setcounter{tocdepth}{number}\end{verbatim}\section{\LaTeX\ Command Sequences}All \LaTeX\ control sequences (or commands) begin with the backslash (\verb|\|) symbol. These control sequences follow two formats\begin{itemize}\item The backslash is followed by just one special character.\item The backslash is followed by the \textit{name} of the control sequence. The name of the control sequence consists \textit{only} of letters and is case sensitive.\end{itemize}

The \textit{named} control sequences may require additional \verb|{parameters}| and/or \verb|[options]| which immediately follow the name (with no intervening space). These control sequences are terminated by a space, a number, or any other \lq\lq nonletter\rq\rq, and \LaTeX\ ignores any whitespace after a named control sequence. In order to produce a space after a named control sequence you must enter either \verb|{}| followed by a space, or you must enter a special spacing command. Thecontrol sequences for printing special characters, however, are treated like any other letter or symbol as far as spacing is concerned.\subsection{Active Characters}The \textit{active characters} \verb| $ % & \ ^ _ { } ~| have special purposes within \LaTeX\ . Thus they cannot be produced in the final document simply by typing them directly. On the rare occasions when one needs to use the special characters \# \$ \% \& \_ \{ \} in the final document, they can be produced by typing the control sequences \verb|\# \$ \% \& \_ \{ \}| respectively. However the characters \textbackslash, \verb|^| and \verb|~| cannot be produced simply by preceding them with a backslash. They can however be produced using \verb|\char92|(in the \verb|\texttt| font only), \verb|\char94| and \verb|\char126| respectively. (The decimal numbers 92, 94 and 126 are the ASCII codes of these characters.) \subsection{Miscellany}\textsc{Adjusting Margin Sizes.} Use the \texttt{geometry} package with the margin option.\begin{verbatim}\usepackage[margin=2cm]{geometry}\end{verbatim}\textsc{Optional Arguments for documentclass.} \verb|\documentclass| takes optional arguments. Such as \texttt{12pt, twocolumn}.\subsection{Quotes}

To enclose a word in single quotes you simply enclose theword on the left with the \lq\ symbol (or with the \verb|\lq| command) and on the right with the \rq\ symbol (or with the \verb|\rq| command). For double quotes you simply repeat the character or command string.\subsection{Accents Used In Text}The accents provided by \LaTeX\ include the following\begin{table}\begin{center}\begin{tabular}{|l|c|}\hline \textbf{Input} & \textbf{Output} \\ \hline \verb|\'{e}| & \'{e} \\ \verb|\`{e}| & \`{e} \\ \verb|\^{e}| & \^{e} \\ \verb|\"{o}| & \"{o} \\ \verb|\~{n}| & \~{n} \\ \verb|\={o}| & \={o} \\ \verb|\.{o}| & \.{o} \\ \verb|\u{o}| & \u{o} \\ \verb|\v{c}| & \v{c} \\ \verb|\H{o}| & \H{o} \\ \verb|\t{oo}| & \t{oo} \\ \verb|\c{c}| & \c{c} \\ \verb|\d{o}| & \d{o} \\ \verb|\b{o}| & \b{o} \\\hline \end{tabular} \end{center}\caption{Accents in \LaTeX}\end{table}

These accents are for use in ordinary text. They cannot be used within mathematical formulae, since different control sequences are used to produce accents within mathematics. The control sequences \verb|\i| and \verb|\j| produce dotless \i\ and \j. These are required when placing an accent on the letter. Thus \'{\i} is produced by typing \verb|\'{\i}|.\subsection{Number Times Spacing}There will be times when you will need to submit a draft that is double-spaced, to permit a grader or editor to make comments. LaTeX does not explicitly support doing this, because, well, it looks ugly. To $n-times$ space a paper, put\begin{verbatim}\renewcommand{\baselinestretch}{n}\end{verbatim}in Preamble.\subsection{Sloppy Line Breaks}\LaTeX\ works very hard to find an optimal line break for each line of your document. It you are not happy with its result, surround the offending paragraph with\begin{verbatim}\begin{sloppypar}...\end{sloppypar}\end{verbatim}Then \LaTeX\ will not break words up but rather will allow more spacing between words in the given paragraph.

\subsection{Enlarging Pages}\LaTeX\ works very hard to find the best place to break between pages. If you are unhappy with the result, you can change it with the following two commands \verb|\newpage| (will force the start of a new page), \verb|\enlargethispage{size}| (will increase the number of lines added to a page, where size is a measurement with units).\subsection{The \LaTeX\ Logo}You can typeset the \LaTeX\ logo with the \verb|\LaTeX| command. As with most commands, it consumes any space behind it, so if it isn't at the end of a sentence, use \verb|\LaTeX\| instead.\subsection{Indenting}The default for a \LaTeX\ document is to indent new paragraphs unless the paragraph follows a section heading. If you want to change the indentation, use the \verb|\indent| and \verb|\noindent| commands respectively, at the beginning of the paragraph in question.

If you wish to choose the amount of indentation for some reason, then use the command \begin{verbatim}\setlength{\parindent}{size of indentation with unit}\end{verbatim}

Since this is a command that affects the whole document, it should go in the preamble, between the \verb|\documentclass| and \verb|\begin{document}| commands.\subsection{Centering Text}By default, \LaTeX\ will start all text at the left margin. If you want to center a title, a table, etc., surround what you want centered with the commands\begin{verbatim}\begin{center}...\end{center}\end{verbatim}\subsection{Filling A Line}You can insert an arbitrary amount of space into a line with the \verb|\hspace{length}| command. If you want a spacing in a line that will push the surrounding words to the left and right margins, use the \verb|\hfill| command. If instead of spacing, you want either dots or a line, use \verb|\dotfill| or \verb|\hrulefill|, respectively.\subsection{Line Breaks}\LaTeX\ works very hard to find optimal places to split lines of text in making paragraphs. You can help it by indicating when it should avoid a line break. Use a \verb|~| for a space that should not be used to break a line. \LaTeX\ inserts more space at the end of a sentence then between its words. If you use an abbreviation like \textit{Dr.} in the middle of a sentence, then you need to let \LaTeX\ know that the period is not the end of a sentence, with a \verb|~| (if the line should not be broken there) or a \verb|\| followed by a space (if the line could be broken there). If you need to force a line to break at a given point, use \verb|\\|.\subsection{Special Headers}A header is the text automatically included at the top of each document. If you use \begin{verbatim}\pagestyle{myheadings}\end{verbatim}then you will need some way to indicate what your heading is. The command

\begin{verbatim}\markright{Your Header Text Here}\end{verbatim}will do the job for you.

The name of the command \verb|\markright| requires a little explanation. An option that we will not use in this tutorial is\begin{verbatim}\documentclass[twoside]{article}\end{verbatim}which produces pages formatted as in a book, i.e., with a left page and a right page. Using this option it is possible to produce different headings for the left and right pages. When using the default of one-sided pages, all pages are thought of as right pages, and we use \verb|\markright| to mark our headings on these right-sided pages.\subsection{Counters And Length Parameters}\textsc{Counters.} \LaTeX\ maintains many counter variables (e.g. page, part, equation, footnote, chapter, paragraph, section, subsection, subsubsection, enumi, etc). You can set these counters yourself.\begin{verbatim}\setcounter{page}{0}\addtocounter{chapter}{2}\end{verbatim}\textsc{Length parameters.} \LaTeX\ accepts the following units of length \textit{in}, \textit{cm}, \textit{mm}, \textit{pt} (there are 72.27 pts to an inch), \textit{em} (width of an M), \textit{ex} (height of an x). These units can be used to set the values of length variables using \verb|\setlength|.\begin{verbatim}\setlength{\parindent}{0in}\end{verbatim}sets to zero the amount by which the first line of a paragraph is indented.

Other useful length parameters are\\\\\textsc{Parskip.} determines the gap between paragraphs.\\\\\textsc{Baselineskip.} determines the usual distance from the bottom of one line to the bottom of the next. You can adjust this to produce double spacing, but a better way, which takes a stretch factor as argument is to use \verb|\linespread|. For instance before \verb|\begin{document}| you can do\verb|\linespread{1.6}| to get doublespacing through your document. The setspace package offers more options.\subsection{Big Font Sizes}If \texttt{Huge} isn't big enough for you, you can scale a postscript font up using the commands in the graphicx package. \begin{verbatim}\resizebox{!}{size}{text}\end{verbatim}\subsection{Postscript Fonts}It is easy to write a document that has postscript fonts. We have package support for helvetica (helvetic), utopia, times, optima, newcentury (newcentu), palatino and courier. To use palatino, for instance, all you need to do is add \verb|\usepackage{palatino}| to your file. The \textit{pifont} package has special commands for using the Zapf Dingbats font. \verb|\dingfill{40}| completes the line with the specified symbol and \verb|\dingline{36}| draws a whole line of symbols.\subsection{Font Attributes}

Every text font in \LaTeX\ has five attributes\begin{description}\item[encoding] This specifies the order that characters appear in the font. The most common values for the font encoding is OT1.\item[family] The name for a collection of fonts, usually grouped under a common name by the font foundry. For example, \lq Adobe Times\rq\ and Knuth's \lq Computer Modern Roman' are font families. There are far too many font families to listthem all, but some common ones are\begin{table}\begin{center}\begin{tabular}{|l|l|c|}\hline\textbf{Internal} & \textbf{fontname Fontname} & \textbf{In ljmr1?}\\\hline\texttt{cmr}& Computer Modern Roman &No\\\texttt{cmss}& Computer Modern Sans &No\\\texttt{cmtt}& Computer Modern Typewriter &No\\\texttt{cmm}& Computer Modern Math Italic &No\\\texttt{cmsy}& Computer Modern Math Symbols &No\\\texttt{cmex}& Computer Modern Math Extensions &No\\\texttt{ptm}& Adobe Times &Yes\\\texttt{phv}& Adobe Helvetica &Yes\\\texttt{pcr}& Adobe Courier &Yes\\\texttt{pun}& Univers &No\\\texttt{ppl} &Palatino &Yes\\\texttt{pagk}& AvantGarde-Book &Yes\\\texttt{pagd}& AvantGarde-Demi &Yes\\\texttt{pbk}& Bookman &Yes\\\texttt{put} &Utopia &No\\\texttt{pop} &Optima &No\\\texttt{pnc} &New Century Schoolbook &Yes\\\texttt{pzd} &ZapfDingbats &Yes\\\texttt{rpad} &Garamond &No\\\hline\end{tabular}\end{center}\caption{Common font families}\end{table}\item[series] How heavy or expanded a font is. For example, \lq medium weight\rq, \lq narrow\rq and \lq bold extended\rq are all series. The most common values for the font series are \texttt{m} (medium), \texttt{b} (bold), \texttt{bx} (bold extended), \texttt{sb} (semi-bold), \texttt{c} (condensed).\item[shape] The form of the letters within a font family. For example, \lq italic\rq, \lq oblique\rq and \lq upright\rq are all font shapes. The most common values for the font shape are \texttt{n} (Normal, that is \textit{upright} or \textit{roman}), \texttt{it} (Italic), \texttt{sl} (Slanted, or \textit{oblique}), \texttt{sc} (Caps and small caps).\item[size] The design size of the font, for example \lq 10pt\rq.\end{description}These five parameters specify every \LaTeX\ font.\subsection{Selection Commands}The low-level commands used to change font attributes are as follows.\begin{verbatim}\fontencoding{encoding},\fontfamily{family},\fontseries{series},\fontshape{shape},\fontsize{size}{baselineskip}\end{verbatim}

Each of these commands sets one of the font attributes; \verb|\fontsize| also sets \verb|\baselineskip|. The actual font in use is not altered by these commands, but the current attributes are used to determine which font to use after the next \verb|\selectfont| command.\verb|\selectfont| selects a text font, based on the current values of the font attributes. There must be a \verb|\selectfont| command immediately after any settings of the font parameters by (some of) the five \verb|\font<parameter>| commands, before any following text.\subsection{Pagebreaks, Space, Footnotes, References, Boxes}\textsc{Page Breaks.} you can force a page break using \verb|\newpage|.\\\\\textsc{Preventing line breaks.} If there's a word that you don't want broken, put it in an \texttt{mbox}.\\\\\textbf{Space.} \verb|\vspace*| will createspace even at the top of a page. It's sometimes useful to create stretchablespace. The following creates space that pushes the letters to the edge of thepage\begin{verbatim}\noindent A\hspace{\stretch{1}} B\\C\hspace{\stretch{1}} D\end{verbatim}\noindent A\hspace{\stretch{1}} B\\C\hspace{\stretch{1}} D\\\\\textsc{Footnotes.} The footnotes are numbered by default. If you want to usesymbols (stars, daggers etc) then you need to redefine how the footnote counter is displayed. \\\verb|\de\thefootnote{\fnsymbol{footnote}}|\\\\\textsc{Margin notes.} Use the following command \verb|\marginpar{text}| \dotfill \marginpar{text}. \\\\\textsc{Boxed Text.} For short pieces of text, use \verb|\fbox{...}|.\\\\\textsc{Rules.} The \verb|\rule| takes 2 arguments; a width and a height, so\begin{verbatim}\rule{\textwidth}{1pt}\end{verbatim}produces\\\rule{\textwidth}{1pt}\subsection{Inserting References}To easily cite references and create bibliographies in your document, use BibTeX file to store the details of your references.\\\\\textsc{The BibTeX file.} Enter each of references in the BibTeX file in the following format\begin{verbatim}@article{WalterRudin1968,Author={W. Rudin}, Title={Principles of mathematical analysis}, Journal={Applied mathematics}, Volume={1}, Pages={1-100}, Year={1968} }

\end{verbatim}

Each reference starts with the \textit{reference type} @article, @book, @incollection (for a chapter in an edited book), @inproceedings (for papers presented at conferences).

The reference type declaration is followed by a curly bracket, then the \textit{citation key}. Each reference's citation key must be unique - you can use anything you want, but a system based on the first author's name and year (as in the example above) is probably easiest to keep track of. The remaining lines contain the reference information in the format \begin{verbatim}Field name = {field contents},\end{verbatim}

Surround any letters in a journal article title that need to be capitalised with curly brackets \{...\}. BibTeX automatically uncapitalises any capital letters within the journal article title.\\\\\textsc{Inserting the bibliography.} Type the following where you want the bibliography to appear in your document (usually at the end)\begin{verbatim}\bibliographystyle{plain}\bibliography{Doc1}\end{verbatim}Where references is the name of your .bib file.\\\\\textsc{Citing references.} Type \verb|\cite{citationkey}| where you want to cite a reference in your .tex document. If you don't want an in text citation, but still want the reference to appear in the bibliography, use \verb|\notice{citationkey}|. To include a page number in your in-text citation put it in square brackets before the citation key\begin{verbatim}\cite[p. 215]{citationkey}\end{verbatim}

To cite multiple references include all the citation keys within the curly bracketsseparated by commas \verb|\cite{citation01,citation02,citation03}|.\\\\\textsc{Styles.} \begin{description}\item[Numerical citations.] \LaTeX\ comes with several styles with numerical in-text citations, these include \texttt{Plain} (The citation is a number in square brackets (e.g. [1]). The bibliographyis ordered alphabetically by first author surname. All of the authors' names are written in full), \texttt{Abbrv} (The same as \texttt{plain} except the authors' first names are abbreviatedto an initial), \texttt{Unsrt} (The same as \texttt{plain} except the references in the bibliography appear in the order that the citations appear in the document), \texttt{Alpha} (The same as \texttt{plain} except the citation is an alphanumeric abbreviation based on the author(s) surname(s) and year of publication, surroundedby square brackets (e.g. [Kop10])).\\\item[Authordate citations.] Use the \textit{natbib} package if you want to include author-date citations. \textit{Natbib} uses the command \verb|\cite{...}| for a citation in brackets (e.g. [Koppe,2010]) and \verb|\

citet{...}| for a citation where only the year is in brackets (e.g. Koppe [2010]). There are lots of other ways that you can modify citations when using the natbib package.\\Natbib comes with three bibliography styles \textit{plainnat}, \textit{abbrvnat} and \textit{un-srtnat}. These format the bibliography in the same way as the \textit{plain, abbrv} and \textit{unsrt} styles, respectively.\\\item[Other bibliography styles.] If you want to use a different style (e.g. one provided by the journal you are submitting an article to) you should save the style file (.bst file) in the same folder as your .tex and .bib files. Include the name of the .bst file in the \verb|\bibliographystyle{...}| commmand.\end{description}\subsection{Making Custom Commands}In long documents, you may find yourself typing similar sequences of text over and over again. \LaTeX\ provides a command that defines new commands. This is one of \LaTeX\ 's most useful features. Custom commands are the most conceptually difficult subject.\\\\\textsc{Custom Commands without Arguments.}\begin{verbatim}\newcommand{\abbrText}{text you want to abbreviate}\end{verbatim}

You can use \verb|\newcommand| anywhere in the document, but the command it defines will only work after the place where \verb|\newcommand| appears. It’s therefore good style to place any \verb|\newcommand| in the preamble of the document. Also, \verb|\newcommand| cannot make commands that already exist. There are also subtle rules regarding command names in general, command names should contain only letters.\\\\\textsc{Custom Commands with Arguments.} To make commands taking arguments, \verb|\newcommand| has an optional argument specifying the number of arguments taken by the new command.\begin{verbatim}\newcommand{\abbrText}[numberOfArguments]{expression withnumberOfArguments argument #1,#2,... #numberOfArguments}\end{verbatim}

A completely new command can be created using \begin{verbatim}\newcommand{\commandname}[number of arguments]{command text, using#1, #2 etc to denote arguments}.\end{verbatim}

A new environment is just as easily created - give the name of the environment, and what you want to happen on entering and leaving the environment.\subsection{Modifications}Many of the features of a \LaTeX\ document are easily customised, but you'll oftenhave to look at the class (.cls) files to find out what to do. For example, supposeyou wanted to have \textit{References} in a book rather than \textit{Bibliography}. If you look in \texttt{book.cls} you'll see \verb|\newcommand{\bibname}{Bibliography}| \\so adding

\verb|\renewcommand{\bibname}{References}| to your file should achieve what you want. Counters (e.g. figure) have related commands (e.g. thefigure) to controltheir appearance, so they're easy to customize\begin{verbatim}\renewcommand{\thefigure}{\roman{figure}}\end{verbatim}be adapted too. Remember however, that if the command involves a @ you have to enclose your changes in \verb|\makeatletter ... \makeatother|. Here's an example that changes the appearance of section headings\begin{verbatim}\makeatletter\renewcommand{\section{\@startsection{section}{1}{0mm}{\baselineskip}%{\baselineskip}{\normalfont\normalsize\scshape\centering}}%\makeatother\begin{document}\end{verbatim}\subsection{Some Useful \LaTeX\ Command}\begin{enumerate}\item \verb|\'| in \texttt{tabbing} environment moves current column to the right of the previous column. Elsewhere, acute accent, as \'{o}.\item \verb|\(| start math mode. Same as \verb|begin{math}| or \$.\item \verb|\)| end math mode. Same as \verb|end{math}| or \$.\item \verb|\*| is a discretionary multiplication sign, at which a line break is allowed.\item \verb|\+| moves left margin to the right by one tab stop. Begin tabbed line.\item \verb|\-| in tabbing environment, moves left margin to the left by one tab stop. Elsewhere, optional hyphenation.\item \verb|\/| inserts italics adjustment space.\item \verb|\<| in tabbing environment, puts text to left of local left margin.\item \verb|\=| in tabbing environment, sets a tab stop. Elsewhere, makes a macron accent, as \={o}.\item \verb|\>| in tabbing environment is a forward tab. Otherwise, medium space = $2/9$ quad (math mode).\item \verb|\@| declares the period that follows is to be a sentence-ending period. \item \verb|\[| same as \verb|\begin{displaymath}| or \verb|$$|.\item \verb|\\*| terminates a line, but disallows a pagebreak.\item \verb|\]| same as \verb|\end{displaymath}| or \verb|$$|.\item \textbackslash \lq\ in tabbing environment moves all text which follows (up to \verb|\\|) to the right margin. Elsewhere, grave accent.\item \verb|\a'| makes an acute accent in tabbing environment.\item \verb|\a`| makes a grave accent in tabbing environment.\item \verb|\a=| makes a macron accent in tabbing environment.\item \verb|\aa| is \aa. \verb|\AA| is \AA.\item \verb|\addcontentsline{toc}{section}{name}| adds the command\\ \verb|\contentsline{section}{name}| to the .toc file.\item \verb|\address{text}| declares the return address in the letter document style.\item \verb|\addtocontents{toc}{text}| writes text to the .toc file.\item \verb|\addtocounter{name}{amount}| adds amount to counter name.

