Essential L^{A}TEX ++

Jon Warbrick

with additions by David Carlisle, Michel Goossens, Sebastian Rahtz, Adrian Clark January 1994

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 How Does L^{A}TEX Work? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 A Sample L^{A}TEX File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Simple Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Document Classes and Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 Type Styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 Sectioning Commands and Tables of Contents . . . . . . . . . . . . . . . . . . . . 8 8 Producing Special Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 Titles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 Tabular Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 Cross-References and Citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 13 Mathematical Typesetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 14 What about $’s? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 15 Letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 16 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 17 A Final Reminder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 A Mathematical symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 B Horrible Mathematical Examples to Study . . . . . . . . . . . . . . . . . . . . . . 24 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

List of Tables

1 Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Binary operation symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Relation symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 Large delimiters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5 Delimiters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 6 Arrow symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 7 Miscellaneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 8 Log-like symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 9 Math mode accents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 10 Variable-sized symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 11 L^{A}TEX math constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 12 AMS miscellaneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 13 AMS Greek and Hebrew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 14 AMS delimiters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 15 AMS arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 16 AMS negated arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 17 AMS binary operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 18 AMS binary relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 19 AMS negated binary relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1 Introduction

This document is an attempt to give you all the essential information that you will need in order to use the L^{A}TEX document preparation system[1].^{1}. Only basic features are covered, and a vast amount of detail has been omitted. In a document of this size it is not possible to include everything that you might need to know, and if you intend to make extensive use of the program you should refer to a more complete reference. Attempting to produce complex documents using only the information found below will require much more work than it should, and will probably produce a less than satisfactory result.

The main reference for L^{A}TEX is The L^{A}TEX User’s guide and Reference Manual by Leslie Lamport[1]. This contains all the information that you will ever need to know about the program, and you will need access to a copy if you are to use L^{A}TEX seriously.

Both the Manual and this document avoid mentioning anything that depends on the particular computer system that you are using. This is because L^{A}TEX is available on a number of systems and they all differ in one way or another. Instead, they both refer to a local guide for their particular system.

2 How Does L^{A}TEX Work?

In order to use L^{A}TEX, you generate a file containing both the text that you wish to typeset and instructions to tell L^{A}TEX how you want it to appear. You will normally create this file using your system’s text editor. You can give the file any name you like, but it should end “.tex ” to identify the file’s contents. You then get L^{A}TEX to process the file, and it creates a new file of typesetting commands; this has the same name as your file but the “.tex ” ending is replaced by “.dvi ”. This stands for ‘Device Independent’ and, as the name implies, this file can be used to create output on a range of printing devices. Your local guide will go into more detail.

1For those readers who have some familiarity with L^{A}TEX, this document assumes the L^{A}TEX 2ε release of January 1994 or later

Rather than encourage you to dictate exactly how your document should be laid out, L^{A}TEX instructions allow you to describe its logical structure. For example, you can think of a quotation embedded within your text as an element of this logical structure: you would normally expect a quotation to be displayed in a recognizable style to set it off from the rest of the text. A human typesetter would recognize the quotation and handle it accordingly, but since L^{A}TEX is only a computer program it requires your help. There are therefore L^{A}TEX commands that allow you to identify quotations and consequently allow L^{A}TEX to typeset them correctly.

Fundamental to L^{A}TEX is the idea of a document class that determines exactly how a document will be formatted. L^{A}TEX provides standard document classes that describe how common logical structures (such as quotations) should be formatted. You may have to supplement these styles by specifying the formatting of logical structures peculiar to your document, such as mathematical formulae. You can also modify the standard document classes or even create an entirely new one, though you should know the basic principles of typographical design before creating a radically new style.

There are a number of good reasons for concentrating on the logical structure rather than on the appearance of a document. Doing so prevents you from making elementary typographical errors in the mistaken belief that they improve the æsthetics of a document—you should remember that the primary function of document design is to make documents easier to read, not prettier. It is also more flexible, since you need only alter the definition of the quotation style to change the appearance of all the quotations in a document. Most important of all, logical design encourages better writing. A visual system makes it easier to create visual effects rather than a coherent structure; logical design encourages you to concentrate on your writing and makes it harder to use formatting as a substitute for good writing.

3 A Sample L^{A}TEX File

Have a look at the example L^{A}TEX file in Figure 1. It is a slightly modified copy of the standard L^{A}TEX example file small.tex . Your local guide will tell you how you can make your own copy of this file. The line numbers down the left-hand side are not part of the file, but have been added to make it easier to refer to various portions. Also have a look at Figure 2 which shows, more or less, the result of processing this file.

3.1 Running Text

Most documents consist almost entirely of running text—words formed into sentences, which are in turn formed into paragraphs—and the example file is no exception. Describing running text poses no problems, you just type it in naturally. In the output that it produces, L^{A}TEX will fill lines and adjust the spacing between words to give tidy left and right margins. The spacing and distribution of the words in your input file will have no effect at all on the eventual output. Any number of spaces in your input file are treated as a single space by L^{A}TEX. It also regards the end of each line as a space between words (see lines 15–17). A new paragraph is indicated by a blank line in your input file, so don’t leave any blank lines unless you really wish to start a paragraph.

L^{A}TEX reserves a number of the less common keyboard characters for its own use. The ten characters

     #  $  %  &  ~  _^\  {  }

should not appear as part of your text—if they do, L^{A}TEX will get confused.

4 Essential L^{A}TEX

 1: % SMALL.TEX -- Released 5 July 1985
 2: % USE THIS FILE AS A MODEL FOR MAKING YOUR OWN LaTeX
 3: % INPUT FILE. EVERYTHING TO THE RIGHT OF A  %  IS A
 4: % REMARK TO  YOU AND IS IGNORED BY LaTeX.
 5: %
 6: % WARNING!  DO NOT TYPE ANY OF THE FOLLOWING 10 CHARACTERS
 7: % EXCEPT AS DIRECTED:         &   $   #   %   _{   }   ^~   \
 8:
 9: \documentclass[11pt]{article}% YOUR INPUT FILE MUST CONTAIN
10: \begin{document}               % THESE TWO LINES PLUS
11:                                  % THE \end COMMAND AT THE END
12:
13: \section{Simple Text}     % THIS COMMAND MAKES A SECTION TITLE.
14:
15: Words are separated by one or     more       spaces.  Paragraphs are
16:      separated by one or more blank lines.  The output is not affected
17: by adding extra spaces or extra blank lines to the input file.
18:
19:
20: Double quotes are typed like this: ``quoted text''.
21: Single quotes are typed like this: `single-quoted text'.
22:
23: Long dashes are typed as three dash characters---like this.
24:
25: Italic text is typed like this: \emph{this is italic text}.
26: Bold   text is typed like this: \textbf{this is  bold  text}.
27:
28: \subsection{A Warning or Two}         % THIS MAKES A SUBSECTION TITLE.
29:
30: If you get too much space after a mid-sentence period---abbreviations
31: like etc.\ are the common culprits)---then type a backslash followed by
32: a space after the period, as in this sentence.
33:
34: Remember, don't type the 10 special characters (such as dollar sign and
35: backslash) except as directed!  The following seven are printed by
36: typing a backslash in front of them:  \$  \&  \#  \%  \_\{  and  \}.
37: The manual tells how to make other symbols.
38:
39: \end{document}                       % THE INPUT FILE ENDS LIKE THIS

Figure 1: A Sample L^{A}TEX File

1 Simple Text

Words are separated by one or more spaces. Paragraphs are separated by one or more blank lines. The output is not affected by adding extra spaces or extra blank lines to the input file.

Double quotes are typed like this: “quoted text”. Single quotes are typed like this: ‘singlequoted text’.

Long dashes are typed as three dash characters—like this. Italic text is typed like this: this is italic text. Bold text is typed like this: this is bold text.

1.1 A Warning or Two

If you get too much space after a mid-sentence period—abbreviations like etc. are the common culprits)—then type a backslash followed by a space after the period, as in this sentence.

Remember, don’t type the 10 special characters (such as dollar sign and backslash) except as directed! The following seven are printed by typing a backslash in front of them: $ & # % { and }. The manual tells how to make other symbols.

Figure 2: The Result of Processing the Sample File

3.2 L^{A}TEX Commands

There are a number of words in the file that start with ‘\’ (see lines 9, 10 and 13). These are L^{A}TEX commands and they describe the structure of your document. There are several things that you should realize about these commands:

• All L^{A}TEX commands consist of a ‘\’ followed by one or more characters.

• L^{A}TEX commands should be typed using the correct mixture of upper- and lower-case letters. \BEGIN and \Begin are not the same as \begin.

• Some commands are placed within your text. These are used to switch things, like different typestyles, on and off. The \small command is used like this to emphasize text, normally by changing to an italic typestyle (see line 25). The command and the text are always enclosed between ‘{’ and ‘}’—the ‘{\em’ turns the effect on and and the ‘}’ turns it off. All the typeface-changing switches like this have a corresponding command with an argument — all the possibilities are shown on page 7.

• There are other commands that look like

         \command{text}

In this case, text is called the “argument” of the command. The \section command is like this (see line 13). Sometimes you have to use curly brackets ‘{}’ to enclose the argument, sometimes square brackets ‘[]’, and sometimes both. There is method behind this apparent madness, but for the time being you should be sure to copy the commands exactly as given.

• When a command’s name is made up entirely of letters, you must make sure that the end of the command is marked by something that isn’t a letter. This is usually either the opening bracket around the command’s argument, or a space. When it’s a space, that space is always ignored by L^{A}TEX. We shall see later that this can sometimes be a problem.

3.3 Overall Structure

There are some L^{A}TEX commands that must appear in every document. The actual text of the document always starts with a \begin{document} command and ends with an \end{document} command (see lines 10 and 39). Anything that comes after the \end{document} command is ignored. Everything that comes before the \begin{document} command is called the preamble. The preamble should contain only L^{A}TEX commands to describe the document’s style.

One command that must appear in the preamble is the \documentclass command (see line 9). This command specifies the overall style for the document. Our example file is a simple technical document and uses the article style, modified to print in eleven-point fonts. There are other styles that you can use, as you will discover in Section 4.

3.4 Other Things to Look At

L^{A}TEX can print both opening and closing quote characters, and can manage either of these either single or double. To do this, it uses the two quote characters from your keyboard: ` (which sometimes resembles a grave accent or back-quote) and ' (apostrophe). You type these characters once for single quote (see line 21), and twice for double quotes (see line 20). The double quote character itself " is almost never used.

L^{A}TEX can produce three different kinds of dashes. A long dash, for use as a punctuation symbol, as is typed as three dash characters in a row, like this ‘---’ (see line 23). A shorter dash, used between numbers as in ‘10–20’, is typed as two dash characters in a row, while a single dash character is used as a hyphen.

From time to time, you will need to include one or more of the L^{A}TEX special symbols in your text. Seven of them can be printed by making them into commands by proceeding them by backslash (see line 36). The remaining three symbols can be produced by more advanced commands, as can symbols that do not appear on your keyboard such as †, ‡, §, $, \begin{matrix}c \\ ◯ \end{matrix}, ♯ and ♣.

It is sometimes useful to include comments in a L^{A}TEX file, to remind you of what you have done or why you did it. Everything to the right of a %-sign is ignored by L^{A}TEX, and so it can be used to introduce a comment.

4 Document Classes and Options

There are four standard document classes available in L^{A}TEX:

article intended for short documents and articles for publication. Articles do not have chapters, and when \maketitle is used to generate a title (see Section 9), the title appears at the top of the first page rather than on a page of its own.

report intended for longer technical documents. It is similar to article, except that it contains chapters and the title appears on a page of its own.

book intended as a basis for book publication. Page layout is adjusted assuming that the output will eventually be used to print on both sides of the paper.

letter intended for producing personal letters. This style will allow you to produce all the elements of a well laid out letter: addresses, date, signature, etc..

These standard styles can be modified by a number of options. They appear in square brackets after the \documentclass command. Only one class can be used in a document but you can have more than one option, in which case their names should be separated by commas. The standard options are:

11pt prints the document using eleven-point type for the running text rather that the ten-point type normally used. Eleven-point type is about ten percent larger than ten-point.

12pt prints the document using twelve-point type for the running text rather than the ten-point

type normally used. Twelve-point type is about twenty percent larger than ten-point. twoside causes documents in the article or report styles to be formatted for printing on both

sides of the paper. This is the default for the book style. twocolumn produces two columns of text on each page. titlepage causes the \maketitle command to generate a title on a separate page for doc-

uments in the article style. A separate page is always used in both the report and book styles.

There is further option which is very useful in European countries. The a4paper option causes the output in all of the standard styles to be adjusted to fit correctly on A4 paper. (L^{A}TEX was designed in America where the standard paper is shorter and slightly wider than A4; without this option you will find that your output looks a little strange.)

5 Environments

We mentioned earlier the idea of identifying a quotation to L^{A}TEX so that it could arrange to typeset it correctly. To do this you enclose the quotation between the commands \begin{quotation} and \end{quotation}. This is an example of a L^{A}TEX construction called an environment. A number of special effects are obtained by putting text into particular environments.

5.1 Quotations

There are two environments for quotations: quote and quotation . quote is used either for a short quotation or for a sequence of short quotations separated by blank lines:

US presidents have been known for their pithy remarks:

The buck stops here. I am not a crook.

                                                      US presidents have been known for
                                                      their pithy remarks:
                                                      \begin{quote}
                                                      The buck stops here.
                                                      I am not a crook.
                                                      \end{quote}

Use the quotation environment for quotations that consist of more than one paragraph. Paragraphs in the input are separated by blank lines as usual:

Here is some advice to remember:

Environments for making quotations can be used for other things as well.

Many problems can be solved by novel applications of existing environments.

                                                      Here is some advice to remember:
                                                      \begin{quotation}
                                                      Environments for making quotations
                                                      can be used for other things as well.
                                                      Many problems can be solved by
                                                      novel applications of existing
                                                      environments.
                                                      \end{quotation}

5.2 Centering and Flushing

Text can be centred on the page by putting it within the center environment, and it will appear flush against the left or right margins if it is placed within the flushleft or flushright environments. Notice the spelling of center —unfortunately L^{A}TEX doesn’t understand the British English spelling.

Text within these environments will be formatted in the normal way; in particular, the ends of the lines that you type are regarded as spaces. To indicate a new line, you type the \\ command. For example:

one two three four five

                                                      \begin{center}
                                                      one
                                                      two
                                                      three \\
                                                      four \\
                                                      five
                                                      \end{center}

5.3 Lists

There are three environments for constructing lists. In each one, each new item is begun with an \item command. In the itemize environment, the start of each item is given a marker, while, in the enumerate environment, each item is marked by a number. These environments can be nested within each other, in which case the amount of indentation used and the marker are adjusted accordingly:

• Itemized lists are handy.

• However, don’t forget

1. The ‘item’ command.

2. The ‘end’ command.

                                                      \begin{itemize}
                                                      \item Itemized lists are handy.
                                                      \item However, don't forget
                                                        \begin{enumerate}
                                                        \item The `item' command.
                                                        \item The `end' command.
                                                        \end{enumerate}
                                                      \end{itemize}

The third list-making environment is description . In a description you specify the item labels inside square brackets after the \item command. For example:

Three animals that you should know about are:

gnat A small animal that causes no end of trouble.

gnu A large animal that causes no end of trouble.

armadillo A medium-sized animal.