\item \verb|\addtolength{\nl}{length}| adds length to length command \verb|\nl|. \\See also \verb|\setlength,\newlength,\settowidth|.\item \verb|ae| is \ae. \verb|\AE| is \AE.\item \verb|\alph{counter}| prints counter as lower-case letters. \item \verb|\Alph{counter}| prints upper-case letters. \item \verb|\and| separates multiple authors for the \verb|\maketitle| command.\item \verb|\appendix| starts appendices.\item \verb|\arabic{counter}| prints counter as arabic numerals 1, 2, etc.\item \verb|\arraycolsep| width of the space between columns in an array environment.\item \verb|\arrayrulewidth| width of the rule created in tabular or array environment by $|$, \verb|\hline|, or \verb|\vline|.\item \verb|\arraystretch| scale factor for interrow spacing in array and tabular environments.\item \verb|\baselineskip| distance from bottom of one line of a paragraph to bottom of the next line.\item \verb|\baselinestretch| factor by which \verb|\baselineskip| is multiplied each time a type size changing command is executed.\item \verb|\begin{list}{labeling}{spacing}| starts a general list environment. labeling specifies how items are labeled when \verb|\item| has no argument. spacing is an optional list of spacing parameters.\item \verb|\begin{minipage}[pos]{vsize}| starts a box of height \texttt{vsize}. Text will be positioned according to \texttt{pos}.\item \verb|\begin{titlepage}| is an environment with no page number, and causes following page to be numbered \lq 1 \rq.\item \verb|\begin{verse}| starts an environment for poetry with wider margins, no paragraph indenting, and ragged right margin.\item \verb|\bibliography{file}| insert bibliography from file name.bib at this point in text.\item \verb|\bibliographystyle{style}| a format specifier, like \verb|\documentstyle|.\item \verb|\bigskip| standard \lq big\rq vertical skip.\item \verb|\bigskipamount| default length for \verb|\bigskip|.\item \verb|\bottomfraction| maximum fraction of page occupied by floats at the bottom.\item \verb|\caption[loftitle]{text}| creates a numbered caption in a figure or table environment. Optional loftitle contains entry for the list of figures if different from text. \item \verb|\cc{text}| declares list of copy recipients for letter document style.\item \verb|\chapter[toctitle]{text}| begins a new section, automatically headed and numbered. Optional toctitle contains entry for the tableof contents if different from text.\item \verb|\check{}| makes a h\'{a}\u{c}ek, as a (math mode).\item \verb|\circle{diameter}| as a valid argument for \verb|\put| in a picture environment, draws a circle.\item \verb|\circle*{diameter}| is like \verb|\circle|, but draws a solid circle.\item \verb|\cite[subcit]{ref}| produces a reference, in square brackets, to a bibliographic item created with \verb|\bibitem{ref}|. Optional sub-citation subcit can be inserted in the entry.\item \verb|\cleardoublepage| forces next page to be a right-hand, odd-numbered page.\item \verb|\clearpage| ends a page where it is, and puts pending figures or tables on separate float pages with no text.

\item \verb|\cline{i-j}| draws a horizontal line across columns $i$ through $j$ inclusive in array or tabular environments.\item \verb|\closing{text}| declares the closing in letter document style.\item \verb|\columnsep| distance between columns in two-column text.\item \verb|\columnseprule| width of the rule between columns on two-column pages.\item \verb|\columnwidth| width of the current column. Equals \verb|\item \textwidth| in single-column text.\item \verb|\dashbox{dwid}(width,height)[pos]{text}| creates a dashed rectangle around text in a picture environment. Dashes are dwid unitswide; dimensions of rectangle are width and height; text is positioned at optional pos.\item \verb|\day| current day of the month.\item \verb|\dblfloatpagefraction| minimum fraction of a float page that must be occupied by floats, for two-column float pages.\item \verb|\dblfloatsep| distance between floats at the top or bottom of a two-column float page.\item \verb|\dbltextfloatsep| distance between double-width floats at the top or bottom of a two-column page and the text on that page.\item \verb|\dbltopfraction| maximum fraction at the top of a two-column page that may be occupied by floats.\item \verb|\displaystyle| switches to displaymath or equation environment typesetting (math mode).\item \verb|\doublerulesep| horizontal distance betweenvertical rules created by $||$ in tabular orarray environment.\item \verb|\ell| is $\ell$ (math mode).\item \verb|\encl{text}| declares a list of enclosures for letter document style.\item \verb|\evensidemargin| distance between left side of page and text's normal left margin, for even-numbered pages in two-sided printing.\item \verb|\fbox{text}| makes a \fbox{framed box} around text.\item \verb|\fboxrule| thickness of ruled frame for \verb|\fbox| and \verb|\framebox|. \item \verb|\fboxsep| space between frame and text for \verb|\fbox| and \verb|\framebox|.\item \verb|\fill| rubber length (glue) that can stretch to arbitrary length. Usually used to justify text a particular way.\item \verb|\floatpagefraction| minimum fraction of a float page occupied by floats.\item \verb|\floatsep| distance between floats that appear at the top or bottom of a text page.\item \verb|\flushbottom| causes pages to be stretched to \verb|\textheight|.\item \verb|\fnsymbol{counter}| prints counter as one of the set of \lq footnote symbols\rq. counter must be less than 10.\item \verb|\footheight| height of box at bottom of page that holds page number.\item \verb|\footnotemark| puts a footnote number into the text.\item \verb|\footnotesep| height of strut placed at beginning of footnote.\item \verb|\footskip| vertical distance between bottom of last line of text and bottom of page footing. \item \verb|\footnotetext{text}| specifies the text for a footnote which was indicated by a \verb|\footnotemark|.\item \verb|\frame{text}| makes a framed (outlined) box around text, with no margin between the text and the frame.

\item \verb|\framebox[size][pos]{text}| produces a \fbox{framed box }of dimension size containing text, optionally positioned \texttt{l} or \texttt{r}.\\ In \texttt{picture} environment, \verb|\framebox(width,height)[pos]{text}| creates a rectangle around text; dimensions of rectangle are width and height; text is positioned at optional pos.\item \verb|\fussy| is the default declaration for the line-breaking algorithm\\(cf. \verb|\sloppy|).\item \verb|\glossary{text}| appends text to the .glo file by writing a \verb|\glossaryentry| command.\item \verb|\glossaryentry{text}{ref}| is written to the .glo file for \verb|\glossary{text}| occurring at reference \texttt{ref}.\item \verb|\headheight| height of box at top of page that holds running head.\item \verb|\headsep| vertical distance between bottom of head and top of text.\item \verb|\hfill| is \verb|\hspace{\fill}| (cf. \verb|\fill|).\item \verb|\hrulefill| expands to fill horizontal space with horizontal rule.\item \verb|\hyphenation{wordlist}| declares hyphenation as indicated; wordlist contains words separated by spaces, with hyphens indicated.\item \verb|\include{filename}| brings in filename text at that point.\item \verb|\includeonly{file1,file2,...}| limits recognition of \verb|\include| files.\item \verb|\index{text}| appends text to the .idx file by writing an \verb|\indexentry| command.\item \verb|\indexentry{text}{ref}| is written to the .idx file for \verb|\index{text}| occurring at reference \texttt{ref}.\item \verb|\indexspace| puts blank space before first index entry starting with a new letter.\item \verb|\input{file}| brings in text from file.tex at that point.\item \verb|\intextsep| vertical space placed above and below float in middle of text.\item \verb|\itemindent| extra indentation before label in list item. Default is 0mm.\item \verb|\itemsep| vertical space between successive list items.\item \verb|\kill| in a \verb|\tabbing| environment, deletes previous line so tabs can be set without outputting text.\item \verb|\label{text}| provides a reference point that is accessed with \verb|\ref{text}| or\\ \verb|\pageref{text}|.\item \verb|\labelwidth| width of box containing list item label.\item \verb|\labelsep| space between box containing list item label and text of the item.\item \verb|\left*| (where * is a delimiter) must be paired with \verb|\right*| (not necessarily using the same delimiter). \lq .\rq acts as a null delimiter (math mode).\item \verb|\lefteqn{formula}| is used in the eqnarray environment to break a long formula across lines.\item \verb|\leftmargin|, in list environment, horizontal distance between left margin of enclosing environment and left margin of list. Settable for nesting levels 1 through 6, as \verb|\leftmargini| \verb|through \leftmarginvi|.\item \verb|\line(x,y){len}| in picture environment, in \verb|\put| command, draws line from \verb|\put| argument with length len and slope $(x,y)$.\item \verb|\linebreak[n]| forces a line to break exactly at this point, and adjusts line just terminated (cf. newline). \texttt{n} is optional 0 is an

optional break, 4 is a mandatory break, 1, 2 and 3 are intermediate levels of insistence.\item \verb|\linethickness{dimen}| sets the thickness for all lines in a picture.\item \verb|\linewidth| is the width of the current line in a paragraph.\item \verb|\listoffigures| begins a list of figures with heading.\item \verb|\listoftables| begins a list of tables with heading.\item \verb|\listparindent| extra indentation added to first line of every paragraph of an item after the first, in list environment.\item \verb|\makebox[size][pos]{text}| creates a box of dimension size containing text at optional \texttt{pos}. \verb|\makebox(width,height)[pos]{text}| puts text in a box; dimensions of box are width and height; text is positioned at optional \texttt{pos}.\item \verb|\makeglossary| enables writing of \verb|\glossaryentry| commands to a .glo file.\item \verb|\makeindex| enables writing of \verb|\indexentry| commands to a .idx file.\item \verb|\marginpar{text}| puts text in the margin as a note.\item \verb|\marginparpush| minimum amount of vertical space between two marginal notes.\item \verb|\marginparsep| horizontal space between margin and marginal note.\item \verb|\marginparwidth| width of a marginal note. \item \verb|\markboth{lhd}{rhd}| defines the left-hand heading lhd and the right-hand heading rhd for the headings and myheadings page styles.\item \verb|\markright{rhd}| defines the right-hand heading rhd for the headings and myheadings page styles.\item \verb|\medskip| standard \lq medium\rq vertical skip.\item \verb|\medskipamount| default length for \verb|\medskip|.\item \verb|\month| current month of the year.\item \verb|\multicolumn{noc}{fmt}{text}| in tabular environment puts text across noc columns using positioning format fmt (\texttt{c, r, l}, and/or $|$).\item \verb|\multiput|$\left( {x,y} \right)\left( {\Delta x,\Delta y} \right)$\verb|{n}{obj}| is\begin{center}\textbackslash put$(x,y)$\{obj\}\\\textbackslash put$(x+\Delta x, y +\Delta y)$\{obj\}\\cdots\\\textbackslash put$(x+ (n−1)\Delta x, y + (n−1)\Delta y)$\{obj\}.\\\end{center}\item \verb|\newcommand{\cs}[narg]{def}| defines a new control sequence \verb|\cs| with definition \texttt{def}. Optionally, \texttt{narg} is the number of arguments, indicated in def as \#1, \#2, etc.\item \verb|\newcounter{counter}[name]| defines a counter optionally to be zeroed whenever the name counter is incremented.\item \verb|\newenvironment{envname}[narg]{def1}{def2}| defines a new environment, optionally with some number of arguments \texttt{narg. def1} is executed when the environment in entered and \texttt{def2} is executed when it is exited.\item \verb|\newfont{cs}{name}| defines a control sequence \verb|\cs| that chooses the font name.\item \verb|\newlength{\nl}| sets up \verb|\nl| as a length of 0in. \\See also \verb|\setlength,\addtolength,\settowidth.|\item \verb|\newsavebox{\binname}| declares a new bin to hold a \verb|\savebox|.\item \verb|\newtheorem{env}[env2]{label}[sectyp]| defines a new theorem environment \texttt{env} optionally with the same numbering scheme as

environment \texttt{env2}) with labels \texttt{label}. Optionally, theorem numbers can be related to document section \texttt{sectyp}.\item \verb|\nofiles| suppresses writing of auxiliary files .idx, .toc, etc.\item \verb|\noindent| suppresses indentation of first line of paragraph.\verb|\nolinebreak[n]| prevents a line break at that point.\item \verb|\nonumber| is used in an eqnarray environment to suppress equation numbering.\item \verb|\nopagebreak[n]| prevents a page break at that point.\item \verb|\normalmarginpar| is default declaration for placement of marginal notes \\(cf. \verb|\reversemarginpar|).\item \verb|\obeycr| makes embedded carriage returns act like line terminators.\item \verb|\oddsidemargin| distance between left side of page and text's normal left margin.\item \verb|\opening{text}| declares an opening for letter document style.\item \verb|\pagebreak[n]| forces a page break at that point. (cf \verb|\linebreak|).\item \verb|\pagenumbering{style}| determines page number style; style may be arabic (3), roman (iii), Roman (III), alph (c), Alph (C).\item \verb|\pageref{text}| is the page number on which \verb|\label{text}| occurs.\\\verb|\pagestyle{sty}| determines characteristics of a page's head and foot. sty may be \textit{plain} (page number only), \textit{empty} (no page number), \textit{headings} (running headings on each page), \textit{myheadings} (user headings).\item \verb|\paragraph[toctitle]{text}| begins a new paragraph, automatically headed and numbered. Optional toctitle contains entryfor the table of contents if different from text. \item \verb|\paragraph*{text}| begins a paragraph and prints a title, but doesn't include a number or make a table of contents entry.\item \verb|\parbox[pos]{size}{text}| is a box created in paragraph mode. \texttt{text} is positioned optionally at \texttt{pos}. Width is \texttt{size}.\item \verb|\parindent| horizontal indentation added at beginning of paragraph.\item \verb|\parsep| extra vertical space between paragraphs within a list item.\item \verb|\parskip| extra vertical space between paragraphs, normally.\\\item \verb|\part[toctitle]{text}| begins a new part, automatically headed and numbered. Optional toctitle contains entry for the table ofcontents if different from text. \item \verb|\part*{text}| begins a part and prints a title, but doesn't include a number or make a table of contents entry.\item \verb|\partopsep| extra vertical space added before first list item if environment starts a new paragraph.\item \verb|\poptabs| undoes the previous \verb|\pushtabs| command (restore prior tab settings).\texttt{positions}, for boxing commands t=top, b=bottom, h=here, l=left, c=center, r=right, p=new page (figure environment), p=parbox (tabular environment).\item \verb|\protect| permits the use of \lq dangerous\rq commands in @-expressions, or in sectioning command and \verb|\caption| arguments.\item \verb|\ps| in letter document style permits additional text after \verb|\closing|.\item \verb|\pushtabs| in tabbing environment lets you stack tab stop defitions. Undo with \verb|\poptabs|.