                                                      Three animals that you should
                                                      know about are:
                                                      \begin{description}
                                                        \item[gnat] A small animal that causes
                                                          no end of trouble.
                                                        \item[gnu] A large animal that causes
                                                          no end of trouble.
                                                        \item[armadillo] A medium-sized animal.
                                                      \end{description}

5.4 Verbatim Output

Sometimes you will want to include text exactly as it appears on a terminal screen. For example, you might want to include part of a computer program. Not only do you want L^{A}TEX to stop playing around with the layout of your text, you also want to be able to type all the characters on your keyboard without confusing L^{A}TEX. The verbatim environment has this effect:

The section of program in question is:

{ this finds %a & %b }
for i := 1 to 27 do
 begin
 table[i] := fn(i);
 process(i)
 end;

                                                   The section of program in
                                                   question is:
                                                   \begin{verbatim}
                                                   { this finds %a & %b }
                                                   for i := 1 to 27 do
                                                      begin
                                                      table[i] := fn(i);
                                                      process(i)
                                                      end;
                                                   \end{verbatim}

6 Type Styles

We have already come across the \emph command for changing the typeface to emphasis. Here is a full list of the available typeface changing commands:

Command  or  Effect

\textrm{...}       {\rmfamily...}  Text is set in roman family
\textsf{...}       {\sffamily...}  Text is set in sans serif family
\texttt{...}       {\ttfamily...}  Text is set in typewriter family
\textmd{...}       {\mdseries...}  Text is set in medium series
\textbf{...}       {\bfseries...}  Text is set in bold series
\textup{...}       {\upshape...}  Text is set in upright shape
\textit{...}       {\itshape...}  Text is set in italic shape
\textsl{...}       {\slshape...}  Text is set in slanted shape
\textsc{...}       {\scshape...}  Text is set in small caps shape

\emph{...}         {\em...}  Text is set emphasized

\textnormal{..}    {\normalfont..}  Text is set in the document font

Remember that the declaration versions (second column) are used inside a pair of braces to limit the amount of text that they affect. It is recommended that you use the commands (first column) with a parameter of the text to typeset differently. In addition to the typeface commands, there are a set of commands that alter the size of the type. These commands are:

tiny scriptsize footnotesize small normalsize large Large

LARGE huge Huge

                                                   \tiny tiny
                                                   \scriptsize scriptsize
                                                   \footnotesize footnotesize
                                                   \small small
                                                   \normalsize normalsize
                                                   \large large
                                                   \Large Large
                                                   \LARGE LARGE
                                                   \huge huge
                                                   \Huge Huge

7 Sectioning Commands and Tables of Contents

Technical documents, like this one, are often divided into sections. Each section has a heading containing a title and a number for easy reference. L^{A}TEX has a series of commands that will allow you to identify different sorts of sections. Once you have done this, L^{A}TEX takes on the responsibility of laying out the title and of providing the numbers.

The commands that you can use are:

     \chapter       \subsection         \paragraph
     \section       \subsubsection     \subparagraph

The naming of these last two is rather unfortunate, since they do not really have anything to do with ‘paragraphs’ in the normal sense of the word: they are just lower levels of section. In most document styles, headings made with \paragraph and \subparagraph are not numbered. \chapter is not available in document style article . The commands should be used in the order given, since sections are numbered within chapters, subsections within sections, etc..

A seventh sectioning command, \part, is also available. Its use is always optional, and it is used to divide a large document into series of parts. It does not alter the numbering used for any of the other commands.

Including the command \tableofcontents in your document will cause a contents list to be included, containing information collected from the various sectioning commands. You will notice that each time your document is run through L^{A}TEX the table of contents is always made up of the headings from the previous time you ran L^{A}TEX on it. This is because L^{A}TEX collects information for the table as it processes the document, and then includes it the next time it is run. This can sometimes mean that the document has to be processed through L^{A}TEX twice to get a correct table of contents.

8 Producing Special Symbols

You can include in your L^{A}TEX document a wide range of symbols that do not appear on your keyboard. For a start, you can add an accent to any letter:

                    ò \`{o} õ \~{o}  ǒ \v{o}
                    o̧ \c{o} ó \'{o}  ō \={o}
                    ő \H{o}   o. \d{o}  ô \^{o}
                    ȯ \.{o} oo \t{oo}   ō \b{o}
                    ö \"{o} ŏ \u{o}

Several other symbols are available and are generated using the following commands:

     †  \dag  §  \S            \begin{matrix}c \\ ◯ \end{matrix} \copyright
     ‡  \ddag  ¶ \P  $  \pounds
     œ \oe  Œ \OE  æ \AE
     Æ \AE  å  \aa  Å \AA
     ø  \o  Ø \O  �  \l
     �  \E  ß  \ss  ¿  ?`
     ¡  !`  ... \ldots  L^{A}TEX \LaTeX

There is also a \today command that prints the current date. When you use these commands remember that L^{A}TEX will ignore any spaces that follow them, so that you can type ‘\pounds 20’ to get ‘$20’. However, if you type ‘\LaTeX is wonderful’ you will get ‘L^{A}TEXis wonderful’— notice the lack of space after L^{A}TEX. To overcome this problem you can follow any of these commands by a pair of empty braces and then any spaces that you wish to include, and you will see that \LaTeX{} really is wonderful! (L^{A}TEX really is wonderful!).

Finally, L^{A}TEX ‘math’ mode, normally used to layout mathematical formulae, gives access to an even larger range of symbols, including the upper and lower case greek mathematical alphabet, calligraphic letters, mathematical operators and relations, arrows and a whole lot more. This will be discussed in Section 13.

9 Titles

Most documents have a title. To title a L^{A}TEX document, you include the following commands in your document, usually just after \begin{document}.

      \title{required title}
      \author{required author}
      \date{required date}
      \maketitle

If there are several authors, then their names should be separated by \and in the \author command; they can also be separated by \\ if you want them to be centred on different lines. If the \date command is left out, then the current date will be printed.

   \title{Essential \LaTeX}
   \author{Jon Warbrick \and A N Other}
   \date{14th February 1988}
   \maketitle

Essential L^{A}TEX

J Warbrick A N Other

14th February 1988

The exact appearance of the title varies depending on the document style. In the report and book styles, the title appears on a page of its own. In the article style, it normally appears at the top of the first page; use the class option titlepage to alter this (see Section 4).

10 Tabular Material

Because L^{A}TEX will almost always convert a sequence of spaces into a single space, it can be rather difficult to lay out tables. See what happens in this example

Income Expenditure Result 20s 0d 19s 11d happiness 20s 0d 20s 1d misery

                                                      \begin{flushleft}
                                                      Income  Expenditure Result     \\
                                                      20s 0d  19s 11d      happiness \\
                                                      20s 0d  20s 1d       misery
                                                      \end{flushleft}

The tabbing environment overcomes this problem. Within it, you set tab-stops and tab to them much as you would do on a typewriter. Tab-stops are set with the \= command, and the \> command moves to the next stop. The \\ command is used to separate each line. A line that ends in \kill produces no output, and can be used to set tab-stops:

Income Expenditure Result 20s 0d 19s 11d Happiness 20s 0d 20s 1d Misery

                             \begin{tabbing}
                             Income \=Expenditure \=        \kill
                             Income \>Expenditure \>Result \\
                             20s 0d \>19s 11d \>Happiness  \\
                             20s 0d \>20s 1d  \>Misery
                             \end{tabbing}

Unlike a typewriter’s tab key, the \> command always moves to the next tab-stop in sequence, even if this means moving to the left. This can cause text to be overwritten if the gap between two tab-stops is too small.