\item \verb|\put(x,y){stuff}| is the basic picture-drawing command. $(x,y)$ is the reference point, whose meaning varies for different \texttt{stuff. stuff} may be anything that goes in an \verb|\mbox|.\item \verb|\raggedbottom| causes pages to assume natural height.\item \verb|\raggedleft| declares all text that follows is to be flush against the right margin (cf. \verb|\begin{flushright}|).\item \verb|\raggedright| declares all text that follows is to be flush against the left margin (cf. \verb|\begin{flushleft}|).\item \verb|\raisebox{dim}[d2][d3]{text}| moves text up by \texttt{dim} (which may be negative). Optional \texttt{d2} makes system think that \texttt{text} extends \texttt{d2} above the baseline (and optionally \texttt{d3} below it).\item \verb|\renewcommand{\cs}[narg]{def}| redefines an existing control sequence \verb|\cs| with definition \texttt{def}. Optionally, \texttt{narg} is the number of arguments, indicated in \texttt{def} as \#1, \#2, etc.\item \verb|\renewenvironment{envname}[narg]{def1}{def2}| redefines an existing environment. See \verb|\newenvironment|.\item \verb|\restorecr| undoes the \verb|\obeycr| command (makes carriage return a space-producing character).\item \verb|\reversemarginpar| causes opposite margin to be used for marginal notes (e.g., left margin on odd-numbered pages).\item \verb|\rightmargin| in list environment, horizontal distance between right margin of enclosing environment and right margin of list. Default 0 in.\item \verb|\roman{counter}| prints counter in lower-case roman numerals.\\\verb|\Roman{counter}| prints upper-case roman numerals.\item \verb|\rule[height]{length}{width}| makes a rectangular blob of ink length long, width wide, with optional height above baseline.\item \verb|\savebox{\binname}[width][pos]{text}| is exactly like \verb|\makebox| (q.v.), but saves box definition in bin \verb|\binname|. Access with \verb|\usebox{\binname}|.\item \verb|\sbox{\binname}{text}| saves text in box \verb|\binname| (see \verb|\savebox|, above).\item \verb|\section[toctitle]{text}| begins a new section, automatically headed and numbered. Optional toctitle contains entry for the tableof contents if different from text.\item \verb|\setcounter{counter}{value}| resets the value of counter.\item \verb|\setlength{\nl}{length}| sets value of length command \verb|\nl| to length. See also \verb|\addtolength,\newlength,\settowidth|.\item \verb|\settowidth{\nl}{text}| sets value of length command \verb|\nl| to the width of text. See also \verb|\setlength, \newlength,\addtolength|.\item \verb|\shortstack[pos]{x\\y\\z}| yields a one-column tabular arrangement of its arguments. Optional pos can be l or r for text position.\item \verb|\signature{text}| declares a signature for letter document style.\\\item \verb|\sloppy| relaxes the line-breaking algorithm to allow more or less distance between words. Default is \verb|\fussy|.\item \verb|\smallskip| standard \lq small\rq\ vertical skip. \item \verb|\smallskipamount| default length for \verb|\smallskip|.\item \verb|\stackrel{stuff}{delim}| puts stuff above the delimiter (math mode).\item \verb|\stop| type this if \TeX\ stops with a * and no error message.\item \verb|\subparagraph[toctitle]{text}| begins a subparagraphs, automatically headed and numbered. Optional toctitle contains entryfor the table of contents if different from text.\item \verb|\subsection[toctitle]{text}|, \verb|\subsubsection[toctitle]{text}| begin new subsections, automatically headed and numbered. Optional toctitle contains entry for the table of contents if different from text.

\item \verb|\symbol{cc}| produces the symbol (glyph) character code cc in the current font.\item \verb|\tabbingsep| distance to left of a tab stop moved by \textbackslash \rq.\item \verb|\tabcolsep| half the width of the space between columns in tabular environment.\item \verb|\textfloatsep| distance between floats at the top or bottom of a single-column page and the text on that page.\item \verb|\textfraction| minimum fraction of a text page that must contain text.\item \verb|\textheight| is the normal vertical dimension of the body of the page.\item \verb|\textstyle| switches to math environment typesetting (math mode).\item \verb|\textwidth| is the normal horizontal dimension of the body of the page.\item \verb|\thanks{footnote}| adds an acknowledgement footnote to an author's name used in a \verb|\maketitle| command.\item \verb|\thicklines| is an alternate line thickness for lines in a picture environment. See also \texttt{linethickness}.\item \verb|\thinlines| is the default declaration for line thicknesses in a picture environment. See \verb|\thicklines|.\item \verb|\thinspace| is the proper space between single and double quotes.\item \verb|\thispagestyle{sty}| determines characteristics of head and foot for the current page only. Used to override \verb|\pagestyle| (q.v.) temporarily.\item \verb|\topfraction| maximum fraction at the top of a single-column page that may be occupied by floats.\item \verb|\topmargin| space between top of \TeX\ page (1 inch from top of paper) and top of header.\item \verb|\topsep| extra vertical space added before first list item and after last list item.\item \verb|\topskip| minimum distance between top of page body to bottom of first line of text.\item \verb|\twocolumn[text]| declares a two-column page, with optional full-page width heading text.\item \verb|\typein[\cs]{text}| displays text on the screen and waits for you to enter stuff which will be put in the document at that point. Optional control sequence \verb|\cs| can be assigned the valueof your input, to be used later.\item \verb|\typeout{text}| displays text on the screen and writes it to the .lis file.\item \verb|\unboldmath| unemboldens math italics and math symbols. Should be used outside of math mode.\item \verb|\unitlength| length of coordinate units for picture environment.\item \verb|\usebox{\binname}| recalls box definition saved in box \verb|\binname|.\item \verb|\usecounter{counter}| is used in a list environment to cause counter to be used to number the items.\item \verb|\value{counter}| produces the numeric value of counter.\item \verb|\vector(x,y){len}| in picture environment, in \verb|\put| command, draws vector from \verb|\put| argument with length len and slope $(x,y)$, with arrowhead.\item \textbackslash verb $|text|$ creates a local \texttt{verbatim} environment for text, printed in typewriter font. Note that text is not in curly braces; it is between two identical delimiters, neither of which appears in text.

\item \textbackslash verb*$|text|$ is like \textbackslash verb$|text|$, but spaces print out as \_.\item \verb|\vfill| is \verb|\vspace{\fill}| (cf. \verb|\fill|).\item \verb|\vspace*{len}| is like \verb|\vspace{len}| but space is not removed at the beginning or end of a page.\end{enumerate}\section{Formatting}\subsection{Text Formatting}\textsc{Font effects.} \begin{verbatim}\textit{},\textbf{},\textsc{},\textsf{},\textsl{},\texttt{},\textrm{},\underline{},\textup{},textmd{},\emph{}\end{verbatim}\textsc{Colored text.} The basic color names that \verb|\usepackage{color}| knows about are black, red, green, blue, cyan, magenta, yellow and white. Use\begin{verbatim}\color{color_name}{text}| or \verb|{\{color{color_name}text}\end{verbatim}\begin{center}\textbf{{\color{black}black}, {\color{red}red}, {\color{green}green}, {\color{blue}blue}, {\color{cyan}cyan}, {\color{magenta}magenta}, {\color{yellow}yellow}, {\color{white}white}.} \end{center}Do you see the word \lq\lq white\rq\rq\ at the end of the above line? Of course, you can't see it because its color is white!\\\\\textsc{Font sizes.} \begin{verbatim}\tiny,\scriptsize,\footnotesize,\normalsize,\large,\Large,\LARGE,\huge,\Huge\end{verbatim}\textsc{Hyphenation.} To specify how some words are hyphenated\begin{verbatim}\hyphenation{word_list}\end{verbatim}\subsection{Colored Text}Commands that control foreground and background colors need\begin{verbatim}\usepackage[dvips]{color}\end{verbatim}after the \verb|\documentclass| line but before \verb|\begin{document}|.\begin{enumerate}\item \verb|\textcolor{colorname}{text}| writes text in a color which can be specified by name (black, white, red, green, blue or a color name you've defined), RGB components, or grayscale.\item \verb|\colorbox{colorname}{text}| writes text in a box with a colored background.\item \verb|\fcolorbox{framecolor}{boxcolor}{text}| writes text in a colored frame.\item \verb|\pagecolor{colorname}| sets the color of the page's background.\item \verb|\definecolor{colorname}{color_specification}| lets you define new color names. For example, \verb|\definecolor{gold}{rgb}{0.85,.66,0}|.\end{enumerate}\subsection{Producing White Space in \LaTeX}\textsc{White space units.} To produce (horizontal) blank space within a paragraph, use \textbackslash hspace, followed by the length of the blank

space enclosed within curly brackets. The length of the skip should be expressed in a unit recognized by \LaTeX. These recognized units are given in the following \texttt{pt} (point, 1 in = 72.27 pt), \texttt{pc} (pica, 1 pc = 12 pt), \texttt{in} (inch, 1 in = 25.4 mm), \texttt{bp} (big point, 1 in = 72 bp), \texttt{cm} (centimetre), \texttt{mm} (milimetre), \texttt{dd} (didot point, 1157 dd = 1238 pt), \texttt{cc} (cicero, 1 cc = 12 dd), \texttt{sp} (scaled point 65536 sp = 1 pt).\\\\\textsc{Hspace.} If \LaTeX\ decides to break between lines at a point in the document where an \verb|\hspace| is specified, then no white space is produced. To ensure that white space is produced even at points in the document where line breaking takes place, one should replace \verb|\hspace| by \verb|\hspace*|.\\\\\textsc{Vspace.} To produce (vertical) blank space between paragraphs, use \verb|\vspace|, followed by the length of the blank space enclosed within curly brackets. If \LaTeX\ decides to introduce at a point in the document where a \verb|\vspace| is specified, then no white space is produced. To ensure that white space is produced even at points in the document where page breaking takes place, one should replace \textbackslash vspace by \verb|\vspace*|.\\\\\textsc{Non-breaking up.} \LaTeX\ determines itself how to break up a paragraph into lines, and will occasionally hyphenate long words where this is desirable. However it is sometimes necessary to tell \LaTeX\ not to break at a particular blank space. The special character used for this purpose is \verb|~|. It represents a blank space at which \LaTeX\ is not allowed to break between lines. It is often desirable to use \verb|~| in names where the forenames are represented by initials.\\\\\textsc{Indent.} \LaTeX\ will automatically indent paragraphs (with the exception of the first paragraph of a new section). One can prevent \LaTeX\ from indenting a paragraph though by beginning the paragraph with the control sequence \verb|\noindent|. Conversely, the control sequence \verb|\indent| forces \LaTeX\ to indent the paragraph.\section{Lists}\subsection{Sub-lists}\LaTeX\ supports three types of lists \textit{enumerate} produces numbered lists, while \textit{itemize} is for bulleted lists and \textit{description} as below. Each list item is defined by \verb|\item|. Lists can be nested to produce sub-lists.\begin{verbatim}\begin{enumerate}\item First thing\item Second thing\begin{itemize}\item A sub-thing\item Another sub-thing\end{itemize}\item Third thing\end{enumerate}\end{verbatim}\textsc{Change the bullet symbol.}\begin{verbatim}\item[-], \item[+], \item[One], \item[anything]\end{verbatim}\subsection{Enumerate, Itemize, Description}

\LaTeX\ provides the following list environments \texttt{enumerate} for numbered lists, \texttt{itemize} for un-numbered lists, \texttt{description} for description lists.\\\\\textsc{enumerate.} Numbered lists are produced using\begin{verbatim}\begin{enumerate}...\end{enumerate}\end{verbatim}

The items in the list should be enclosed between \verb|\begin{enumerate}| and \verb|\end{enumerate}| and should each be preceded by the control sequence \verb|\item| (which will automatically generate the number labelling the item).\\\\\textsc{Itemize.} Un-numbered lists are produced using\begin{verbatim}\begin{itemize}...\end{itemize}\end{verbatim}

\LaTeX\ generates an itemized list in which each item is preceeded by a \lq bullet\rq.\\\\\textsc{Description.} Description lists (for glossaries etc.) are produced using\begin{verbatim}\begin{description}...\end{description}\end{verbatim}

The items in the list should be enclosed between\verb|\begin{description}| and \verb|\end{description}| and should each be preceded by \verb|\item[label]|, where label is the label to be assigned to each item.\section{Tables}The tabular command is used to typeset tables. By default, \LaTeX\ tables are drawn without horizontal and vertical lines $|$ you need to specify if you want lines drawn. The code starts a table\texttt{\textbackslash begin\{tabular\}\{*\}}. Where * are replaced by code defining the columns \texttt{l} (for column of left-aligned text), \texttt{r} (for column of right-aligned text), \texttt{c} (for column of center-aligned text), $|$ (for a vertical line).\\The table data follows the \verb|\begin| command \& is placed between columns. \verb|\\| is placed at the end of a row (to start a new one). \verb|\hline| inserts a horizontal line. \verb|\cline{1-2}| inserts a partial horizontal line between columns 1 and 2.\\The command \verb|\end{tabular}| finished the table.\\\\\textsc{Tables.} Tables can be produced in \LaTeX\ using the \texttt{tabular} environment. In a tabular environment, the format specification after \verb|\begin{tabular}| should consist of one or more of the following, enclosed within braces \{ and \} \texttt{l} (specifies a column of left-justified text), \texttt{c} (specifies a column of centered text), \texttt{r} (specifies

a column of right-justified text), \texttt{p\{width\}} (specifies a left-justified column of the given width), $|$ (inserts a vertical line between columns), @\{text\} (inserts the given \textit{text} between columns).

A string \textit{str} of characters in the format specification can be repeated num times using the construction \verb|*{num}{str}|. For example, a table with 15 columns of rightjustified text enclosed within vertical lines can be produced using the format specification \{$|$*\{15\}\{r$|$\}\}.

If additional vertical space is required between rows of the table, then this can be produced by specifying the amount of space within square brackets after \verb|\\|. For example, on would use \verb|\\[6pt]| to separate two rows of the table by 6 points of blank space.

A horizontal line in a table from column $i$ to column $j$ inclusive can be produced using \verb|\cline{i-j}|. For example \verb|\cline{3-5}| produces a horizontal line spanning columns 3, 4 and 5 of some table.

A command of the form \verb|\multicolumn{num}{fmt}{text}| can be used within the body of a table to produce an entry spanning several columns. Here \textit{num} specifies the number of columns to be spanned, \textit{fmt} specifies the format for the entry (e.g., \texttt{l} if the entry is to be left-justified entry, or \texttt{c} if the entry is to be centred), and \textit{text} is the text of the entry.\section{Figures}To insert an image to document, use \texttt{graphicx} package. Images should be PDF, PNG, JPEG or GIF files. To insert an image called myimage\begin{verbatim}\begin{figure}[option]\centering\includegraphics[width=1\textwidth]{myimage}\caption{This is my image}\label{image-myimage}\end{figure}\end{verbatim}\textsc{Options.} \texttt{h} (put the figure approximately here), \texttt{t} (at the top of the page), \texttt{b} (at the bottom of the page) and \texttt{p} (on a separate page for firgures). You can also add !, whichoverrides the rule \LaTeX\ uses for choosing where to put the figure, and makes it more likely it will put it where you want (even if it doesn't look so good).\subsection{Including Graphics}To include figures in your document, you will need to include the \textit{graphicx} package at the beginning of your document. You accomplish this with the \verb|\usepackage{graphicx}| command. Within the input document, you will use the associated \verb|\includegraphics| command in the form\begin{verbatim}\includegraphics[options]\{graphics-filename.ext}\end{verbatim}\subsection{Graphics With Multiple Columns}To display graphics using multiple columns\begin{verbatim}\begin{figure}[h]\centerline{\includegraphics[width=0.40\textwidth,height=0.40\textwidth]{file_1}\hspace{1cm}\includegraphics[width=0.40\textwidth,height=0.40\textwidth]{file_2}}

\caption{\label{figs1} (a) This is the left figure.\hspace{1cm} (b) This is the right figure.}\end{figure}\end{verbatim}\subsection{Graphics}\begin{verbatim}\begin{figure}[ht]\centering\includegraphics[options]{graphics-file}\caption{text}\end{figure}\end{verbatim}Print graphic in separated page\begin{verbatim}\newpage\begin{landscape}\begin{figure}[ht]\centering\includegraphics[options]{graphics-file}\caption{text}\end{figure}\end{landscape}\end{verbatim}\subsection{Graphics}\textsc{The includegraphics command.} Supported options are \texttt{scale=number} magnifies the figure by number over its natural size. \texttt{width=length} specifies the width to which the figure should be scaled. \texttt{height=length} specifies the height to which the figure should be scaled. \texttt{angle=number} rotates the figure counterclockwise over the specified angle (in degrees). \texttt{bb=llx lly urx ury} enters the coordinates of the bounding box manually.\\\\\textsc{Inline floats.} The package \texttt{wrapfig} makes it possible to place text next to floats\begin{verbatim}\begin{wrapfigure}{placement}[overhang]{width}\includegraphics[width=\linewidth]{image}\end{wrapfigure}\end{verbatim}where,\begin{description}\item[placement] horizontal placement \texttt{l} (left) or \texttt{r} (right). For two-sided documents \texttt{i} (inside edge) or \texttt{o} (outside edge).\item[overhang] overhang of the float into the margin (default 0pt).\item[width] width of the figure or table (use \texttt{wraptable} for tables).\end{description}\subsection{Two Floats Next To Each Other}\textsc{No caption.}\begin{verbatim}\includegraphics[width=0.45\linewidth]{pic 1}\hfill\includegraphics[width=0.45\linewidth]{pic 2}\end{verbatim}\textsc{One caption.}\begin{verbatim}\begin{figure}[ht]\includegraphics[width=0.45\linewidth]{pic 1}

\hfill\includegraphics[width=0.45\linewidth]{pic 2}\caption{a response surface.}\label{fig surface}\end{figure}\end{verbatim}\textsc{Two captions.} Now we need the package \texttt{caption}. This package has very extensive functionality to change the appearance of captions. In this case we are only going to use the new command \verb|\captionof|.\begin{verbatim}\parbox[t]{0.45\textwidth}{\includegraphics[width=\linewidth]{ pic 1}\captionof{figure}{the first figure}}\hfill\parbox[t]{0.45\textwidth}{\includegraphics[width=\linewidth]{pic 2}\captionof{figure}{the second figure}}\end{verbatim}For tables, just repace \textit{figure} by \textit{table}.\\\\\textsc{Sub-captions.} Use the package \texttt{subfig}\begin{verbatim}\begin{figure}[ht]\begin{center}\subfloat[First figure]{\includegraphics[width =0.45\textwidth]{pic 1}}\subfloat[Second figure]{\includegraphics[width=0.45\textwidth]{pic 2}}\caption{Two figures}\end{center}\end{figure}\end{verbatim}\section{Mathematics Mode}Type in the preamble of document \verb|\usepackage{amsmath,amssymb}|.\subsection{Inserting Equations}To enter math mode within a sentence, use \$...\$. To make \lq\lq displayed\rq\rq\ equation on its own line use \$\$...\$\$. For a numbered displayed equation, use \begin{verbatim}\begin{equation}...\end{equation}\end{verbatim}

To write equation arrays for a series of equations or inequalities, use\begin{verbatim}\begin{eqnarray}...\end{eqnarray}\end{verbatim}

For unnumbered equations add the star symbol * after the \texttt{equation} or \texttt{eqnarray} command (i.e. use \verb|{equation*}| or \verb|{eqnarray*}|).

\subsection{Dots}Typesetting an $n \times n$ matrix requires vertical, horizontal, and downward-sloped ellipses \verb|\ldots,\cdots,\vdots,\ddots|.

The distinction between \verb|\ldots| and \verb|\cdots| is subtle \verb|\ldots| aligns the ellipsis with the bottom of the text while \verb|\cdots| centers the ellipsis. Typographical style considerations dictate which of the two commands to use. For matrix entries and binary operations, use \verb|\cdots|. For lists, use \verb|\ldots|.\subsection{Texts In Math Mode}The command \verb|$\text{...}$| typesets its argument as regular text.\subsection{Accents And Font Styles In Math Mode}Some formulas require accents or special font styles. The following are some common accents and styles\begin{verbatim}\mathbb,\mathcal,\mathfrak,\dot,\ddot,\overline{},\vec,\hat,\widehat, \tilde,\widetilde{}.\end{verbatim}

Unfortunately,\texttt{ mathbf} does not work with Greek characters. To make bold Greek characters, load the \texttt{bm} (bold math) package and use the newly provided command \verb|\bm{...}|.\subsection{Spacing In Math Mode}\LaTeX\ allows fine control over spacing in math mode \verb|\!|, (\textit{negative} space of $-3/18$ quad), \verb|\,| (for $3/18$ quad), \verb|\| (for $4/18$ quad), \verb|\>|, \verb|\;| (for $5/18$ quad), \verb|\quad| (the size of a \textit{quad} corresponds to the width of the character M of the current font), \verb|\qquad|, \verb|\phantom{a+b}|.

The command \verb|\!| adds \textit{negative} space. Use it if \LaTeX\ adds too much space to your formula and you want to tighten it. The command \verb|\phantom{}| adds as much white space as its argument takes up. We already encountered it in the section on the cases environment.\subsection{Equation Numbering}It’s often useful to number equations that are particularly important so that they may be referred to later. The command \verb|\label{text}| tells \LaTeX\ that the name of the equation is \textit{text}. We can reference it in the text using the command \verb|\eqref|, which is like \verb|\ref| but with added parentheses.

To number a series of aligned equations, use the \texttt{align} environment. If you do not want to number a specific line in a series of aligned equations, place the command \verb|\nonumber| on that line.\subsection{Making Math Operators}\LaTeX\ comes with predefined commands for the mose commobly used math operators. But sometimes you may need to use an operator that has not already been defined. The proper way to do this is with the \verb|\operatorname| command. \verb|$\operatorname{text}$|.\subsection{Boxed Equations}You may find a need to set a particular equation apart from others. It may have a particular signigicance, such as the final result of a long series of calculations. To do this you use the \lq\lq boxed\rq\rq\ environment.\begin{verbatim}\begin{equation}\boxed{...}\end{equation}\end{verbatim}

\subsection{Characters In Mathematics Mode}All the characters on the keyboard have their standard meaning in mathematics mode, with the exception of the characters \verb|# $ % & ~ _ ^ \ { } '|. To obtain the characters \verb|# $ % & _ { }| in mathematics mode, one should type \verb|\# \$ \% \& \_ \{ \}|. To obtain \verb|\| in mathematics mode, one may type \verb|\backslash|\subsection{Greek Letters}Greek letters are produced in mathematics mode by preceding the name of the letter by a backslash \verb|\| . Here are the control sequences for the standard forms of the lowercase Greek letters\begin{table}\begin{center}\begin{tabular}{|l|c|}\hline\textbf{Input} & \textbf{Output} \\\hline\verb|\alpha| & $\alpha$\\\verb|\beta| & $\beta$ \\\verb|\gamma| & $\gamma$\\\verb|\delta| & $\delta$ \\\verb|\epsilon| & $\epsilon$ \\\verb|\zeta| & $\zeta$ \\\verb|\eta| & $\eta$ \\\verb|\theta| & $\theta$ \\\verb|\iota| & $\iota$ \\\verb|\kappa| & $\kappa$ \\\verb|\lambda| & $\lambda$ \\\verb|\mu| & $\mu$ \\\verb|\nu| & $\nu$ \\\verb|\xi| & $\xi$ \\\verb|\o| & $\o$ \\\verb|\pi| & $\pi$ \\\verb|\rho| & $\rho$ \\\verb|\sigma| & $\sigma$ \\\verb|\tau| & $\tau$ \\\verb|\upsilon| & $\upsilon$ \\\verb|\phi| & $\phi$ \\\verb|\chi| & $\chi$ \\\verb|\psi| & $\psi$ \\\verb|\omega| & $\omega$ \\\hline\end{tabular}\end{center}\caption{Lowercase Greek letters}\end{table}There is no special command for omicron just use \texttt{o}.

Some Greek letters occur in variant forms. The variant forms are obtained by preceding the name of the Greek letter by \lq var\rq. The following table lists the usual form of these letters and the variant forms\begin{table}\begin{center}\begin{tabular}{|l|c|}\hline\textbf{Input} & \textbf{Output} \\\hline\verb|\varepsilon| & $\varepsilon$\\

\verb|\vartheta| & $\vartheta$\\\verb|\varpi| & $\varpi$\\\verb|\varrho| & $\varrho$\\\verb|\varsigma| & $varsigma$\\ \verb|\varphi| & $\varphi$\\\hline\end{tabular}\caption{Variant forms of Greek letters.}\end{center}\end{table}

Upper case Greek letters are obtained by making the first character of the name upper case.

Here are the control sequence for the uppercase letters\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output} \\\hline\verb|\Gamma| & $\Gamma$ \\\verb|\Delta| & $\Delta$ \\\verb|\Theta| & $\Theta$ \\\verb|\Lambda| & $\Lambda$ \\\verb|\Xi| & $\Xi$ \\\verb|\Pi| & $\Pi$ \\\verb|\Sigma| & $\Sigma$ \\\verb|\Upsilon| & $\Upsilon$ \\\verb|\Phi| & $\Phi$ \\\verb|\Psi| & $\Psi$ \\\verb|\Omega| & $\Omega$\\\hline\caption{Greek letters.}\end{longtable}\end{center}\subsection{Mathematical Symbols}There are numerous mathematical symbols that can be used in mathematics mode. These are obtained by typing an appropriate control sequence.\\\\\textsc{Miscellaneous Symbols.} \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output} \\\hline\verb|\aleph| & $\aleph$\\\verb|\prime| & $\prime$\\\verb|\forall| & $\forall$\\\verb|\hbar| & $\hbar$\\\verb|\emptyset| & $\emptyset$\\\verb|\exists| & $\exists$\\\verb|\imath| & $\imath$\\\verb|\nabla| & $\nabla$\\\verb|\neg| & $\neg$ \\\verb|\jmath| & $\jmath$\\\verb|\surd| & $\surd$\\\verb|\flat| & $\flat$\\

\verb|\ell| & $\ell$\\\verb|\top| & $\top$\\\verb|\natural| & $\natural$\\\verb|\wp| & $\wp$\\\verb|\bot| & $\bot$\\\verb|\sharp| & $\sharp$\\\verb|\Re| & $\Re$\\\verb|\|| & $\|$\\\verb|\clubsuit| & $\clubsuit$\\\verb|\Im| & $\Im$\\\verb|\angle| & $\angle$\\\verb|\diamondsuit| & $\diamondsuit$\\\verb|\partial| & $\partial$\\\verb|\triangle| & $\triangle$\\\verb|\heartsuit| & $\heartsuit$\\\verb|\infty| & $\infty$\\\verb|\backslash| & $\backslash$\\\verb|\spadesuit| & $\spadesuit$\\\hline\caption{Miscellaneous symbols}\end{longtable}\end{center}\textsc{Large Operators.}\begin{table}\begin{center}\begin{tabular}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\sum| & $\sum$\\\verb|\prod| & $\prod$\\\verb|\coprod| & $\coprod$\\\verb|\int| & $\int$\\\verb|\oint| & $\oint$\\\verb|\bigcap| & $\bigcap$\\\verb|\bigcup| & $\bigcup$\\\verb|\bigsqcup| & $\bigsqcup$\\\verb|\bigvee| & $\bigvee$\\\verb|\bigwedge| & $\bigwedge$\\\verb|\bigodot| & $\bigodot$\\\verb|\bigotimes| & $\bigotimes$\\\verb|\bigoplus| & $\bigoplus$\\\verb|\biguplus| & $\biguplus$\\\hline\end{tabular}\end{center}\caption{Large operators}\end{table}\newpage\textsc{Binary Operations.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\pm| & $\pm$\\\verb|\cap| & $\cap$\\

\verb|\vee| & $\vee$\\\verb|\mp| & $\mp$ \\\verb|\cup| & $\cup$\\\verb|\wedge| & $\wedge$\\\verb|\setminus| & $\setminus$\\\verb|\uplus| & $\uplus$\\\verb|\oplus| & $oplus$\\\verb|\cdot| & $\cdot$\\\verb|\sqcap| & $\sqcap$\\\verb|\ominus| & $\ominus$\\\verb|\times| & $\times$\\\verb|\sqcup| & $\sqcup$\\\verb|\otimes| & $\otimes$\\\verb|\ast| & $\ast$\\\verb|\triangleleft| & $\triangleleft$\\\verb|\oslash| & $\oslash$\\\verb|\star| & $\star$\\\verb|\triangleright| & $\triangleright$\\\verb|\odot| & $\odot$\\\verb|\diamond| & $\diamond$\\\verb|\wr| & $\wr$ \\\verb|\dagger| & $\dagger$\\\verb|\circ| & $\circ$\\\verb|\bigcirc| & $\bigcirc$\\\verb|\ddagger| & $\ddagger$\\\verb|\bullet| & $\bullet$\\\verb|\bigtriangleup| & $\bigtriangleup$\\\verb|\amalg| & $\amalg$\\\verb|\div| & $\div$\\\verb|\bigtriangledown| & $\bigtriangledown$\\\hline\caption{Binary operations}\end{longtable}\end{center}\textsc{Relations.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\leq| & $\leq$\\\verb|\geq| & $\geq$\\\verb|\equiv| & $\equiv$\\\verb|\prec| & $\prec$\\\verb|\succ| & $\succ$\\\verb|\sim| & $\sim$\\\verb|\preceq| & $\preceq$\\\verb|\succeq| & $\succeq$\\\verb|\simeq| & $\simeq$\\\verb|\ll| & $\ll$\\\verb|\gg| & $\gg$\\\verb|\asymp| & $\asymp$\\\verb|\subset| & $\subset$\\\verb|\supset|& $\supset$\\\verb|\approx| & $\approx$\\\verb|\subseteq| & $\subseteq$\\\verb|\supseteq| & $\supseteq$\\

\verb|\cong| & $\cong$\\\verb|\sqsubseteq| & $\sqsubseteq$\\\verb|\sqsupseteq| & $\sqsupseteq$\\\verb|\bowtie| & $\bowtie$\\\verb|\in| & $\in$\\\verb|\ni| & $\ni$\\\verb|\propto| & $\propto$\\\verb|\vdash| & $\vdash$\\\verb|\dashv| & $\dashv$\\\verb|\models| & $\models$\\\verb|\smile| & $\smile$\\\verb|\mid| & $\mid$\\\verb|\doteq| & $\doteq$\\\verb|\frown| & $\frown$\\\verb|\parallel| & $\parallel$\\\verb|\perp| & $\perp$\\\hline\caption{Relations}\end{longtable}\end{center}\textsc{Negated Relations.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\not<| & $\not<$\\\verb|\not>| & $\not>$\\\verb|\not=| & $\not=$\\\verb|\not\leq| & $\not\leq$\\\verb|\not\geq| & $\not\geq$\\\verb|\not\equiv| & $\not\equiv$\\\verb|\not\prec| & $\not\prec$\\\verb|\not\succ| & $\not\succ$\\\verb|\not\sim| & $\not\sim$\\\verb|\not\preceq| & $\not\preceq$\\\verb|\not\succeq| & $\not\succeq$\\\verb|\not\simeq| & $\not\simeq$\\\verb|\not\subset| & $\not\subset$\\\verb|\not\supset| & $\not\supset$\\\verb|\not\approx| & $\not\approx$\\\verb|\not| & $\not$\\\verb|\subseteq| & $\subseteq$\\\verb|\not\supseteq| & $\not\supseteq$\\\verb|\not\cong| & $\not\cong$\\\verb|\not\sqsubseteq| & $\not\sqsubseteq$\\\verb|\not\sqsupseteq| & $\not\sqsupseteq$\\\verb|\not\asymp| & $\not\asymp$\\\hline\caption{Negated Relations}\end{longtable}\end{center}\textsc{Arrows.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\

\hline\verb|\leftarrow| & $\leftarrow$\\\verb|\rightarrow| & $\rightarrow$\\\verb|\longleftarrow| & $\longleftarrow$\\\verb|\longrightarrow| & $longrightarrow$\\\verb|\Leftarrow| & $\Leftarrow$\\\verb|\Rightarrow| & $\Rightarrow$\\\verb|\Longleftarrow| & $\Longleftarrow$\\\verb|\Longrightarrow| & $\Longrightarrow$\\\verb|\leftrightarrow| & $\leftrightarrow$\\\verb|\Leftrightarrow| & $\Leftrightarrow$\\\verb|\longleftrightarrow| & $\longleftrightarrow$\\\verb|\Longleftrightarrow| & $\Longleftrightarrow$\\\verb|\hookleftarrow| & $\hookleftarrow$\\\verb|\hookrightarrow| & $\hookrightarrow$\\\verb|\leftharpoonup| & $\leftharpoonup$\\\verb|\rightharpoonup| & $\rightharpoonup$\\\verb|\leftharpoondown| & $\leftharpoondown$\\\verb|\rightharpoondown| & $\rightharpoondown$\\\verb|\uparrow| & $\uparrow$\\\verb|\downarrow| & $\downarrow$\\\verb|\Uparrow| & $\Uparrow$\\\verb|\Downarrow| & $\Downarrow$\\\verb|\updownarrow| & $\updownarrow$\\\verb|\Updownarrow| & $\Updownarrow$\\\verb|\nearrow| & $\nearrow$\\\verb|\nwarrow| & $\nwarrow$\\\verb|\searrow| & $\searrow$\\\verb|\swarrow| & $\swarrow$\\\verb|\mapsto| & $\mapsto$\\\verb|\longmapsto| & $\longmapsto$\\\verb|\rightleftharpoons| & $\rightleftharpoons$\\\hline\caption{Arrows.}\end{longtable}\end{center}\textsc{Openings.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\lbrack| & $\lbrack$\\\verb|\lfloor| & $\lfloor$\\\verb|\lceil| & $\lceil$\\\verb|\lbrace| & $\lbrace$\\\verb|\langle| & $\langle$\\\hline\caption{Openings}\end{longtable}\end{center}\textsc{Alternative Names.}\\\verb|\ne| or \verb|\neq| (same as \verb|\ not=|), \verb|\le| (same as \verb|\leq|), \verb|\ge| (same as \verb|\geq|), \verb|\{| (same as \verb|\lbrace|), \verb|\}| (same as \verb|\rbrace|), \verb|\to| (same as \verb|\rightarrow|), \verb|\gets| (same as \verb|\leftarrow|), \verb|\owns| (same as \verb|\ni|), \verb|\land| (same as \verb|\ wedge|), \verb|\lor| (same as \verb|\vee|), \

verb|\lnot| (same as \verb|\neg|), \verb|\vert| (same as $|$), \verb|\Vert| (same as \textbackslash $|$), \verb|\iff| (same as \verb|\Longleftrightarrow|, but with extra space at each end), \verb|\colon| (same as , but less space around it and less likelihood of a line break after it).\\\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\ne| & $\ne$\\\verb|\le| & $\le$\\\verb|\ge| & $\ge$\\\verb|\{| & $\{$\\\verb|\}| & $\}$\\\verb|\to| & $\to$\\\verb|\gets| & $\gets$\\\verb|\owns| & $\owns$\\\verb|\land| & $\land$\\\verb|\lor| & $\lor$\\\verb|\lnot| & $\lnot$\\\verb|\vert| & $\vert$\\\verb|\Vert| & $\Vert$\\\verb|\iff| & $\iff$\\\verb|\colon| & $\colon$\\\hline\caption{Alternative names.}\end{longtable}\end{center}\subsection{Changing Fonts In Mathematics Mode}The \lq math italic\rq\ font is automatically used in mathematics mode unless you explicitly change the font. The rules for changing the font in mathematics mode are rather different to those applying when typesetting ordinary text.In mathematics mode any change only applies to the single character or symbol that follows (or to any text enclosed within curly brackets immediately following the control sequence). Also, to change a character to the roman or boldface font, the control sequences \verb|\mathrm| and \verb|\mathbf| must be used (rather than \verb|\textrm| and \verb|\textbf|).