If you have more sophisticated tabular work, you will need the tabular environment. This differs from tabbing in that you need not worry about widths of columns—L^{A}TEX will look at the whole table and see how wide columns need to be to cope with the widest entries in them. You must, however, tell L^{A}TEX how many columns there are and how you wish to lay them out. You do this by supplying a template after \begin{tabular} with a letter for each column:

l means the column will be left justified
r means the column will be right justified
c means the column will be centred

Items within a row are separated by the & character (now you know why it is treated specially), and the row is ended, as before, with \\. A simple table with three columns and two rows looks like:

Name  Age Height
Sebastian 45 195cm
Mathew  1 68cm

                                                      \begin{tabular}{lrr}
                                                      \em Name & \em Age &\em Height \\
                                                      Sebastian & 45 & 195cm          \\
                                                      Mathew     & 1 & 68cm
                                                      \end{tabular}

Various other bells and whistles can be used to make the layout nicer:

1. You can put \hline between rows to draw a line across the table.

2. Type a | in the template where you want a vertical bar down every row of the table.

3. You can specify that a column is of a fixed width with text flowing within it by using the symbol p in the template, followed by a width between { and }. The width can be given in any of ‘cm’, ‘mm’ or ‘in’ (but not ‘inches’!).

Thus, a more sophisticated table might look like this:

Group  Type  Sherds
Groups 1–9  Grey wares  218

Groups 40–44 Black (mostly ‘black burnished’) wares

116

Groups 61–67 Buff-red-orange wares

46

Groups 81–85 Colour-coated fine wares

67

Groups 91–2, 93–4 Mortaria and miscellaneous

35

Group 96  Samian  56

538

                                                      \begin{tabular}{|l|p{1in}|r|}  \hline
                                                      \em Group &\em Type &Sherds  \\\hline
                                                      Groups 1--9   &Grey wares&218\\
                                                      Groups 40--44 &Black (mostly
                                                      `black burnished')  wares&116\\
                                                      Groups 61--67 &Buff-red-orange
                                                      wares & 46                      \\
                                                      Groups 81--85 &Colour-coated
                                                      fine wares & 67                \\
                                                      Groups 91--2, 93--4&Mortaria
                                                      and miscellaneous & 35        \\
                                                      Group 96 &Samian & 56         \\\hline
                                                       &&538                          \\\hline
                                                      \end{tabular}

Note that line-endings in what you type are not important; rows end only when a \\ is found.

11 Tables and Figures

When you lay out some text and numbers in a table, it is almost always intended that the whole unit stays together, not breaking over a page. What do you do when you are at the bottom of a page with not enough space left? Similarly, what do you do when you want to leave space for a photograph to be pasted in? When you are typing the text, you do not know where L^{A}TEX will start a new page, so it is often very difficult to leave space just where you want. L^{A}TEX solves this by a system of ‘floats’, objects that will be placed in a nice position on the page, but not necessarily exactly where you put it in your file. They will often be placed at the bottom of the current page, or at the top of the next, or on a page by themselves, if they need that much space. L^{A}TEX lets you specify two sorts of float, namely tables and figures; in each of them you can specify a caption. The following shows how you would set up space for a figure in which you wanted to leave 3 inches of space, followed by a caption:

  \begin{figure}
  \vspace{3in}
  \caption{A Photograph of my Subject}
  \end{figure}

Figures and tables are automatically numbered, like sections; just as \tableofcontents lists your sections, subsections, etc. with their page numbers, \listoffigures and \listoftables will list the figures and tables with their captions.

12 Cross-References and Citations

One of the most useful things L^{A}TEX can do for you is to to automatically generate a section, page, figure, table, or equation number in a cross-reference. For example, to refer to Section 4 of this report (on document styles) and Figure 2 (the output of processing sample.tex ) in this sentence, the commands used were:

to refer to Section~\ref{sec:styles} of this report (on document
styles) and Figure~\ref{fig:result} (the output of processing

You will see that the \ref command inserted the cross-references number into the printed document. The ~ simply inserts a space while prohibiting L^{A}TEX from breaking a line.

Of course, to refer to a cross-reference, there must be an indication in the L^{A}TEX input file of the point being referred to. This is done via the \label command. The label for a section is most conveniently done immediately after the section heading, as in:

\section{Document Classes and Options}
\label{sec:styles}

and that for a figure or table in or immediately following the \caption command:

\caption{The Result of Processing the Sample File}
\label{fig:result}

Any text may be used in \label and \ref commands, though the convention impled above is a good one to follow. Page references use \label in the same way, but are referred to using

\pageref instead of \ref.

In much the same way that you can refer to other parts of your document from the L^{A}TEX file symbolically, you may cite other documents. To do this, you include the \cite command in your text, as in

The book by Lamport \cite{Lamport-LaTeX} is the principal
reference work on \LaTeX.

The argument to the \cite command, known as the citation key, is used to uniquely identify a paper, book, or other document that has been described in a bibliographic database.

Having cited other work from your document, you can generate a list of references by including the commands

\bibliographystyle{plain}
\bibliography{mybib1,mybib2}

where you want the list to appear. The \bibliographystyle command tells L^{A}TEX how you want the citations to appear, the standard ones being:

plain Citations are sorted alphabetically in the list, with each entry being assigned a number; entries in the text are indicated in square brackets.

unsrt Citations are ordered in the reference list in the order of their first appearance and assigned a number; entries in the text are indicated in square brackets.

alpha Citations are sorted alphabetically in the list but have labels like “Lam86” instead of a number; the same label appears in the text in square brackets.

abbrev Citations are similar to alpha but are more compact (e.g., by abbreviating month and journal names).

The argument of the \bibliography command is a comma-separated list of filenames, which should end in .bib (i.e., mybib1.bib and mybib2.bib in the example above). These files contain the expanded references referred to by the \cite commands. A full description of the format of these .bib files and how the citations are converted to a L^{A}TEX-compatible form are beyond the scope of this (introductory) guide; details are given in Appendix B of Lamport’s book.

13 Mathematical Typesetting

13.1 Math, Display-math and Equation

Mathematics is treated by TEX completely differently from ordinary text. There are two special modes for mathematics, known as math mode and display math mode.

Math mode commands are surrounded by \(...\) or by $...$.

Some mathematics set inline 2 × 3 = 6. Note that spaces in the input file are ignored in math mode.

                                                      Some mathematics set inline
                                                      \( 2\times 3 =   6 \).
                                                      Note that spaces in the input file
                                                      are ignored in math mode.

Display math mode commands are surrounded by \[...\].

A larger equation to be displayed on a line by itself.

f(x) = ∑_{i=0}^{∞} \frac{f^{(i)}(x)}{i!}

                                                      A larger equation to be displayed on a line by itself.
                                                      \[ f(x) = \sum_{i=0}^{\infty}\frac{f^{(i)}(x)}{i!} \]

There is a variant of display math mode, the equation environment, which automatically generates an equation number.

( \begin{matrix}1 & 2 \\ 0 & 1 \end{matrix} ) ( \begin{matrix}2 & 0 \\ 1 & 3 \end{matrix} ) = ( \begin{matrix}4 & 6 \\ 1 & 3 \end{matrix} ) (1)

                                                      \begin{equation}
                                                      \left(\begin{array}{cc}
                                                      1 & 2 \\0 & 1
                                                      \end{array}\right)
                                                      \left(\begin{array}{cc}
                                                      2 & 0\\1 & 3
                                                      \end{array}\right)
                                                      =
                                                      \left(\begin{array}{cc}
                                                      4 & 6 \\1 & 3
                                                      \end{array}\right)
                                                      \end{equation}

These short examples show the main types of commands available in math mode. A few things to note are:

1. Subscripts and superscripts are produced with _and ^, as in x_{1} = p^{2} for x_{1} = p^{2}.

2. Fractions are produced by the \frac command: \(\frac\{a + b\}\{c\}\) gives \frac{a+b}{c}.

3. Various commands give names to mathematical symbols:

     \infty \Rightarrow \surd \bigotimes generate ∞ ⇒ √ ⨂

4. Arrays are produced by the array environment. This is identical to the tabular environment described in Section 10 except that the entries are typeset in math mode instead of LR mode. Note that the array environment does not put brackets arround the array, so it can also be used for setting determinants—or even sets of equations in which you want the columns to line up.