There is also a \lq calligraphic\rq\ font available in mathematics mode. This is obtained using the control sequence \verb|\cal|. This font can only be used for uppercase letters.$$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$\subsection{Standard Functions}The names of certain standard functions and abbreviations are obtained by typing a backlash \verb|\| before the name. The following standard functions are represented by control sequences defined in\LaTeX\ \\\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\arccos| & $\arccos$\\\verb|\cos| & $\cos$\\\verb|\csc| & $\csc$\\\verb|\exp| & $\exp$\\\verb|\ker| & $\ker$\\

\verb|\limsup| & $\limsup$\\\verb|\min| & $\min$\\\verb|\sinh| & $\sinh$\\\verb|\arcsin| & $\arcsin$\\\verb|\cosh| & $\cosh$\\\verb|\deg| & $\deg$\\\verb|\gcd| & $\gcd$\\\verb|\lg| & $\lg$\\\verb|\ln| & $\ln$\\\verb|\Pr| & $\Pr$\\\verb|\sup| & $\sup$\\\verb|\arctan| & $\arctan$\\\verb|\cot| &$\cot$\\\verb|\det| & $\det$\\\verb|\hom| & $\hom$\\\verb|\lim| &$\lim$\\\verb|\log| & $\log$\\\verb|\sec| &$\sec$\\\verb|\tan| &$\tan$\\\verb|\arg| &$\arg$\\\verb|\coth| & $\coth$\\\verb|\dim| & $\dim$\\\verb|\inf| & $\inf$\\\verb|\liminf| & $\liminf$\\\verb|\max| & $\max$\\\verb|\sin| & $\sin$\\\verb|\tanh| & $\tanh$\\\hline\caption{Standard functions.}\end{longtable}\end{center}

Names of functions and other abbreviations not in this list can be obtained by converting to the roman font.\begin{verbatim}$\mathrm{text}$\end{verbatim}\subsection{Text Embedded In Displayed Equations}Text can be embedded in displayed equations (in \LaTeX) by using\begin{verbatim}\mbox{embedded text} \end{verbatim}In Plain \TeX\ one should use \verb|\hbox| in place of \verb|\mbox|.\subsection{Accents In Mathematics Mode}There are various control sequences for producing underlining, overlining and various accents in mathematics mode\\\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\underline{a}| & $\underline{a}$\\\verb|\overline{a}| & $\overline{a}$\\\verb|\hat{a}| & $\hat{a}$\\\verb|\check{a}| & $\check{a}$\\\verb|\tilde{a}| & $\tilde{a}$\\\verb|\acute{a}| & $\acute{a}$\\

\verb|\grave{a}| & $\grave{a}$\\\verb|\dot{a}| & $\dot{a}$\\\verb|\ddot{a}| & $\ddot{a}$\\\verb|\breve{a}| & $\breve{a}$\\\verb|\bar{a}| & $\bar{a}$\\\verb|\vec{a}| & $\vec{a}$\\\hline\caption{Accents in mathematics mode.}\end{longtable}\end{center}\subsection{Multiline Formulae In \LaTeX}\begin{verbatim}\begin{eqnarray*}text &= text\\text &= text\end{eqnarray*}\end{verbatim}

Note the use of the special character \& as an alignment tab. When the formula is typeset, the part of the second line of the formula beginning with an occurrence of \& will be placed immediately beneath that part of the first line of the formula which begins with the corresponding occurrence of \&. Also \verb|\\| is used to separate the lines of the formula.

The asterisk in eqnarray* is put there to suppress the automatic equation numbering produced by \LaTeX\ . If you wish for an automatically numbered multiline formula, you should use\begin{verbatim}\begin{eqnarray}...\end{eqnarray}\end{verbatim}\subsection{Notag In Mathematics Mode}\begin{verbatim}\begin{align}text \notag \\text \label{text}\end{align}\end{verbatim}Use the \verb|\notag| to ensure that the equation is labeled only once (at the end).\subsection{Short Math Guide}\textsc{Classes of math symbols.} The symbols in a math formula fall into different classes that correspond more or less to the part of speech each symbol would have if the formula were expressed in words. Certain spacing and positioning cues are traditionally used forthe different symbol classes to increase the readability of formulas.\newpage\begin{center}\begin{longtable}{|c|c|c|}\hline\textbf{Class number} & \textbf{Mnemonic} & \textbf{Description (part of speech)} \\\hline0& Ord& simple/ordinary (“noun”)\\1& Op& prefix operator\\2& Bin& binary operator (conjunction) \\

3& Rel& relation/comparison (verb)\\4& Open& left/opening delimiter\\5& Close& right/closing delimiter \\6& Pun& postfix/punctuation \\\hline\caption{Classes of math symbols.}\end{longtable}\end{center}\textsc{Number equations.} To give your equation numbers the form $m.n$ (section number.equation number), use the \verb|\numberwithin| command in the preamble of your document \\\verb|\numberwithin{equation}{section}|\\\\\textsc{Other Alphabetic symbols.} These are also class 0.\\\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\aleph| & $\aleph$\\\verb|\beth| & $\beth$\\\verb|\daleth| & $\daleth$\\\verb|\gimel| & $\gimel$\\\verb|\complement| & $\complement$\\\verb|\ell| & $\ell$\\\verb|\eth| & $\eth$\\\verb|\hbar| & $\hbar$\\\verb|\hslash| & $\hslash$\\\verb|\mho| & $\mho$\\\verb|\partial| & $\partial$\\\verb|\wp| & $\wp$\\\verb|\circledS| & $\circledS$\\\verb|\Bbbk| & $\Bbbk$\\\verb|\Finv| & $\Finv$\\\verb|\Game| & $\Game$\\\verb|\Im| & $\Im$\\\verb|\Re| & $\Re$\\\hline\caption{Other alphabetic symbols.}\end{longtable}\end{center}\textsc{Miscellaneous Simple symbols.} These symbols are also of class 0 (ordinary) which means they do not have any built-in spacing.\newpage \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\angle| & $\angle$\\\verb|\backprime| & $\backprime$\\\verb|\bigstar| & $\bigstar$\\\verb|\blacklozenge| & $\blacklozenge$\\\verb|\blacksquare| & $\blacksquare$\\\verb|\blacktriangle| & $\blacktriangle$\\\verb|\blacktriangledown| & $\blacktriangledown$\\\verb|\bot| &$\bot$\\

\verb|\clubsuit| & $\clubsuit$\\\verb|\diagdown| & $\diagdown$\\\verb|\diagup| &$\diagup$\\\verb|\diamondsuit| & $\diamondsuit$\\\verb|\emptyset| & $\emptyset$\\\verb|\exists| & $\exists$\\\verb|\flat| &$\flat$\\\verb|\forall| & $\forall$\\\verb|\heartsuit| & $\heartsuit$\\\verb|\infty| & $\infty$\\\verb|\lozenge| & $\lozenge$\\\verb|\measuredangle| &$\measuredangle$\\\verb|\nabla| & $\nabla$\\\verb|\natural| & $\natural$\\\verb|\neg| & $\neg$\\\verb|\nexists| & $\nexists$\\\verb|\prime| & $\prime$\\\verb|\sharp| & $\sharp$\\\verb|\spadesuit| & $\spadesuit$\\\verb|\sphericalangle| & $\sphericalangle$\\\verb|\square| & $\square$\\\verb|\surd| &$\surd$\\\verb|\top| & $\top$\\\verb|\triangle| & $\triangle$\\\verb|\triangledown| & $\triangledown$\\\verb|\varnothing| & $\varnothing$\\\hline\caption{Miscellaneous simple symbols.}\end{longtable}\end{center}\newpage\textsc{binary operator symbols.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\amalg| & $\amalg$\\\verb|\ast| & $\ast$\\\verb|\barwedge| & $\barwedge$\\\verb|\bigcirc| & $\bigcirc$\\\verb|\bigtriangledown| & $\bigtriangledown$\\\verb|\bigtriangleup| & $\bigtriangleup$\\\verb|\boxdot| & $\boxdot$\\\verb|\boxminus| & $\boxminus$\\\verb|\boxplus| & $\boxplus$\\\verb|\boxtimes| & $\boxtimes$\\\verb|\bullet| & $\bullet$\\\verb|\cap| & $\cap$\\\verb|\Cap| & $\Cap$\\\verb|\cdot| & $\cdot$\\\verb|\centerdot| & $\centerdot$\\\verb|\circ| & $\circ$\\\verb|\circledast| & $\circledast$\\\verb|\circledcirc| & $\circledcirc$\\\verb|\circleddash| & $\circleddash$\\\verb|\cup| & $\cup$\\

\verb|\Cup| & $\Cup$\\\verb|\curlyvee| &$\curlyvee$\\\verb|\curlywedge| & $\curlywedge$\\\verb|\dagger| & $\dagger$\\\verb|\ddagger| & $\ddagger$\\\verb|\diamond| & $\diamond$\\\verb|\div| & $\div$\\\verb|\divideontimes| & $\divideontimes$\\\verb|\dotplus| & $\dotplus$\\\verb|\doublebarwedge| & $\doublebarwedge$\\\verb|\gtrdot| & $\gtrdot$\\\verb|\intercal| & $\intercal$\\\verb|\leftthreetimes| & $\leftthreetimes$\\\verb|\lessdot| & $\lessdot$\\\verb|\ltimes| & $\ltimes$\\\verb|\mp| & $\mp$\\\verb|\odot| & $\odot$\\\verb|\ominus| & $\ominus$\\\verb|\oplus| & $\oplus$\\\verb|\oslash| & $\oslash$\\\verb|\otimes| & $\otimes$\\\verb|\pm| & $\pm$\\\verb|\rightthreetimes| & $\rightthreetimes$\\\verb|\rtimes| & $\rtimes$\\\verb|\setminus| & $\setminus$\\\verb|\smallsetminus| & $\smallsetminus$\\\verb|\sqcap| & $\sqcap$\\\verb|\sqcup| & $\sqcup$\\\verb|\star| & $\star$\\\verb|\times| & $\times$\\\verb|\triangleleft| & $\triangleleft$\\\verb|\triangleright| & $\triangleright$\\\verb|\uplus| & $\uplus$\\\verb|\vee| & $\vee$\\\verb|\veebar| & $\veebar$\\\verb|\wedge| & $\wedge$\\\verb|\wr| & $\wr$\\\verb|\land| & $\land$\\\verb|\lor| & $\lor$\\\verb|\doublecup| & $\doublecup$\\\verb|\doublecap| & $\doublecap$\\\hline\caption{Binary operator symbols.}\end{longtable}\end{center}\textsc{Relation symbols. $<=>$ and variants.} \begin{center}\begin{longtable}{|l|c|}\verb|\approx| & $\approx$\\\verb|\approxeq| & $\approxeq$\\\verb|\asymp| & $\asymp$\\\verb|\backsim| & $\backsim$\\\verb|\backsimeq| & $\backsimeq$\\\verb|\bumpeq| & $\bumpeq$\\\verb|\Bumpeq| & $\Bumpeq$\\\verb|\circeq| & $\circeq$\\\verb|\cong| & $\cong$\\

\verb|\curlyeqprec| & $\curlyeqprec$\\\verb|\curlyeqsucc| & $\curlyeqsucc$\\\verb|\doteq| & $\doteq$\\\verb|\doteqdot| & $\doteqdot$\\\verb|\eqcirc| & $\eqcirc$\\\verb|\eqsim| & $\eqsim$\\\verb|\eqslantgtr| & $\eqslantgtr$\\\verb|\eqslantless| & $\eqslantless$\\\verb|\equiv| & $\equiv$\\\verb|\fallingdotseq| &$\fallingdotseq$\\\verb|\geq| & $\geq$\\\verb|\geqq| & $\geqq$\\\verb|\geqslant| & $\geqslant$\\\verb|\gg| & $\gg$\\\verb|\ggg| & $\ggg$\\\verb|\gnapprox| & $\gnapprox$\\\verb|\gneq| & $\gneq$\\\verb|\gneqq| & $\gneqq$\\\verb|\gnsim| & $\gnsim$\\\verb|\gtrapprox| & $\gtrapprox$\\\verb|\gtreqless| & $\gtreqless$\\\verb|\gtreqqless| & $\gtreqqless$\\\verb|\gtrless| & $\gtrless$\\\verb|\gtrsim| & $\gtrsim$\\\verb|\gvertneqq| & $\gvertneqq$\\\verb|\leq| & $\leq$\\\verb|\leqq| & $\leqq$\\\verb|\leqslant| & $\leqslant$\\\verb|\lessapprox| & $\lessapprox$\\\verb|\lesseqgtr| & $\lesseqgtr$\\\verb|\lesseqqgtr| & $\lesseqqgtr$\\\verb|\lessgtr| & $\lessgtr$\\\verb|\lesssim| & $\lesssim$\\\verb|\ll| & $\ll$\\\verb|\lll| & $\lll$\\\verb|\lnapprox| & $\lnapprox$\\\verb|\lneq| & $\lneq$\\\verb|\lneqq| & $\lneqq$\\\verb|\lnsim| & $\lnsim$\\\verb|\lvertneqq| & $\lvertneqq$\\\verb|\ncong| & $\ncong$\\\verb|\neq| & $\neq$\\\verb|\ngeq| & $\ngeq$\\\verb|\ngeqq| & $\ngeqq$\\\verb|\ngeqslant| & $\ngeqslant$\\\verb|\ngtr| & $\ngtr$\\\verb|\nleq| & $\nleq$\\\verb|\nleqq| & $\nleqq$\\ \verb|\nleqslant| & $\nleqslant$\\\verb|\nless| & $\nless$\\\verb|\nprec| & $\nprec$\\\verb|\npreceq| & $\npreceq$\\\verb|\nsim| & $\nsim$\\\verb|\nsucc| & $\nsucc$\\\verb|\nsucceq| & $\nsucceq$\\\verb|\prec| & $\prec$\\\verb|\precapprox| & $\precapprox$\\

\verb|\preccurlyeq| & $\preccurlyeq$\\\verb|\preceq| & $\preceq$\\\verb|\precnapprox| & $\precnapprox$\\\verb|\precneqq| & $\precneqq$\\\verb|\precnsim| & $\precnsim$\\\verb|\precsim| & $\precsim$\\\verb|\risingdotseq| & $\risingdotseq$\\\verb|\sim| & $\sim$\\\verb|\simeq| & $\simeq$\\\verb|\succ| & $\succ$\\\verb|\succapprox| & $\succapprox$\\\verb|\succcurlyeq| & $\succcurlyeq$\\\verb|\succeq| & $\succeq$\\\verb|\succnapprox| & $\succnapprox$\\\verb|\succneqq| &$\succneqq$\\\verb|\succnsim| & $\succnsim$\\\verb|\succsim| & $\succsim$\\\verb|\thickapprox| & $\thickapprox$\\\verb|\thicksim| & $\thicksim$\\\verb|\triangleq| & $\triangleq$\\\verb|\ne | & $\ne$\\\verb|\le| & $\le$\\\verb|\ge| & $\ge$\\\verb|\Doteq| & $\Doteq$\\\verb|\llless| & $\llless$\\\verb|\gggtr| & $\gggtr$\\\hline\caption{Relation symbols $<=>$ and variants.}\end{longtable}\end{center}\textsc{Relation symbols arrow.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\circlearrowright| & $\circlearrowright$\\\verb|\curvearrowleft| & $\curvearrowleft$\\\verb|\curvearrowright| & $\curvearrowright$\\\verb|\downdownarrows| & $\downdownarrows$\\\verb|\downharpoonleft| & $\downharpoonleft$\\\verb|\downharpoonright| & $\downharpoonright$\\\verb|\hookleftarrow| & $\hookleftarrow$\\\verb|\hookrightarrow| & $\hookrightarrow$\\\verb|\leftarrow| & $\leftarrow$\\\verb|\Leftarrow| & $\Leftarrow$\\\verb|\leftarrowtail| & $\leftarrowtail$\\\verb|\leftharpoondown| & $\leftharpoondown$\\\verb|\leftharpoonup| & $\leftharpoonup$\\\verb|\leftleftarrows| & $\leftleftarrows$\\\verb|\leftrightarrow| & $\leftrightarrow$\\\verb|\Leftrightarrow| & $\Leftrightarrow$\\\verb|\leftrightarrows| & $\leftrightarrows$\\\verb|\leftrightharpoons| & $\leftrightharpoons$\\\verb|\leftrightsquigarrow| & $\leftrightsquigarrow$\\\verb|\Lleftarrow| & $\Lleftarrow$\\\verb|\longleftarrow| & $\longleftarrow$\\

\verb|\Longleftarrow| & $\Longleftarrow$\\\verb|\longleftrightarrow| & $\longleftrightarrow$\\\verb|\Longleftrightarrow| & $\Longleftrightarrow$\\\verb|\longmapsto| & $\longmapsto$\\\verb|\longrightarrow| & $\longrightarrow$\\\verb|\Longrightarrow| & $\Longrightarrow$\\\verb|\looparrowleft| & $\looparrowleft$\\\verb|\looparrowright| & $\looparrowright$\\\verb|\Lsh| & $\Lsh$\\\verb|\mapsto| & $\mapsto$\\\verb|\multimap| & $\multimap$\\\verb|\nLeftarrow| & $\nLeftarrow$\\\verb|\nLeftrightarrow| & $\nLeftrightarrow$\\\verb|\nRightarrow| & $\nRightarrow$\\\verb|\nearrow| & $\nearrow$\\\verb|\nleftarrow| & $\nleftarrow$\\\verb|\nleftrightarrow| & $\nleftrightarrow$\\\verb|\nrightarrow| & $\nrightarrow$\\\verb|\nwarrow| & $\nwarrow$\\\verb|\rightarrow| & $\rightarrow$\\\verb|\Rightarrow| & $\Rightarrow$\\\verb|\rightarrowtail| & $\rightarrowtail$\\\verb|\rightharpoondown| & $\rightharpoondown$\\\verb|\rightharpoonup| & $\rightharpoonup$\\\verb|\rightleftarrows| & $\rightleftarrows$\\\verb|\rightleftharpoons| & $\rightleftharpoons$\\\verb|\rightrightarrows| & $\rightrightarrows$\\\verb|\rightsquigarrow| & $\rightsquigarrow$\\\verb|\Rrightarrow| & $\Rrightarrow$\\\verb|\Rsh| & $\Rsh$\\\verb|\searrow| & $\searrow$\\\verb|\swarrow| & $\swarrow$\\\verb|\twoheadleftarrow| & $\twoheadleftarrow$\\\verb|\twoheadrightarrow| & $\twoheadrightarrow$\\\verb|\upharpoonleft| & $\upharpoonleft$\\\verb|\upharpoonright| & $\upharpoonright$\\\verb|\upuparrows| & $\upuparrows$\\\verb|\gets| & $\gets$\\\verb|\to| & $\to$\\\verb|\restriction| & $\restriction$\\\hline\caption{Relation symbols arrow.}\end{longtable}\end{center}\textsc{relation symbols Miscellaneous.}\begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\backepsilon| & $\backepsilon$\\\verb|\because| & $\because$\\\verb|\between| & $\between$\\\verb|\blacktriangleleft| & $\blacktriangleleft$\\\verb|\blacktriangleright| & $\blacktriangleright$\\\verb|\bowtie| & $\bowtie$\\\verb|\dashv| & $\dashv$\\

\verb|\frown| & $\frown$\\\verb|\in| & $\in$\\\verb|\mid| &$\mid$\\\verb|\models| & $\models$\\\verb|\ni| & $\ni$\\\verb|\nmid| & $\nmid$\\\verb|\notin| & $\notin$\\\verb|\nparallel| & $\nparallel$\\\verb|\nshortmid| & $\nshortmid$\\\verb|\nshortparallel| & $\nshortparallel$\\\verb|\nsubseteq| & $\nsubseteq$\\\verb|\nsubseteqq| & $\nsubseteqq$\\\verb|\nsupseteq| & $\nsupseteq$\\\verb|\nsupseteqq| & $\nsupseteqq$\\\verb|\ntriangleleft| & $\ntriangleleft$\\\verb|\ntrianglelefteq| & $\ntrianglelefteq$\\\verb|\ntriangleright| & $\ntriangleright$\\\verb|\ntrianglerighteq| & $\ntrianglerighteq$\\\verb|\nvdash| & $\nvdash$\\\verb|\nVdash| & $\nVdash$\\\verb|\nvDash| & $\nvDash$\\\verb|\nVDash| & $\nVDash$\\\verb|\parallel| & $\parallel$\\\verb|\perp| & $\perp$\\\verb|\pitchfork| & $\pitchfork$\\\verb|\propto| & $\propto$\\\verb|\shortmid| &$\shortmid$\\\verb|\shortparallel| & $\shortparallel$\\\verb|\smallfrown| & $\smallfrown$\\\verb|\smallsmile| & $\smallsmile$\\\verb|\smile| & $\smile$\\\verb|\sqsubset| & $\sqsubset$\\\verb|\sqsubseteq| & $\sqsubseteq$\\\verb|\sqsupset| & $\sqsupset$\\\verb|\sqsupseteq| & $\sqsupseteq$\\\verb|\subset| & $\subset$\\\verb|\Subset| & $\Subset$\\\verb|\subseteq| & $\subseteq$\\ \verb|\subseteqq| & $\subseteqq$\\\verb|\subsetneq| & $\subsetneq$\\\verb|\subsetneqq| & $\subsetneqq$\\\verb|\supset| & $\supset$\\\verb|\Supset| & $\Supset$\\\verb|\supseteq| & $\supseteq$\\\verb|\supseteqq| & $\supseteqq$\\\verb|\supsetneq| & $\supsetneq$\\\verb|\supsetneqq| & $\supsetneqq$\\\verb|\therefore| & $\therefore$\\\verb|\trianglelefteq| & $\trianglelefteq$\\\verb|\trianglerighteq| & $\trianglerighteq$\\\verb|\varpropto| & $\varpropto$\\\verb|\varsubsetneq| &$\varsubsetneq$\\\verb|\varsubsetneqq| & $\varsubsetneqq$\\\verb|\varsupsetneq| & $\varsupsetneq$\\\verb|\varsupsetneqq| & $\varsupsetneqq$\\\verb|\vartriangle| & $\vartriangle$\\\verb|\vartriangleleft| & $\vartriangleleft$\\

\verb|\vartriangleright| & $\vartriangleright$\\\verb|\vdash| & $\vdash$\\\verb|\Vdash| & $\Vdash$\\\verb|\vDash| & $\vDash$\\\verb|\Vvdash| & $\Vvdash$\\\verb|\owns| & $\owns$\\\hline\caption{Relation symbols miscellaneous.}\end{longtable}\end{center}\textsc{Cumulative (variable-size) operators.} \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\int| & $\int$\\\verb|\oint| & $\oint$\\\verb|\bigcap| & $\bigcap$\\\verb|\bigcup| & $\bigcup$\\\verb|\bigodot| & $\bigodot$\\\verb|\bigoplus| & $\bigoplus$\\\verb|\bigotimes| & $\bigotimes$\\\verb|\bigsqcup| & $\bigsqcup$\\\verb|\biguplus| & $\biguplus$\\\verb|\bigvee| & $\bigvee$\\\verb|\bigwedge| & $\bigwedge$\\\verb|\coprod| & $\coprod$\\\verb|\prod| & $\prod$\\\verb|\smallint| & $\smallint$\\\verb|\sum| & $\sum$\\\hline\caption{Cumulative (variable-size) operators.}\end{longtable}\end{center}\newpage\textsc{Punctuation.} \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\colon| & $\colon$\\\verb|\dotsb| &$\dotsb$\\\verb|\dotsc| & $\dotsc$\\\verb|\dotsi| & $\dotsi$\\\verb|\dotsm| & $\dotsm$\\\verb|\dotso| & $\dotso$\\\verb|\ddots| & $\ddots$\\\verb|\vdots| & $\vdots$\\\hline\caption{Punctuation.}\end{longtable}\end{center}\textbf{Note 1.} The by itself produces a colon with class-3 (relation) spacing. The command \verb|\colon| produces special spacing for use in constructions such as \verb|f\colon A\to B| gives $f\colon A\to B$.\\

\textbf{Note 2.} Although the commands \verb|\cdots| and \verb|\ldots| are frequently used, we recommend the more semantically oriented commands\begin{verbatim}\dotsc \dotsi \dotsm \dotsobatim\end{verbatim}for most purposes.\\\\\textsc{Pairing Delimiters (extensible).} \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\lbrace| &$\lbrace$\\\verb|\rbrace| & $\rbrace$\\\verb|\lvert| & $\lvert$\\\verb|\rvert| & $\rvert$\\\verb|\lVert| & $\lVert$\\\verb|\rVert| & $\rVert$\\\verb|\langle| & $\langle$\\\verb|\rangle| & $\rangle$\\\verb|\lceil| & $\lceil$\\\verb|\rceil| & $\rceil$\\\verb|\lfloor| & $\lfloor$\\\verb|\rfloor| & $\rfloor$\\\verb|\lgroup| & $\lgroup$\\\verb|\rgroup| & $\rgroup$\\\verb|\lmoustache| & $\lmoustache$\\\verb|rmoustache| & $\rmoustache$\\\hline\caption{Pairing delimiters (extensible).}\end{longtable}\end{center}\textsc{Nonpairing Extensible symbols.} \begin{verbatim}\vert,\Vert,\backslash,\arrowvert,\Arrowvert,\bracevert\end{verbatim}produce\\$$\vert,\Vert,\backslash,\arrowvert,\Arrowvert,\bracevert$$\\\textit{Note 1.} Using \verb|\vert|, $|$, \verb|\Vert|, or \textbackslash $|$ for paired delimiters is not recommended.\\ Synonyms $\|$ \textbackslash $|$.\\\\\textsc{Extensible vertical arrows.} \begin{center}\begin{longtable}{|l|c|}\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\uparrow| & $\uparrow$\\\verb|\Uparrow| & $\Uparrow$\\\verb|\downarrow| & $\downarrow$\\\verb|\Downarrow| & $\Downarrow$\\\verb|\updownarrow| & $\updownarrow$\\\verb|\Updownarrow| & $\Updownarrow$\\\hline\caption{Extensible vertical arrows.}

\end{longtable}\end{center}

To define additional named operators outside the above list, use the \begin{verbatim}\DeclareMathOperator\end{verbatim}command. For example, after\begin{verbatim}\DeclareMathOperator{\rank}{rank}\DeclareMathOperator{\esssup}{ess\,sup}\end{verbatim}one could write \begin{verbatim}\rank(x),\esssup(y,z)\end{verbatim}

The star form \verb|\DeclareMathOperator*| creates an operator that takes limits in a displayed formula like sup or max. When predefining such a named operator is problematic (e.g., when using one in thetitle or abstract of an article), there is an alternative form that can be used directly \verb|\operatorname{rank}(x)| to produce $\operatorname{rank}(x)$\\\\\textsc{Math font switches.} Not all of the fonts necessary to support comprehensive math font switching are commonly available in a typical \LaTeX\ setup. Here are the results of applying various font switches to a wide range of math symbols when the standard setof Computer Modern fonts is in use. It can be seen that the only symbols that respond correctly to all of the font switches are the uppercase Latin letters. In fact, nearly all math symbols apart from Latin letters remain unaffected by font switches; and although thelowercase Latin letters, capital Greek letters, and numerals do respond properly to some font switches, they produce bizarre results for other font switches. (Use of alternative math font sets such as Lucida New Math may ameliorate the situation somewhat.)\begin{verbatim}default,\mathbf,\mathsf,\mathit,\mathcal,\mathbb,\mathfrak\end{verbatim}\textsc{Calligraphic letters (cmsy; no lowercase).} Use \verb|\mathcal{}| to produce$$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$\\\textsc{Blackboard Bold letters (msbm; no lowercase).} Use \verb|\mathbb{}| to produce$$\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$\\\textsc{Fraktur letters (eufm).} Use \verb|\mathfrak{}| to produce$$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz}$$\\\textsc{Top and bottom embellishments.} These are visually similar to accents but generally span multiple symbols rather than being applied to a single base symbol. For ease of reference, \verb|\widetilde| and \verb|\widehat| are redundantly included here and in the table ofmath accents.\begin{center}\begin{longtable}{|l|c|}

\hline\textbf{Input} & \textbf{Output}\\\hline\verb|\widetilde{xxx}| & $\widetilde{xxx}$\\\verb|\widehat{xxx}| & $\widehat{xxx}$\\\verb|\overline{xxx}| & $\overline{xxx}$\\\verb|\underline{xxx}| & $\underline{xxx}$\\\verb|\overbrace{xxx}| & $\overbrace{xxx}$\\\verb|\underbrace{xxx}| & $\underbrace{xxx}$\\\verb|\overleftarrow{xxx}| & $\overleftarrow{xxx}$\\\verb|\underleftarrow{xxx}| & $\underleftarrow{xxx}$\\\verb|\overrightarrow{xxx}| & $\overrightarrow{xxx}$\\\verb|\underrightarrow{xxx}| & $\underrightarrow{xxx}$\\\verb|\overleftrightarrow{xxx}| & $\overleftrightarrow{xxx}$\\\verb|\underleftrightarrow{xxx}| & $\underleftrightarrow{xxx}$\\\hline\caption{Top and bottom embellishments.}\end{longtable}\end{center}\textsc{Extensible arrows.} \verb|\xleftarrow| and \verb|\xrightarrow| produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts. These commands take one optional argument (the subscript) and one mandatory argument (the superscript, possibly empty). Use \begin{verbatim}\xleftarrow{n+\mu-1}\quad \xrightarrow[T]{n\pm i-1}\end{verbatim}to produce \begin{align}A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1}C\end{align}\textsc{Affixing symbols to other symbols.} In addition to the standard accents, other symbols can be placed above or below a base symbol with the \verb|\overset| and \verb|\underset| commands. For example, writing \verb|\overset{*}{X}| will place a superscript-size * above the $X$, thus $\overset{*}{X}$. See also the description of \verb|sideset|.\\\\\textsc{Matrices.} The environments\begin{verbatim}pmatrix,bmatrix,Bmatrix,vmatrix,smallmatrix,Vmatrix\end{verbatim}

To produce a row of dots in a matrix spanning a given number of columns, use \verb|\hdotsfor|. For example, \verb|\hdotsfor{3}| in the second column of a four-column matrix will print a row of dots across the final three columns.\\\\\textsc{Math spacing commands.} There are also three commands that leave a space equal to the height and/or width of a given fragment of \LaTeX\ material \verb|\phantom{XXX}| (space as wide and high as three X's), \verb|\hphantom{XXX}| (space as wide as three X's; height 0), \verb|\vphantom{X}| (space of width , height = height of X).\\\\\textsc{Dots.} Dots For preferred placement of ellipsis dots (raised or on-line) in various contexts there is no general consensus. It may therefore be considered a matter of taste. By using the semantically oriented commands\begin{itemize}\item \verb|\dotsc| for dots with commas.\item \verb|\dotsb| for dots with binary operators/relations.

\item \verb|\dotsm| for multiplication dots.\item \verb|\dotsi| for dots with integrals.\item \verb|\dotso| for other dots (none of the above).\end{itemize}\textsc{Nonbreaking dashes.} The command \verb|\nobreakdash| suppresses the possibility of a linebreak after the following hyphen or dash.\\\\\textsc{Delimiters sizes.} Unless you indicate otherwise, delimiters in math formulas will remain at the standard size regardless of the height of the enclosed material. To get larger sizes, you can either select a particular size using a \verb|\big...| prefix (see below), or you can use \verb|\left| and \verb|\right| prefixes for autosizing. The automatic delimiter sizing done by \verb|\left| and \verb|\right| has two limitations First, it is applied mechanically to produce delimiters large enough to encompass the largest contained item, and second, the range of sizes has fairly large quantum jumps. This means that an expression that is infinitesimally too large for a given delimiter size will get the next larger size, a jump of 6pt or so (3pt top and bottom) in normal-sized text. There are two or three situations where the delimiter size is commonly adjusted. These adjustments are done using the following commands\begin{verbatim}text size,\left,\right,\bigl,\bigr,\Bigl,\Bigr,\biggl,\biggr,\Biggl,\Biggr\end{verbatim}produce\begin{align}(a),\left(a\right),\bigl(a \bigr),\Bigl(a \Bigr),\biggl(a \biggr), \Biggl( a\Biggr)\end{align}\textsc{The text command.} The main use of the command \verb|\text| is for words or phrases in a display. It is similar to \verb|\mbox| in its effects but, unlike \verb|\mbox|, automatically producessubscript-size text if used in a subscript.\\\\\textsc{mod and its relatives.} Commands \verb|\mod,\bmod,\pmod,\pod| deal with the special spacing conventions of \lq mod\rq notation. \verb|\mod| and \verb|\pod| are variants of \verb|\pmod| preferred by some authors; \verb|\mod| omits the parentheses, whereas \verb|\pod| omits the \lq mod\rq and retains the parentheses. \verb|\mod,\bmod,\pmod,\pod| produce\begin{align}x \mod n,x \bmod n,x \pmod n,x \pod n\end{align}\textsc{Multiple integral signs.} \verb|\iint,\iiint,\iiiint| give multiple integral signs with the spacing between them nicely adjusted, in both text and display style. \verb|\idotsint| is an extension of the same idea that gives two integral signs with dots between them.\begin{align}\int,\iint,\iiint,\iiiint,\idotsint\end{align}\subsection{Multiple Aligned Equations}\begin{verbatim}\begin{align}text &= text \\text &= text \end{align}\end{verbatim}\subsection{Multi-line Equations}

\begin{verbatim}\begin{multiline}text \\ text \end{multiline}\end{verbatim}\section{\LaTeX\ Packages}\subsection{Using Package}\textsc{Some commonly-used packages} \texttt{amsmath, amssymb, setspace} (provide easy way to change linespacing), \texttt{graphicx, fancyhdr }(customize headers and footers), \texttt{rotating} (provide rotations, especially for figures and tables), \texttt{color}. \begin{verbatim}\documentclass[amssymb,amsmath]{amsart}\end{verbatim}\subsection{The \texttt{sinunitx} Package}the \texttt{siunitx} package supports all SI units. It also supportsstandard prefixes, such as giga- and femto-.\begin{verbatim}\SI{3}{\giga\hertz}\SI{3}{GHz}\SI{19}{\meter\per\second}\SI[per-mode=fraction]{19}{\meter\per\second}\SI{54.1}{kg.m/s^2}\SI{32932e-3213}{\micro F}\SI{3.2}{kg/\nano\meter\squared}\SI{8.9}{\kilo\gram\tothe{12}}\SI{27}{\degreeCelsius}\end{verbatim}

By default, reciprocals of units are displayed as negative powers; to display them as fractions, import the package with the command\begin{verbatim}\usepackage[per-mode=fraction]{siunitx}\end{verbatim}

The siunitx package contains several other useful commands \verb|\num| works just like the first argument of \verb|\SI| by itself, and \verb|\si| works like the second part.\begin{verbatim}\num{3.0}\num{3.0e5}\num{3+2i}\si{\kilo\gram\per\tesla}\si{\lumen\per\radian}\end{verbatim}

Additionally, there is a command for typing numbers with the same units. Numbers are separated by semi-colons, and commands and an ``and'' are inserted automatically.\begin{verbatim}\SIlist{1;2.3;-534;7.3e-5}{\joule\per\second}\end{verbatim}

For more information on this package, check out its manual on CTAN at \\\url{http://ctan.org/pkg/siunitx}.\subsection{The \texttt{mhchem} Package}

\LaTeX\ ’s math mode is meant to write mathematics and is thus rather ill-suited for typing chemical equations, mostly because atomic symbols should not be italicized. The \texttt{mhchem} package provides the new command \verb|\ce|, for typing chemical equations.\begin{verbatim}\ce{H2SO4} \ce{AgCl2-} \ce{CrO4^2-} \ce{^{235}_{92}U}\end{verbatim}

We can also use \verb|\ce| to make chemical equations.\begin{verbatim}\ce{CO2+C -> 2CO}\\[0.4em]\ce{H+ + OH- <=>> H20}\end{verbatim}

If you want to learn more, head to the manual at \url{ctan.org/pkg/mhchem}.\subsection{The TikZ Package (Drawing Diagrams)}\begin{verbatim}\usepackage{tikz}\begin{tikzpicture}\draw something\end{tikzpicture}\end{verbatim}

Tikz commands \verb|\draw,\node,\fill.|\subsection{The TikZ Package}TikZ is a package for drawing diagrams within \LaTeX\ . It’s extremely powerful, capable of producing about any figure you could want \footnote{To get an idea just how powerful TikZ is, see the TikZ examples page at \url{texample.net/tikz/examples/}.}. Our goal is to introduce some of the basics of TikZ, so that you can get started making figures. For a more comprehensive introduction, see the superb package documentation at CTAN. \footnote{\url{ctan.org/pkg/pgf}} \subsubsection{Getting Started}First, include the package \verb|\usepackage{tikz}|. Figures in TikZ are made in the environment \texttt{tikzpicture}; this is the only environment we’ll use.\begin{verbatim}\begin{tikzpicture}\draw (0, 0) -- (1, 0) --(0, 1) -- (1, 1) -- (2, 1);\end{tikzpicture}\end{verbatim}

A TikZ command begins with a \LaTeX\ command, like \verb|\draw|, \verb|\node|, or \verb|\fill|, followed by a sequence of instructions, and terminated with a semicolon. Let me say that again, because it constitutes the most common mistake beginning TikZ users make \textit{Every TikZ drawing command ends with a semicolon.}

TikZ has a shorthand for creating simple pictures, which we’ll use in these notes to save space. The command \verb|\tikz| ... is short for the more verbose\begin{verbatim}\begin{tikzpicture}...\end{tikzpicture}\end{verbatim}

\verb|\end{tikzpicture}|, provided that we only give \verb|\tikz| a single command. For instance, the following commands will produce the same output\begin{verbatim}\begin{tikzpicture}\draw (0, 0) -- (1, 0);\end{tikzpicture}

\tikz \draw (0, 0) -- (1, 0);\end{verbatim}

The default coordinate system has the positive x-axis pointing right, the positive y-axis pointing up, and one unit corresponding to one centimeter. To work with different units, you can simply add the units to the coordinates, like (2in,0.3pt). But it's probably a better idea to resize the figure once it's finished.\subsubsection{Styles}If you don’t yet have experience with computer graphics programming, it may be difficult to visualize the coordinates needed to create diagrams. TikZ has a built-in command to ease the transition.\begin{verbatim}\tikz \draw[help lines, step=0.5] (0, 0) grid (3, 3);\end{verbatim}There are two differences between this \verb|\draw| command and the previous one. First, we’re using the grid instruction to draw a grid with corners at $(0;0)$ and $(3;3)$, as opposed to the $--$ instruction we used earlier.