5. The commands \left and \right produce delimiters that grow as large as needed. They can be used with a variety of symbols, e.g., \left(\left\{\left|. The full set of these delimiters is shown in tables 5 and 4 below.

13.2 Spacing

All spaces in the input file are ignored in math mode. Sometimes you may want to adjust the spacing; use one of the following commands to achieve this.

\, thin space  \: medium space
\! negative thin space \; thick space

A good example of where L^{A}TEX needs some help with spacing is

∫∫ z dxdy.. ∫ ∫ zdxdy  \(\int\!\!\int z\, dx dy .. \int\int z dx dy\)

13.3 Changing Fonts in Math Mode

The default math mode font is math italic. This should not be confused with ordinary text italic. The font for ‘ordinary’ letters can be changed with the usual commands, \emph, \textbf, etc.. Note that lower case Greek letters (\alpha, etc.) are regarded as mathematical symbols (which means that they must be typed in math mode) and are not affected by these commands.

\mathbf produces bold face roman letters. If you wish to have bold face math italic letters, and bold face Greek letters and mathematical symbols, use the \boldmath command before going into math mode. This changes the default math fonts to bold.

x = 2π ⇒ x ≃ 6.28 x = 2π ⇒ x ≃ 6.28 x = 2π ⇒ x ≃ 6.28

                                                      \( x = 2\pi \Rightarrow x \simeq 6.28 \)
                                                      \(\mathbf{x} = 2\pi \Rightarrow x \simeq 6.28 \)
                                                      {\boldmath \(x = \mathbf{2}\pi \Rightarrow x
                                                                  \simeq{\mathbf{6.28}}                \)}

There is also a calligraphic font for upper case letters; these are produced by the \mathcal command:

F  \( \mathcal{F} \)

14 What about $’s?

If you have converted to L^{A}TEX from plain or AMS-TEX, you will probably be wondering why there has been no mention of $ and $$.

In these systems math mode is surrounded by $’s and display math mode is surrounded by $$. This has certain drawbacks over the L^{A}TEX system as it is difficult for your text editor to match $’s as it is hard to tell which ones are starting math mode and which are ending it. TEX will also get confused if you miss a $ out.

The (incorrect) input

let (a,b,c)$ be a Pythagorean triple, i.e.\ three
integers such that $a^{2}+b^{2}=c^{2}$.

produces the slightly mysterious error message

! Missing $ inserted.
<inserted text>
                  $
<to be read again>
                      ^
l.56 ...triple, i.e.\ three integers such that $a^
                                                         {2}+b^{2}=c^{2}$
?

Note that it reports the wrong error and in the wrong place, the use of the ^command out of math mode. TEX has typeset ‘be a ... such that’ in math mode and exited math mode at the $ after ‘such that’. If you had made the equivalent L^{A}TEX error, L^{A}TEX has a better idea of what you indended:

let (a,b,c)\) be a Pythagorean triple, i.e.\ three
integers such that \(a^{2}+b^{2}=c^{2}\)

The error message may still be unintelligable, but at least it reports the error in the right place, you have used \) to end math mode when you were not in math mode (as you omitted the \( which should have been before the (a,b,c)).

LaTeX error.  See LaTeX manual for explanation.
                Type  H <return>  for immediate help.
! Bad math environment delimiter.
\@latexerr ...for immediate help.}\errmessage {#1}

\)...ifinner $\else \@badmath \fi \else \@badmath
                                                         \fi
l.56 let (a,b,c)\)
                      be a Pythagorean triple, i.e.\ three integers such that \...
?

The single dollar is sometimes useful for small sections of math.

Let G be a p-group  Let $G$ be a $p$-group

The double dollar is not always equivalent to \[ ... \], and so should not be used if you want your L^{A}TEX file to be compatible with different styles and options (try the fleqn class option).

14.1 Symbols

The following tables show most of the symbols available from the standard L^{A}TEX symbol fonts. Negations of the relational symbols can be made with the \not command:

G ≢ H  $G \not\equiv H$

In the appendix we have brought together a set of tables regrouping all standard L^{A}TEX symbols (tables 1 to 11. Tables 13 to 12 show supplementary AMS-TEX symbols, which are available when you specify the amssymb package.

15 Letters

Producing letters is simple with L^{A}TEX. To do this you use the document style letter. You can make any number of letters with a single input file. Your name and address, which are likely to be the same for all letters, are given once at the top of the file. Each letter is produced by a letter environment, having the name and address of the recipient as its argument. The letter itself begins with an \opening command to generate the salutation.

The letter ends with a \closing command. You can use the commands \encl and \cc to generate lists of enclosures and people to whom you are sending copies. Any text that follows the \closing must be proceeded by a \ps command. This command produces no text—you’ll have to type “P.S.” yourself—but is needed to format the additional text correctly.

An example will make this clearer:

      \documentstyle{letter}
      \begin{document}
      \address{1234 Avenue of the Armadillos \\
                Gnu York, G.Y. 56789}
      \signature{R. (Ma) Dillo \\ Director of Cuisine}
      \begin{letter}{G. Natheniel Picking \\
                       Acme Exterminators \\
                       Illinois}
      \opening{Dear Nat,}
      I'm afraid that the armadillo problem is still with us.
      I did everything ...
      ... and I hope that you can get rid of the nasty

      beasts this time.
      \closing{Best Regards,}
      \cc{Jimmy Carter\\Richard M. Nixon}
      \end{letter}
      \end{document}

16 Errors

When you create a new input file for L^{A}TEX, you will probably make mistakes. Everybody does, and it’s nothing to be worried about. As with most computer programs, there are two sorts of mistake that you can make: those that L^{A}TEX notices and those that it doesn’t. To take a rather silly example, since L^{A}TEX doesn’t understand what you are typing, it isn’t going to be worried if you mis-spell some of the words in your text; you will just have to accurately proof-read your printed output. On the other hand, if you mis-spell one of the environment names in your file then L^{A}TEX won’t know what you want it to do.

When this sort of thing happens, L^{A}TEX prints an error message on your terminal screen and then stops and waits for you to take some action. The error messages that it produces may seem user-unfriendly and not a little frightening at first. Nevertheless, if you know where to look they will probably tell you where the error is and what went wrong.

Consider what would happen if you mistyped \begin{itemize} as \begin{itemie}. When L^{A}TEX processes this instruction, it displays the following on your terminal:

      LaTeX error.  See LaTeX manual for explanation.
                      Type  H <return>  for immediate help.
      ! Environment itemie undefined.
      \@latexerr ...for immediate help.}\errmessage {#1}
                                                               \endgroup
      l.140 \begin{itemie}
      ?

After typing the ‘?’ L^{A}TEX stops and waits for you to tell it what to do.

The first two lines of the message just tell you that the error was detected by L^{A}TEX. The third line, the one that starts ‘!’ is the error indicator. It tells you what the problem is, though until you have had some experience of L^{A}TEX this may not mean a lot to you. In this case it is just telling you that it doesn’t recognise an environment called itemie . The next two lines tell you what L^{A}TEX was doing when it found the error; they are irrelevant at the moment and can be ignored. The final line is called the error locator, and is a copy of the line in your file that caused the problem. It starts with a line number to help you to find it in your file. If the error was in the middle of a line, it will be shown broken at the point where L^{A}TEX realized that there was an error. As with all computer programs, L^{A}TEX can sometimes pass the point where the real error was before discovering that something is wrong, but it doesn’t usually get very far.