Second, the \verb|\draw| command now takes optional arguments, enclosed in [...]. The argument help lines tells TikZ to color the lines gray, and the argument step=0.5 tells TikZ to divide the grid in 05 cm increments. These are examples of a \textit{style} options given to TikZ which control parameters for drawing, such as width or color. The following figures, which show the same path in different styles, should give you a sense of the possibilities.\begin{verbatim}\tikz \draw[color=blue,ultra thick,|->,dashed](0,0)--(2,0)--(2,2);\tikz \draw[color=red,thin,<->](0,0)--(2,0)--(2,2);\tikz \draw[color=teal,semithick,<-, dotted](0,0)--(2,0)--(2,2);\end{verbatim}\subsubsection{Coordinate Systems}There are two alternatives to the absolute Cartesian coordinate system we presented before.

First, polar coordinates.\begin{verbatim}\tikz \draw[color=violet,thick](0:1)--(60:1)--(120:1)--(180:1)--(240:1)--(300:1)--(0:1);\end{verbatim}

Polar coordinates are specified with the syntax \texttt{(angle:radius)}, and can be freely mixed with cartesian coordinates.

Second, relative coordinates. Suppose I wanted to draw a square 3 units above a triangle. Instead of adding 3 to every y-coordinate in the square, I can position one corner of the square, then tell TikZ to position the other corners relative to that corner.\begin{verbatim}\begin{tikzpicture}[scale=0.5]\draw (0, 0) -- (0, 1) -- (1, 0) -- (0, 0);

\draw (0, 2) -- ++(1, 0) -- ++(0, 1) -- ++(-1, 0) --++(0, -1);\end{tikzpicture}\end{verbatim}

The optional argument scale=0.5 tells TikZ to scale the figure by 50\%.\subsubsection{Curves And Colors}We can draw a curved path as follows.\begin{verbatim}\tikz \draw (0, 0) to [out=135, in=100] (1, 1);\end{verbatim}

The \texttt{out} option specifies the angle at which the curve should leave the starting point and the \texttt{in} option specifies the angle at which the curve should arrive at the end point.

In addition to the very general \texttt{in/out} syntax, TikZ provides shortcuts for common shapes and patterns. We’ve already seen one, the \texttt{grid} shape. We can draw a circle as follows.\begin{verbatim}\tikz \draw[orange] (1, 1) circle (0.5);\end{verbatim}The first point is the center, and the second number in parentheses is the radius. We can quickly draw a rectangle as follows.\begin{verbatim}\tikz \draw[brown] (0, 0) rectangle (2, 1);\end{verbatim}

Here the first point is one corner of the rectangle and the second point is the opposite corner. To color the inside of one of these shapes, use the \verb|\fill| command.\begin{verbatim}\tikz \draw[blue,fill=green] (1, 1) circle (0.5);\end{verbatim}\subsection{The \texttt{amsthm} Package}Professional mathematics publications often separate theorems, definitions, and other important information from the text, like so.\\\\\textbf{Theorem 1} (Wiles). \textit{If $n \ge 3$, the equation ${x^n} + {y^n} = {z^n}$ has no nontrivial integer solutions.}\\

Doing this in \LaTeX\ requires the amsthm package, which gives us commands to define environments for theorems, propositions, and the like. To make a theorem, you have to first tell amsthm to define a new environment. The command to use is \verb|\newtheorem|, which takes two arguments. The first is the name of the new environment, and the second is what should be displayed.For instance, placing \verb|\newtheorem{thm}{Theorem}| in the preamble allows us to make a theorem using the newly defined \texttt{theorem} environment.\begin{verbatim}\newtheorem{thm}{Theorem}...\begin{thm}Every finite $p$-grouphas nontrivial center.\end{thm}\end{verbatim}

To prevent \LaTeX\ from numbering the environment, use the \verb|\newtheorem*| command.\begin{verbatim}\newtheorem*{prop}{Proposition}...\begin{prop}Every finite $p$-grouphas nontrivial center.\end{prop}\end{verbatim}

Every environment created in this way takes an optional argument, which indicates text to be places in parentheses.\begin{verbatim}\begin{thm}[Feit-Thompson]Every groupof odd orderis solvable.\end{thm}\end{verbatim}\subsubsection{Proofs}The \texttt{amsthm} package comes with one predefined environment, the \texttt{proof} environment, which does just what you expect.\begin{verbatim}\begin{proof}A trivial exercisefor the reader.\end{proof}\end{verbatim}

If you end a proof with a displayed equation, the Halmos box \footnote{The Halmos box is the symbol $\square$.} may not go in the right position. To place it in a specific spot, use the command \verb|\qedhere|.\begin{verbatim}\begin{proof}Just observe that\[1 + 1 = 2. \qedhere\]\end{proof}\end{verbatim}\subsubsection{Theorem Styles}There are three possible styles for environment defined using \texttt{amsthm} \texttt{plain} (the default), \texttt{definition}, and \texttt{remark}. To specify a style, group \verb|\newtheorem| commands into blocks according to the style you would like them to have, then place \verb|\theoremstyle{<style>}| before each block. For instance, part of your preamble might look like\begin{verbatim}\theoremstyle{theorem}\newtheorem{theorem}{Theorem}\newtheorem{proposition}{Proposition}\newtheorem{lemma}{Lemma}

\theoremstyle{definition}\newtheorem{definition}{Definition}\newtheorem{exercise}{Exercise}

\theoremstyle{remark}\newtheorem*{remark}{Remark}\end{verbatim}

\subsection{The hyperref Package}To add \textit{document information} and \textit{links} (both internal and external) to document\begin{verbatim}\usepackage{hyperref}\hypersetup{plainpages=false, colorlinks, urlcolor=blue,pdftitle={Probability and Statistics},pdfauthor={S Zachary},pdfstartview={FitBH}}\end{verbatim}

Make \textit{external links} with the following command\begin{verbatim}\href{http://www.something}{text}\end{verbatim}This produces a link to \textit{text}.\subsection{Cite Package}\verb|\usepackage{cite}|\subsection{The amsmath Package}\begin{verbatim}\newtheorem{thm}{Theorem}...\begin{thm}[Gauss]...\end{thm}\end{verbatim}To prevent \LaTeX\ from numbering the environment \begin{verbatim}\newtheorem*{prop}{Proposition}...\begin{prop}...\end{prop}\begin{proof}... $ equation $ \qedhere % Halmos box\end{proof}\end{verbatim}\textsc{Theorem styles.}\\There are three possible styles for environment defined using \textit{amsmath} \texttt{plain (default), definition, remark}. Part of your preamble like\begin{verbatim}\theoremstyle{theorem}\newtheorem{theorem}{Theorem}\newtheorem{proposition}{Proposition}\newtheorem{lemma}{Lemma}

\theoremstyle{definition}\newtheorem{definition}{Definition}\newtheorem{exercise}{Exercise}

\theoremstyle{remark}

\newtheorem*{remark}{Remark}\end{verbatim}\subsection{Booktabs Package}There are a few ways to make a table in \LaTeX\; the one we’ll giveuses the package \texttt{booktabs}, which makes tables of high typographical quality. \footnote{Specifically, tables should have as few lines as possible. The booktabs package only hasthree lines in each table.}\begin{verbatim}\usepackage{booktabs}...\begin{center}\begin{tabular}{ l r }\topruletext & text \\\midruletext & text \\text & text \\\bottomrule\end{tabular}\end{center}\end{verbatim}

Our table consists of two environments the \texttt{center} environment, which centers the table on the page, and the \texttt{tabular} environment, which makes the table. The tabular environment takes a second argument, in our case \texttt{l r}, which tells \LaTeX\ how many columns the table will have and how to align them. The letter \texttt{l} is for left-alignment, the letter \texttt{r} is for right-alignment, and the letter \texttt{c}, whichwe did not use, is for centering. Finally, the commands \verb|\toprule|, \verb|\midrule|, and \verb|\bottomrule| tell \LaTeX\ where to place the horizontal lines separating the descriptors and the columns.

To make a table with a caption and a table number, use the \texttt{table} environment instead of the \texttt{center} environment. The \texttt{table} environment is completelyanalogous to the \texttt{figure} environment. Tables can be very complicated, and for this reason there are many \LaTeX\packages that provide special table functionality, such as the \texttt{colortbl} environment for colored tables.\subsection{Special Numbering Environments}\textsc{Equation with section numbers.} In preamble, add\begin{verbatim}\numberwithin{equation}{section}\end{verbatim}or\begin{verbatim}\numberwithin{equation}{subsection} \numberwithin{equation}{subsubsection}\end{verbatim}

If you want subsection, subsubsection numbers.\\\\\textsc{Subequation.}\begin{verbatim}\begin{subequations}...

\end{subequations}\end{verbatim}By putting a \verb|\hspace{5pt},label{grp}| command, immediately following\begin{verbatim}\subequation\end{verbatim}you can get a reference to the parent number.\subsection{Pifont Package}The \texttt{pifont package} includes a variant of the itemize command that will replace the usual \lq bullet\rq\ by a \textit{Zapf Dingbat} symbol of your choice.\begin{verbatim}\begin{dinglist}{43}\item First\item Second\end{dinglist}\end{verbatim}and a variant of the enumerate command that given an initial \textit{Zapf Dingbat} symbol will increment the symbol for each item.\begin{verbatim}\begin{dingautolist}{172}\item First\item Second\end{dingautolist}\end{verbatim}\subsection{Other packages Of Interest}Many other \LaTeX\ packages that address some aspect of mathematical formulas are available from CTAN (the Comprehensive \TeX\ Archive Network). To recommend a few examples\begin{description}\item[accents] Under accents and accents using arbitrary symbols.\item[amsthm] General theorem and proof setup.\item[bm] Bold math package, provides a more general and more robust implementation of \verb|\boldsymbol|.\item[cases] Apply a large brace to two or more equations without losing the individual equation numbers.\item[delarray] Delimiters spanning multiple rows of an array.\item[kuvio] Commutative diagrams and other diagrams.\item[xypic] Commutative diagrams and other diagrams.\item[rsfs] Ralph Smith’s Formal Script, font setup.\end{description}The \TeX\ Catalogue, \\\url{http://www.tex.ac.uk/tex-archive/help/Catalogue/catalogue.html}\\is a good place to look if you know a package’s name.

\section{Environments}\textsc{\LaTeX\ environments.} abstract, figure, quote, array, flushleft, tabbing, center, flushright, table, description, itemize, tabular, displaymath, list, theorem, enumerate, math, titlepage, eqnarray, minipage, verbatim, equation, picture, verse, quotation.

\LaTeX\ is a macro-package for \TeX\ which has many preset environments where much

of the setting up that TEX users have to do explicitly is done for you. An environmenthas the form\begin{verbatim}\begin{environment name}...\end{environment name}\end{verbatim}

The related \verb|\itshape| command doesn't take an argument. It affects all the subsequent text in the environment where it's used.\\\LaTeX\ is expandable. Many macros can be loaded in to provide added features. You can also create your own commands and environments. Commands can take arguments that modify their action\begin{itemize}\item Some commands have a *-form, a variant on the standard command thatyou get by adding a * to the command name.\item Mandatory arguments are enclosed in \{\} braces.\item Optional arguments are enclosed in [ ] brackets.\end{itemize}\subsection{The Quote Environment}This environment is contained between the two commands \begin{verbatim}\begin{quote}...\end{quote}\end{verbatim}

This environment indents the text by an amount predetermined by the document class. In the examples above, you will notice that, in addition to being indented, the font of the indented material is different. This is due to the fact that I had to force the \LaTeX\ document to print out exactly what I typed (with the backslash), rather then allowing it to \textit{interpret} the \LaTeX\ command which would actually type-set the text. This was done using yet another environment - the \textit{verbatim} environment.\subsection{The Verbatim Environment}To print out exactly what is typed, you make use of the the verbatim environment. This can be accomplished by enclosing the text between \verb|\begin{verbatim}| and \verb|\end{verbatim}|, or, within a paragraph by using the \verb|\verb| command (a shortened version of the verbatim environment structure). Any text which is set off by some delimiting characters (which may be anything other than letters, * , or a space), and which follows the \verb|\verb| command will be output just as you typed it!You should notice that within the verbatim environment, you get \textit{exactly} what you type. You control the spacing, the line breaks, etc. In this environment, the text is not automatically formatted to fit the page, it will not wrap as it automaticallydoes for a \LaTeX\ document!\begin{verbatim}\verb| texts which you want to print exactly |\end{verbatim}\subsection{Itemizing Environments}It is often useful to include itemized lists within a document, which may be numbered or simply set off by some symbol. This is accomplished using an \lq itemize\rq, or \lq enumerate\rq\ environment. These environments (and many others) can be easily inserted into your document using the menu tools within

\TeX Maker. Click on the \lq LaTeX\rq\ menu at the top of the editor window and scroll down to \lq List environment\rq.

Here you can select\begin{itemize}\item the \verb|\begin{itemize}| environment (which enters bullets), or\item the \verb|\begin{enumerate}| environment (which enters numbered items)\end{itemize}

You will notice that \TeX Maker enters both the beginning and ending environment statements, and then places the cursor between these two, following the \verb|\item| command - ready to accept your first item in the list. After entering the first item, you continue the list by entering another \verb|\item| command, followed by the next item. In enumerated list, \LaTeX\ keeps up with the correct numbering so that you don't have to worry about it. If you later go back and eliminate an item, or add another item, the numbering is automatically changed.\subsection{Abstract Environment}To create an abstract, place your text in an abstract environment, i.e., between\\\verb|\begin{abstract}| and \verb|\end{abstract}| commands. The abstract should come immediately after your \verb|\maketitle| command, but before any \verb|\tableofcontents| command.\subsection{Comment Environment}\textsc{Line Commenting.} Add \% to the head of each line.\\\textsc{Block commenting.} Use the \texttt{comment} environment\\\verb|\begin{comment} ... \end{comment}|\subsection{Tabbing}Within this environment tabs can be set by \verb|\=| and the next tab moved to by using \verb|\>|.\begin{verbatim}\begin{tabbing}text \= text \> text \> text \\text \= text \> text \> text \end{tabbing}\end{verbatim}\subsection{Special Numbering Environments}\textsc{Equations with Section Numbers.} If you want your equation numbers in the form Equation $(m.n)$, where $m$ is the section number and $n$ is the equation number you use the\begin{verbatim}\numberwithin{equation}{section}\end{verbatim}command in the preamble of your document exactly as shown here (the arguments of this command are not variables.)\\\\\textsc{Subequations.} The subequations environment provides a convenient way to number equations in a group with a subordinate numbering scheme.\begin{verbatim}\begin{subequations}...\end{subequations}\end{verbatim}causes all numbered equations within the \verb|\subequations|environment to be numbered (4.9a), (4.9b),..., if the equation preceding the environment wasnumbered (4.8). By putting a \verb|\label{grp}| command immediately following\begin{verbatim}

\begin{subequations}\end{verbatim}you can get a reference to the parent number. You can also label the individual subequations within this environment.

To enter text within the math environment, use the \verb|$\intertext{}$| command.\subsection{Displayed Quotations}Displayed quotations can be embedded in text using the \texttt{quote} and \texttt{quotation} environments\begin{verbatim}\begin{quote}...\end{quote}\end{verbatim}and\begin{verbatim}\begin{quotation}...\end{quotation}\end{verbatim}

The \texttt{quote} environment is recommended for short quotations. The whole quotation is indended in the \texttt{quote} environment, but the first lines of individual paragraphs are not further indented.

For longer quotations one may use the \texttt{quotation} environment. The whole quotation is indented, and the openings of paragraphs are then further indented in the normal fashion.\subsection{The Quote Environment}\begin{verbatim}\begin{quote}... text ... \end{quote}\end{verbatim}Or use \verb|\lq text\rq, \lq\lq text\rq\rq|\section{Bibliographies}For large documents requiring a good deal of revision, it can be difficult to coordinate references in the body of the document with the bibliography at its end. \LaTeX\ provides a mechanism for automatically linking citations with items in the bibliography. Surround the bibliography with \verb|\begin{thebibliography}{9}| and \verb|\end{thebibliography}|. For each entry in the bibliography, start with \verb|\bibitem{label}|, where \textit{label} is some mnemonic for the reference. With the bibliography in place, a citation in the body of the document is made with \verb|\cite{label}|, where label is the same as what occurs in the corresponding \verb|\bibitem{label}|. In order to keep track of new references that have been added, you will often need to run \LaTeX\ twice before previewing when using \verb|\cite|.\subsection{Bibliography Management And BIB\TeX}BibTeX is an extension to \LaTeX\ for managing references, made to be easy to use and highly convenient. Citations and references are generally bothersome to do by hand, for two reasons.\begin{enumerate}\item Everyone wants a very specific, but slightly different format for citations (e.g. MLA, Chicago).\item Citations are often numbered by order of appearance, so any time you insert a new citation, all the numbers change.