At this point you could do several things. If you knew enough about L^{A}TEX you might be able to fix the problem, or you could type ‘X’ and press the return key to stop L^{A}TEX running while you go and correct the error. The best thing to do, however, is just to press the return key. This will allow L^{A}TEX to go on running as if nothing had happened. If you have made one mistake, then you have probably made several and you may as well try to find them all in one go. It’s much more efficient to do it this way than to run L^{A}TEX over and over again fixing one error at a time. Don’t worry about remembering what the errors were—a copy of all the error messages is being saved in a log file so that you can look at them afterwards. See your local guide to find out what this file is called.

If you look at the line that caused the error, it’s normally obvious what the problem was. If you can’t work out what your problem is, look at the hints below and, if they don’t help, consult Chapter 6 of Lamport’s book: it contains a list of all of the error messages that you are likely to encounter, together with some suggestions as to what may have caused them.

Some of the most common mistakes that cause errors are:

• A mis-spelt command or environment name.

• Improperly matched ‘{’ and ‘}’—remember that they should always come in pairs.

• Trying to use one of the ten special characters # $ % & _{ } ~ ^and \ as an ordinary printing symbol.

• A missing \end command.

• A missing command argument (that’s the bit enclosed in ’{’ and ‘}’). A single error can get L^{A}TEX so confused that it reports a series of spurious errors as a result. If you have an error that you understand, followed by a series that you don’t, then try correcting the first error—the rest may vanish as if by magic.

Sometimes L^{A}TEX may write a * and stop without an error message. This is normally caused by a missing \end{document} command, though other errors can cause it. If this happens type \stop and press the return key.

Finally, L^{A}TEX will sometimes print warning messages. They report problems that were not bad enough to cause L^{A}TEX to stop processing, but nevertheless may require investigation. The most common problems are ‘overfull’ and ‘underfull’ lines of text. A message like:

      Overfull \hbox (10.58649pt too wide) in paragraph at lines 172--175
      []\tenrm Mathematical for-mu-las may be dis-played. A dis-played

indicates that L^{A}TEX could not find a good place to break a line when laying out a paragraph. As a result, it was forced to let the line stick out into the right-hand margin, in this case by 10.6 points. Since a point is 1/72.27 inches, this may be rather hard to see, but it will be there nonetheless.

This particular problem happens because L^{A}TEX is rather fussy about line breaking, and it would rather generate a line that is too long than generate a paragraph that doesn’t meet its high standards. The simplest way around the problem is to enclose the entire offending paragraph between \begin{sloppypar} and \end{sloppypar} commands. This tells L^{A}TEX that you are happy for it to break its own rules while it is working on that particular bit of text.

Alternatively, messages about “Underfull \hboxes” may appear. These are lines that had to have more space inserted between words than L^{A}TEX would have liked. In general there is not much that you can do about these. Your output will look fine, even if the line looks a bit stretched. About the only thing you could do is to re-write the offending paragraph!

17 A Final Reminder

You now know enough L^{A}TEX to produce a wide range of documents. But this document has only scratched the surface of the things that L^{A}TEX can do. This entire document was itself produced with L^{A}TEX (with no sticking things in or clever use of a photocopier) and even it hasn’t used all the features that it could. From this you may get some feeling for the power that L^{A}TEX puts at your disposal.

Please remember what was said in the introduction: if you do have a complex document to produce then go and read Lamport’s book. You will be wasting your time if you rely only on what you have read here. Once you have used L^{A}TEX for some time, you might want to know how to use the many style file extensions, which have been developed to aid L^{A}TEX users to typeset their documents. This and much else (like how to use MakeIndex, for generating indices, or BibTEX, for managing your bibliographies) is covered in The L^{A}TEX Companion[3]. Finally the final word about TEX is Knuth’s TEX book[2].

And one other warning: having dabbled with L^{A}TEX your documents will never be the same again...

20 Essential L^{A}TEX

A Mathematical symbols

α \alpha  β \beta  γ \gamma  δ \delta
ϵ \epsilon ε \varepsilon  ζ \zeta  η \eta
θ \theta  ϑ \vartheta  ι \iota  κ \kappa
λ \lambda  μ \mu  ν \nu  ξ \xi
o o  π \pi  ϖ \varpi  ρ \rho
ϱ \varrho  σ \sigma  ς \varsigma τ \tau
υ \upsilon ϕ \phi  φ \varphi  χ \chi
ψ \psi  ω \omega
Γ \Gamma  Δ \Delta  Θ \Theta  Λ \Lambda
Ξ \Xi  Π \Pi  Σ \Sigma  Υ \Upsilon
Φ \Phi  Ψ \Psi  Ω \Omega

Table 1: Greek letters

± \pm  ∩ \cap  ⋄ \diamond  ⊕ \oplus
∓ \mp  ∪ \cup  △ \bigtriangleup  ⊖ \ominus
× \times  ⊎ \uplus  ▽ \bigtriangledown  ⊗ \otimes
÷ \div  ⊓ \sqcap  ◁ \triangleleft  ⊘ \oslash
∗ \ast  ⊔ \sqcup  ▷ \triangleright  ⊙ \odot
⋆ \star  ∨ \vee  ⊲ \lhd^{a}  ◯ \bigcirc
∘ \circ  ∧ \wedge  ⊳ \rhd^{a}  † \dagger
• \bullet \ \setminus ⊴ \unlhd^{a}  ‡ \ddagger
· \cdot  ≀ \wr  ⊵ \unrhd^{a}  ⨿ \amalg

a Not predefined in L^{A}TEX 2ε. Use the packages latexsym or amssymb

Table 2: Binary operation symbols

≤ \leq  ≥ \geq  ≡ \equiv  ⊧ \models  ≺ \prec
≻ \succ  ∼ \sim  ⊥ \perp  ⪯ \preceq  ⪰ \succeq
≃ \simeq  | \mid  ≪ \ll  ≫ \gg  ≍ \asymp
∥ \parallel ⊂ \subset  ⊃ \supset ≈ \approx  ▷◁ \bowtie
⊆ \subseteq ⊇ \supseteq    ≅ \cong  ⋈ \Join  ⊏ \sqsubset
⊐ \sqsupset ≠ \neq  ⌣ \smile  ⊑ \sqsubseteq  ⊒ \sqsupseteq
≐ \doteq  ⌢ \frown  ∈ \in  ∋ \ni  ∝ \propto
= =  ⊢ \vdash  ⊣ \dashv  < <  > >

Table 3: Relation symbols

  } \rmoustache    { \lmoustache    } \rgroup       { \lgroup
  | \arrowvert     ‖ \Arrowvert     | \bracevert

Table 4: Large delimiters

   ↑ \uparrow ⇑ \Uparrow ↓ \downarrow  ⇓ \Downarrow
   { \{  } \}  ↕ \updownarrow  ⇕ \Updownarrow
   ⌊ \lfloor  ⌋ \rfloor  ⌈ \lceil  ⌉ \rceil
   ⟨ \langle  ⟩ \rangle  / /  \ \backslash
   | |  ∥ \|

Table 5: Delimiters

← \leftarrow  ⟵ \longleftarrow  ↑ \uparrow
⇐ \Leftarrow  ⟸ \Longleftarrow  ⇑ \Uparrow
→ \rightarrow  ⟶ \longrightarrow  ↓ \downarrow
⇒ \Rightarrow  ⟹ \Longrightarrow  ⇓ \Downarrow
↔ \leftrightarrow  ⟷ \longleftrightarrow  ↕ \updownarrow
⇔ \Leftrightarrow  ⟺ \Longleftrightarrow  ⇕ \Updownarrow
↦ \mapsto  ⟼ \longmapsto  ↗ \nearrow
↩ \hookleftarrow  ↪ \hookrightarrow  ↘ \searrow
↼ \leftharpoonup  ⇀  \rightharpoonup  ↙ \swarrow
↽ \leftharpoondown  ⇁  \rightharpoondown  ↖ \nwarrow

Table 6: Arrow symbols

. . . \ldots  · · · \cdots       ⋮ \vdots  ... \ddots  ℵ \aleph
′  \prime  ∀ \forall  ∞ \infty  ℏ \hbar  ∅ \emptyset
∃ \exists  ∇ \nabla  √ \surd  □ \Box^{a}  △ \triangle
◇ \Diamond^{a} ı  \imath  ȷ \jmath  ℓ \ell  ¬ \neg
⊤ \top  ♭ \flat  ♮ \natural  ♯ \sharp  ℘ \wp
⊥ \bot  ♣ \clubsuit ♢ \diamondsuit  ♡ \heartsuit ♠ \spadesuit
℧ \mho^{a}  ℜ \Re  ℑ \Im  ∠ \angle  ∂ \partial

a Not predefined in L^{A}TEX 2ε. Use the packages latexsym or amssymb

Table 7: Miscellaneous symbols

   \arccos   \cos    \csc   \exp   \ker      \limsup   \min   \sinh
   \arcsin   \cosh   \deg   \gcd   \lg       \ln       \Pr    \sup
   \arctan   \cot    \det   \hom   \lim      \log      \sec   \tan
   \arg      \coth   \dim   \inf   \liminf   \max      \sin   \tanh

Table 8: Log-like symbols

â \hat{a}      á \acute{a}    ā \bar{a}   ȧ \dot{a}    ă \breve{a}
ǎ \check{a}    à \grave{a}   a⃗ \vec{a}   ä \ddot{a}   ã \tilde{a}

Table 9: Math mode accents

∑ \sum  ∏ \prod  ∐ \coprod  ∫ \int  ∮ \oint
⋂ \bigcap  ⋃ \bigcup  ⨆ \bigsqcup ⋁ \bigvee  ⋀ \bigwedge
⨀ \bigodot ⨂ \bigotimes ⨁ \bigoplus ⨄ \biguplus

Table 10: Variable-sized symbols

     ãbc  \widetilde{abc}         âbc  \widehat{abc}
     \overleftarrow{abc}  \overleftarrow\{abc\}     \overrightarrow{abc}  \overrightarrow\{abc\}
     \overline{abc}  \overline\{abc\}          \underline{abc}  \underline\{abc\}
     \overbrace{abc} \overbrace\{abc\}         \underbrace{abc} \underbrace\{abc\}
     \sqrt{abc} \sqrt\{abc\}              \sqrt[n]{abc} \sqrt[n]\{abc\}
     f′  f'                      \frac{abc}{xyz}  \frac\{abc\}\{xyz\}

Table 11: L^{A}TEX math constructs

ℏ \hbar  ℏ \hslash  △ \vartriangle
▽ \triangledown  □ \square  ♢ \lozenge
Ⓢ \circledS  ∠ \angle  ∡ \measuredangle
∄ \nexists  ℧ \mho  Ⅎ \Finv^{a}
⅁ \Game^{a}  𝕜 \Bbbk^{a}  ‵ \backprime
∅ \varnothing  ▲ \blacktriangle  ▼ \blacktriangledown
■ \blacksquare  ♦ \blacklozenge  ⋆ \bigstar
∢ \sphericalangle  ∁ \complement  ð \eth
⧸ \diagup^{a}  ⧹ \diagdown^{a}

a Not defined in style amssymb, define using the L^{A}TEX 2ε \DeclareMathSymbol command

Table 12: AMS miscellaneous symbols

  𝟋 \digamma κ \varkappa ℶ \beth ℸ \daleth ℷ \gimel

Table 13: AMS Greek and Hebrew

     ⌜ \ulcorner ⌝ \urcorner ⌞ \llcorner ⌟ \lrcorner

Table 14: AMS delimiters

−−→ \dashrightarrow  ←−− \dashleftarrow  ⇇ \leftleftarrows
⇆ \leftrightarrows  ⇚ \Lleftarrow  ↞ \twoheadleftarrow
↢ \leftarrowtail  ↫ \looparrowleft  ⇋ \leftrightharpoons
↶ \curvearrowleft  ⟲ \circlearrowleft  ↰ \Lsh
⇈ \upuparrows  ↿  \upharpoonleft  ⇃ \downharpoonleft
⊸ \multimap  ↭ \leftrightsquigarrow  ⇉ \rightrightarrows
⇄ \rightleftarrows  ⇉ \rightrightarrows  ⇄ \rightleftarrows
↠ \twoheadrightarrow  ↣ \rightarrowtail  ↬ \looparrowright
⇌ \rightleftharpoons  ↷ \curvearrowright  ⟳ \circlearrowright
↱  \Rsh  ⇊ \downdownarrows  ↾ \upharpoonright
⇂  \downharpoonright  ⇝ \rightsquigarrow

Table 15: AMS arrows

  ↚ \nleftarrow  ↛ \nrightarrow  ⇍ \nLeftarrow
  ⇏ \nRightarrow  ↮ \nleftrightarrow  ⇎ \nLeftrightarrow

Table 16: AMS negated arrows

  ∔ \dotplus  ∖ \smallsetminus  ⋒ \Cap
  ⋓ \Cup  ⊼ \barwedge  ⊻ \veebar
  ⩞ \doublebarwedge  ⊟ \boxminus  ⊠ \boxtimes
  ⊡ \boxdot  ⊞ \boxplus  ⋇ \divideontimes
  ⋉ \ltimes  ⋊ \rtimes  ⋋ \leftthreetimes
  ⋌ \rightthreetimes  ⋏ \curlywedge  ⋎ \curlyvee
  ⊝ \circleddash  ⊛ \circledast  ⊚ \circledcirc
  ▪ \centerdot  ⊺ \intercal

Table 17: AMS binary operators

≦ \leqq  ⩽ \leqslant  ⪕ \eqslantless
≲ \lesssim  ⪅ \lessapprox  ≊ \approxeq
⋖ \lessdot  ≪ \lll  ≶ \lessgtr
⋚ \lesseqgtr  ⪋ \lesseqqgtr  ≑ \doteqdot
≓ \risingdotseq  ≒ \fallingdotseq  ∽ \backsim
⋍ \backsimeq  ⫅ \subseteqq  ⋐ \Subset
⊏ \sqsubset  ≼ \preccurlyeq  ⋞ \curlyeqprec
≾ \precsim  ≾ \precapprox  ◁ \vartriangleleft
⊴ \trianglelefteq  ⊨ \vDash  ⊪ \Vvdash
⌣ \smallsmile  ⌢ \smallfrown  ≏ \bumpeq
≎ \Bumpeq  ≧ \geqq  ⩾ \geqslant
⪖ \eqslantgtr  ≳ \gtrsim  ⪆ \gtrapprox
⋗ \gtrdot  ≫ \ggg  ≷ \gtrless
⋛ \gtreqless  ⪌ \gtreqqless  ≖ \eqcirc
≗ \circeq  ≜ \triangleq  ∼ \thicksim
≈ \thickapprox  ⫆ \supseteqq  ⋑ \Supset
⊐ \sqsupset  ≽ \succcurlyeq  ⋟ \curlyeqsucc
≿ \succsim  ≿ \succapprox  ▷ \vartriangleright
⊵ \trianglerighteq  ⊩ \Vdash  ∣ \shortmid
∥ \shortparallel  ≬  \between  ⋔ \pitchfork
∝ \varpropto  ◀ \blacktriangleleft  ∴ \therefore
϶ \backepsilon  ▶ \blacktriangleright  ∵ \because