\end{enumerate}

BibTeX has two elegant solutions to these problems\begin{enumerate}\item Citation formatting is automatic.\item Citation numbering is automatic.\end{enumerate}

This is one of the best examples of the \LaTeX\ philosophy; BibTeX does all the formatting for you, so you can focus on content.There are three steps to using BibTeX creating a bibliography file, citing with the \verb|\cite| command, and typesetting for BibTeX.\subsection{Creating A Bibliography File}BibTeX requires an external bibliography. There are several external tools to create these quickly, but it’s useful to understand how they work before taking shortcuts. This takes the form of a file in the same folder as your .tex file that has the extension .bib. It’s customary to call it \texttt{references.bib} or \texttt{citations.bib}, or something along those lines. The .bib files contains the information about each thing you want to cite.

BibTeX supports many types of bibliographic entries, including \texttt{book}, (journal) \texttt{article}, (conference) \texttt{proceedings} and many more. Let’s look at a few examples\begin{verbatim}@book{rudin1964principles,title={Principles of mathematical analysis},author={Walter Rudin},volume={3},year={1964},publisher={McGraw-Hill New York}}@article{bardeen1957theory,title={Theory of superconductivity},author={Bardeen, John and Cooper, Leon N and Schrieffer, J Robert},journal={Physical Review},volume={108},number={5},pages={1175},year={1957},publisher={APS}}\end{verbatim}

Each entry starts with @ and the type of the entry. Next comes the name of the specific entry, a unique identifier used to cite that entry. For the second entry above, the name is bardeen1957theory. After that, there are several fields that give the information needed to construct the reference. For book, the required fields are title, author, publisher, year. For article, it’s also necessary to include journal and highly recommended to provide year, volume, page, so that a reader could easily find the article in question. A list of entry types and what information is required for each one is available at the \LaTeX\ wikibook. It is absolutely necessary to include a comma after every field.\subsubsection{External Bibliography Management Systems}\textsc{Google Scholar.} If you click “Cite” in Google Scholar you have the option to receive a citation for that work in several formats, one of which is

BibTeX. These days, most journals have all their articles online and have a similar “generate citation” button for each article.\\\\\textsc{JabRef.} A (free, open source) program for managing BibTeX files. JabRef Works on Windows, Macs, and Linux, and has a nice interface for adding entries. It also gives a way to search online journal databases and turn the results into bibliography entries.\\\\\textsc{BibDesk.} A tool similar to JabRef, but slightly more polished. Bibdesk only works on Macs, and is included with TeXShop.\subsection{Citing In The Text}\verb|\cite{rudin1964principles}|, \verb|\cite{bardeen1957theory}|.\begin{verbatim}\bibliographystyle{plain}\bibliography{references}\end{verbatim}

To cite a bibliographic entry, use the \verb|\cite| command with the name of that entry. The command \verb|\bibliographystyle{plain}| says how the citations should be formatted. In addition to the plain style, which sorts references by author and use square brackets with numbers, there are many other styles available, such as unsrt, which lists references in order of appearance, or alpha, which gives citations like [Rud64]. The natbib package gives many more citation formats, including apa. For MLA-style citations, try the \texttt{biblatex-mla} package.

The command \verb|\bibliography{references}| tells \LaTeX\ which .bib file to use. Make sure to place the .bib file in the same folder as the .tex file.\subsection{Running BibTeX}Since BibTeX has an external file, you need to typeset a little differently. After any changes to the BibTeX file, you must go through the following sequence\begin{enumerate}\item Typset \LaTeX\ normally.\item Typeset BibTeX. This is normally a separate button or menu option.\item Typset \LaTeX\ normally.\item Typset \LaTeX\ normally again.\end{enumerate}

For the computer-savvy, there are ways to automatically perform all four typesets in a single command. This involves writing some sort of script.\subsection{URLs And DOIs In Citations}Almost all journals are online now, so it’s usually more useful to give the DOI or a link to an article than the journal issues. To do this, load the \texttt{hyperref} and \texttt{doi} packages, and add the \texttt{url} and \texttt{doi} packages to your bibtex entries. As an example\begin{verbatim}@article{bardeen1957theory,title={Theory of superconductivity},author={Bardeen, John and Cooper, Leon N and Schrieffer, J Robert},journal={Physical Review},volume={108},number={5},pages={1175},year={1957},publisher={APS}doi = {10.1103/PhysRev.108.1175},

url = {http://link.aps.org/doi/10.1103/PhysRev.108.1175}}\end{verbatim}\section{Slide Class}The \textit{slides} class is easy to use \begin{enumerate}\item Start with \verb|\documentclass{slides}|.\item Surround the document with \verb|\begin{document}| and \verb|\end{document}| commands.\item Surround the text that you want to appear on each slide with \verb|\begin{slide}| and \verb|\end{slide}| commands.\item Preview the slides to see where best to break the material between slides.\end{enumerate}\section{Letters Class}To use the \textit{letter} class\begin{enumerate}\item Start with a \verb|\documentclass{letter}|.\item Include the commands that apply to all letters in the file.\item Begin with a \verb|\begin{document}| command.\item Include the commands for each letter.\item End with a \verb|\end{document}| command.\end{enumerate}\textsc{Letter Commands for the Preamble.} The following commands apply to each letter in the file\begin{enumerate}\item \verb|\address{youraddress}| for your return address.\item \verb|\signature{yournameandtitle}| for your printed name in the signature block.\item \verb|\date{letterdate}| if you want to fix the date on the letter; otherwise the date will default to the current date when the letter is printed.\end{enumerate}\textsc{Commands for each letter.}\begin{enumerate}\item Start with \verb|\begin{letter}|.\item On the next line, type the addressee's address in braces. Separate lines with \verb|\\'s|.\item Put your opening greeting in \verb|\opening{dearjohndoe}|.\item Put the text of your letter.\item Put your closing in \verb|\closing{sincerely}|.\item If their are carbon copies, use \verb|\cc{names}|.\item If their are enclosures, use \verb|\encl{docs}|.\item If their is a postscript, use \verb|\ps|.\item End with \verb|\end{letter}|.\end{enumerate}

\section{Report Class}To make a \textit{report}\begin{verbatim}\documentclass[12pt]{report}\usepackage{graphics,thesis,latexsym}\begin{document}\linespread{1.6} % set double line spacing

\thesistitle{}\authorname{}\degree{}\programme{}\supervisor{}\submitdate{}\coverpage\abstractpage\acknowledgementpage\dedicationpage\tableofcontents\listoffigures\listoftables...\end{document}\end{verbatim}

For \textit{one and a half} line spacing, use 1.3. For \textit{double} line spacing, use 1.6. For default, don't use \verb|\linespread|. \verb|\coverpage| is the comman, defined inside \texttt{thesis.sty}, that generates the first page of the thesis.\\\\\textsc{The command Input.} One sentence can conclude what \verb|\input| has done copy-and-paste.\begin{verbatim}\input ./introduction/introduction.tex\input ./background/background.tex\input ./conclusion/conclusion.tex\end{verbatim}

The content inside a file is copied and is then pasted on the location the \verb|\input| is used.\\\\\textsc{Typesetting the Contents.} There are two template-specific commands\\ \verb|\note{Summary}{...}| (this gives a brief overview for each chapter and is optional), \verb|\chapterend| (this produces a marker at the end of a chapter and is optional).\\ \\\textsc{Oversized Figures.} For oversized figures, we usually either \textit{scale} or \textit{rotate} it.\begin{verbatim}\includegraphics[scale=0.5]{file}\includegraphics[scale=0.5,angle=45]{file}\end{verbatim}\textsc{Oversized Table.} Add \verb|\usepackage{rotating}| at the beginning of the document. To rotate a table, use \texttt{sideways} instead of \texttt{table}. \begin{verbatim}\begin{center}\begin{sideways}\begin{tabular}{...}...\end{tabular}\end{sideways}\end{center}\end{verbatim}\textsc{Too tall table.} Use the package \texttt{longtable}. To make a long table, use the command \verb|\begin{longtable}{...}...\end{longtable}|.\\

\\\textsc{Captions.} A caption must be enclosed in either the figure environment or the table environment. Each label must be placed after a caption. Don't try to place it before the caption.

\section{Useful Links}\textsc{\LaTeX\ project.}\\\url{http://www.latex-project.org/}\\Official website - has links to documentation, information about installing \LaTeX\ on your own computer, and information about where to look for help.\\\\\textsc{The Not So Short Introduction to \LaTeX\ 2e.}\\\url{http://ctan.tug.org/tex-archive/info/lshort/english/lshort.pdf}\\A good tutorial for beginners.\\\\\textsc{\LaTeX\ Wikibook.}\\\url{http://en.wikibooks.org/wiki/LaTeX/}\\Comprehensive and clearly written, although still a work in progress. A downloadable PDF is also available.\\\\\textsc{Comparison of \TeX Editors on Wikipedia.}\\\url{http://en.wikipedia.org/wiki/Comparison\_of\_TeX\_editors}\\Information to help you to choose which \LaTeX\ editor to install on your own computer.\\\\\textsc{TeX Live.}\\\url{http://www.tug.org/texlive/}\\An easy way to get up and running with the TeX document productionsystem. Available for Unix and Windows (links to MacTeX for MacOSXusers). Includes the TeXworks editor.\\\\\textsc{Workbook Source Files.}\\\url{http://edin.ac/17EQPM1}\\Download the .tex file and other files needed to compile this workbook.\\\\\textsc{The Wikibooks \LaTeX\ page.}\\\url{en.wikibooks.org/wiki/LaTeX}\\A compendium of information about \LaTeX\ . If you want to know how to do something with \LaTeX\, this website can probably tell you how.\\\\\textsc{Detexify.}\\\url{detexify.kirelabs.org}\\The \LaTeX\ names for mathematical symbols can be hard to remember or look up because there are so many of them. Detexify lets you draw a symbol on the computer screen, then guesses which symbol you drew and tells you the \LaTeX\ command for it.\\\\\textsc{TeX Stack Exchange.}\\\url{tex.stackexchange.com}\\A question-and-answer site about \TeX, \LaTeX\, and friends. The users of the site – among them people who designed \LaTeX\ – are pros, and can answer about any question you have. Save it for the stumpers, though Stack Exchange discourages questions whose answer can be easily looked up.\\\\\textsc{The Comprehensive \TeX Archive Network (CTAN).}\\\url{ctan.org}\\Members of the \LaTeX\ community have written over 4500 packages that add extra functionality to \LaTeX\ . CTAN houses these packages and their documentation. When you have a question about a package, the documentation is often the best place to start.\\\\

\textsc{Everything.}\\\url{http:\\www.tug.org}\\Including endless documentation.\\

\chapter{My Documents}\textbf{Abstract.} This chapter include my own documents format for references. You can use its form to make your documents. Decorate it by the commands from the previous chapter. Enjoy yourself. \section{My Article Documents}The following form is my \textsc{Article} form. This form include some common commands for the beginning (title, author name, mail, website, abstract,...) and the end (bibliographies,...) of the document. The content of the document is left in three dots.\begin{verbatim}\documentclass{article}\usepackage{tabu,float,hyperref,color,amsmath,amsxtra,amssymb}\usepackage{latexsym,amscd,amsthm,amsfonts,graphicx}\numberwithin{equation}{section}\usepackage{fancyhdr}\pagestyle{fancy}\fancyhf{}\fancyhead[RE,LO]{\footnotesize \textsc \leftmark}\cfoot{\thepage}\renewcommand{\headrulewidth}{0.5pt}\setcounter{tocdepth}{3}\setcounter{secnumdepth}{3}\usepackage{imakeidx}\makeindex[columns=2, title=Alphabetical Index, options= -s index.ist]\title{\Huge Project in \LaTeX}\author{\textsc{Nguyen Quan Ba Hong}\\{\small Students at Faculty of Math and Computer Science,}\\ {\small Ho Chi Minh University of Science, Vietnam} \\{\small \texttt{email. nguyenquanbahong@gmail.com}}\\{\small \texttt{blog. \url{http://hongnguyenquanba.wordpress.com}} \footnote{Copyright \copyright\ 2016 by Nguyen Quan Ba Hong,Student at Ho Chi Minh University of Science, Vietnam.This document may be copied freely for the purposes of educationand non-commercial research. Visit my site \texttt{\url{http://hongnguyenquanba.wordpress.com}} to get more.}}}\begin{document}\maketitle\begin{abstract}...\end{abstract}\tableofcontents\cleardoublepage\phantomsection\addcontentsline{toc}{chapter}{List of Figures}\listoffigures\cleardoublepage\phantomsection

\addcontentsline{toc}{chapter}{List of Tables}\listoftables\section{Preface}\subsection{1}\newpage\printindex\newpage\begin{thebibliography}{999}\bibitem {1} \bibitem {2}\end{thebibliography}\end{document}\end{verbatim}\section{My Book Documents}The following form is my \textsc{book} form. This form include some common commands for the beginning (title, author name, mail, website,...) and the end (bibliographies,...) of the document. The content of the document is left in three dots.\begin{verbatim}\documentclass[a4paper,oneside]{book}\usepackage{tabu,float,hyperref,color,amsmath,amsxtra,amssymb}\usepackage{latexsym,amscd,amsthm,amsfonts,graphicx}\numberwithin{equation}{chapter}\usepackage{fancyhdr}\pagestyle{fancy}\fancyhf{}\fancyhead[RE,LO]{\footnotesize \textsc \leftmark}\cfoot{\thepage}\renewcommand{\headrulewidth}{0.5pt}\setcounter{tocdepth}{3}\setcounter{secnumdepth}{3}\usepackage{imakeidx}\makeindex[columns=2, title=Alphabetical Index, options= -s index.ist]\title{\Huge Project in \LaTeX}\author{\textsc{Nguyen Quan Ba Hong}\\{\small Students at Faculty of Math and Computer Science,}\\ {\small Ho Chi Minh University of Science, Vietnam} \\{\small \texttt{email. nguyenquanbahong@gmail.com}}\\{\small \texttt{blog. \url{http://hongnguyenquanba.wordpress.com}} \footnote{Copyright \copyright\ 2016 by Nguyen Quan Ba Hong,Student at Ho Chi Minh University of Science, Vietnam. This document may be copied freely for the purposes of educationand non-commercial research. Visit my site \texttt{\url{http://hongnguyenquanba.wordpress.com}}to get more.}}}\begin{document}\frontmatter\maketitle\tableofcontents\cleardoublepage\phantomsection\addcontentsline{toc}{chapter}{List of Figures}\listoffigures\cleardoublepage\phantomsection\addcontentsline{toc}{chapter}{List of Tables}

\listoftables

\chapter{Preface}

\mainmatter\part{I}\chapter{Introduction}

\appendix\chapter{Appendix}\backmatter\chapter{Last note}\newpage\printindex\newpage\begin{thebibliography}{999}\bibitem {1} \bibitem {2}\end{thebibliography}\end{document}\end{verbatim}

\begin{thebibliography}{999}\bibitem {1} Jonathan Pechta, Federico Zenith, Holger Danielsson, Thomas Braun, Michel Ludwig, Felix Mauch, \textit{The Kile Handbook}. \bibitem {2} Morag Agmon, \LaTeX\ \textit{- Advanced Topics}, June 30, 2009.\bibitem {3} Mason A. Porter, \textit{A Hitchhiker's Guide to} \LaTeX\, Georgia Institute of Technology, July, 2002.\bibitem {4} Michael Downes, \textit{Short Math Guide for} \LaTeX\, American Mathmatical Society, 2002.\bibitem {5} Dan Parker, David Schwein, \textit{Advanced} \LaTeX, Spring 2015.\bibitem {6} Lambert E. Murray, \textit{Introduction to} \LaTeX, September 19, 2012.\bibitem {7} David R. Wilkins, \textit{Getting Started with} \LaTeX, 2nd edition, 1995.\bibitem {8} Andreas Matthias, \textit{The pdfpages Packages}, 2015.\bibitem {9} Jeff Clark, \LaTeX\ \textit{Tutorial}, February 26, 2002.\bibitem {10} Tim Love, \textit{Advanced} \LaTeX, August 30, 2006.\bibitem {11} Henri P. Gavin, \textit{A brief} \LaTeX\ \textit{Tutorial}, Duke University, September 30, 2002.\bibitem {12} Stan Zachary, \textit{Advanced Use of} \LaTeX, Heriot-Watt University, 14 October 2009.\bibitem {13} Marko Boon, \textit{Including Graphics in} \LaTeX, 14th March 2005.\bibitem {14} Wong Tsz Yeung, \textit{Improving Postgraduate Learning -} \LaTeX \textit{Advanced, Thesis Preparation}, The Chinese University of Hong Kong.\bibitem {15} en.wikibooks.org, \LaTeX, June 6, 2015.\bibitem {16} Stefan Kottwitz, \LaTeX \textit{Beginner's Guide}, Packt Publisher, March 2011.\bibitem {17} George Gr\"{a}tzer, \textit{More Math Into} \LaTeX, 4th edition, Springer, 2007.\bibitem {18} Wikibooks contributors, \LaTeX, 2005.\bibitem {19} Matthias Pospiech, \LaTeX\ \textit{Thesis Template}, version 3.2.2, July 11, 2014.\bibitem {20} Tobias Oetiker, Hubert Partl, Irene Hyna, Elisabeth Schlegl, \textit{The Not So Short Introduction to} \LaTeXe, version 5.05, July 18, 2015.

\bibitem {21} George Gr\"{a}tzer, \textit{Math Into} \LaTeX, \textit{An Introduction to \LaTeX and \AmS \LaTeX}, Birkh\"{a}user, 1996.\bibitem {22} A Primer, Indian \TeX Users Group, \LaTeX\ \textit{Tutorials}, Trivandrum, IndiaSeptember 2003.\bibitem {23} Andr\'{e} Heck, \textit{Learning} \LaTeX\ \textit{by Doing}, \AmS\ TEL Institute, 2001.\bibitem {24} Academic and Research Computing, \textit{Text Formatting with} \LaTeX, \textit{A Tutorial}, April 2007.\bibitem {25} \url{http://tex.stackexchange.com/}\end{thebibliography}\end{document}