Table 18: AMS binary relations

≮ \nless  ≰ \nleq  ⩽̸ \nleqslant
≦̸ \nleqq  ⪇ \lneq  ≨ \lneqq
≨ \lvertneqq  ⋦ \lnsim  ⪉ \lnapprox
⊀ \nprec  ⪯̸ \npreceq  ⋨ \precnsim
⪹ \precnapprox  ≁ \nsim  ∤ \nshortmid
∤ \nmid  ⊬ \nvdash  ⊭ \nvDash
⋪ \ntriangleleft  ⋬ \ntrianglelefteq  ⊈ \nsubseteq
⊊ \subsetneq  ⊊ \varsubsetneq  ⫋ \subsetneqq
⫋ \varsubsetneqq  ≯ \ngtr  ≱ \ngeq
⩾̸ \ngeqslant  ≧̸ \ngeqq  ⪈ \gneq
≩ \gneqq  ≩ \gvertneqq  ⋧ \gnsim
⪊ \gnapprox  ⊁ \nsucc  ⪰̸ \nsucceq
⋩ \succnsim  ⪺ \succnapprox  ≇ \ncong
∦ \nshortparallel  ∦ \nparallel  ⊭ \nvDash
⊯ \nVDash  ⋫ \ntriangleright  ⋭ \ntrianglerighteq
⊉ \nsupseteq  ⫆̸ \nsupseteqq  ⊋ \supsetneq
⊋ \varsupsetneq  ⫌ \supsetneqq  ⫌ \varsupsetneqq

Table 19: AMS negated binary relations Essential L^{A}TEX 25

B Horrible Mathematical Examples to Study

ϕ(t) = \frac{1}{\sqrt{2π}} ∫_{0}^{t} e^{−x^{2}/2}dx (2)

\begin{equation}
  \phi(t)=\frac{1}{\sqrt{2\pi}}
  \int^t_0 e^{-x^2/2} dx
\end{equation}

∏_{j≥0} (∑_{k≥0} a_{jk}z^{k}) = ∑_{k≥0} z^{n} ( ∑_{{k_{0},k_{1},...≥0 \atop k_{0}+k_{1}+...=n}} a_{0}k_{0}a_{1k_{1}} …)(3)

\begin{equation}
  \prod_{j\geq 0}
  \left(\sum_{k\geq 0}a_{jk} z^k\right)
= \sum_{k\geq 0} z^n
  \left( \sum_{{k_0,k_1,\ldots\geq 0}
           \atop{k_0+k_1+\ldots=n}     }
         a{_0k_0}a_{1k_1}\ldots  \right)
\end{equation}

π(n) = ∑_{m=2}^{n} ⌊( ∑_{k=1}^{m−1}⌊(m/k)/⌈m/k⌉⌋)^{−1}⌋ (4)

\begin{equation}
\pi(n) = \sum_{m=2}^{n}
  \left\lfloor \left(\sum_{k=1}^{m-1}
        \lfloor(m/k)/\lceil m/k\rceil
        \rfloor \right)^{-1}
  \right\rfloor
\end{equation}

\{\underbrace{\overbrace{a, …, a}^{k a′s}, \overbrace{b, …, b}^{l b′s}}_{k+1 elements}\} (5)

\begin{equation}
\{\underbrace{%
     \overbrace{\mathstrut a,\ldots,a}^{k\ a's},
     \overbrace{\mathstrut b,\ldots,b}^{l\ b's}}
  _{k+1\ \mathrm{elements}}                      \}
\end{equation}

W^{+} \begin{matrix}↗ μ^{+} + ν_{μ} \\ → π^{+} + π^{0} \\ → κ^{+} + π^{0} \\ ↘ e^{+} + ν_{e} \end{matrix}

\begin{displaymath}
\mbox{W}^+\
\begin{array}{l}
\nearrow\raise5pt\hbox{$\mu^+ + \nu_{\mu}$}\\
\rightarrow          \pi^+ +\pi^0          \\[5pt]
\rightarrow \kappa^+ +\pi^0                \\
\searrow\lower5pt\hbox{$\mathrm{e}^+
           +\nu_{\scriptstyle\mathrm{e}}$}
\end{array}
\end{displaymath}

F (x, y) = 0 and | \begin{matrix}F′′_{xx} & F′′_{xy} & F′_{x} \\ F′′_{yx} & F′′_{yy} & F′_{y} \\ F′_{x} & F′_{y} & 0 \end{matrix} | = 0

\begin{displaymath}
{F}(x,y)=0\quad\mathrm{and}\quad
 \left|\begin{array}{ccc}
  F_{xx}'' & F_{xy}'' & F_{x}' \\
  F_{yx}'' & F_{yy}'' & F_{y}' \\
  F_{x}'   & F_{y}'   & 0
        \end{array}       \right| =0
\end{displaymath}

\frac{± | \begin{matrix}x_{1} − x_{2} & y_{1} − y_{2} & z_{1} − z_{2} \\ l_{1} & m_{1} & n_{1} \\ l_{2} & m_{2} & n_{2} \end{matrix} |}{\sqrt{| \begin{matrix}l_{1} & m_{1} \\ l_{2} & m_{2} \end{matrix} |^{2} + | \begin{matrix}m_{1} & n_{1} \\ n_{1} & l_{1} \end{matrix} |^{2} + | \begin{matrix}m_{2} & n_{2} \\ n_{2} & l_{2} \end{matrix} |^{2}}}

                                                      \begin{displaymath}
                                                      \frac{\pm
                                                      \left|\begin{array}{ccc}
                                                      x_1-x_2  & y_1-y_2 & z_1-z_2 \\
                                                      l_1       & m_1      & n_1      \\
                                                      l_2       & m_2      & n_2
                                                      \end{array}\right|}{
                                                      \sqrt{\left|\begin{array}{cc}l_1&m_1\\
                                                      l_2&m_2\end{array}\right|^2
                                                      +      \left|\begin{array}{cc}m_1&n_1\\
                                                      n_1&l_1\end{array}\right|^2
                                                      +      \left|\begin{array}{cc}m_2&n_2\\
                                                      n_2&l_2\end{array}\right|^2}}
                                                      \end{displaymath}

σ_{0}^{f}(Q, T_{3R}, β, s) = \frac{4πα^{2}}{3s} β × [\frac{Q^{2} \{\frac{3 − β^{2}}{2} \} − 2QC_{V}C′_{V}s(s − M_{Z)}^{2}}{(s − M_{Z)}^{2}^{2} + M_{Z}^{2}Γ_{Z}^{2} \{\frac{3 − β^{2}}{2} \}}

(6)

+ \frac{(C_{V}^{2} + C_{A}^{2})s^{2}}{(s − M_{Z)}^{2}^{2} + M_{Z}^{2}Γ_{Z}^{2} \{C′_{V}^{2} \{\frac{3 − β^{2}}{2} \} + C′_{A}^{2}\{β^{2}\}\}}]

\newcommand{\CA}{C_{\rm A}}      \newcommand{\CV}{C_{\rm V}}
\newcommand{\CPA}{{C'}_{\rm A}} \newcommand{\CPV}{{C'}_{\rm V}}
\newcommand{\GZ}{\Gamma^2_{\rm Z}}
\newcommand{\MZ}{M^2_{\rm Z}}   \newcommand{\MZs}{{(s-M^2_{\rm Z})}}
\newcommand{\BE}{\left\{\frac{\displaystyle 3-\beta^2}{\displaystyle 2}\right\}}
\begin{eqnarray}
\sigma^f_0(Q,T_{3R},\beta,s) & = &
       \frac{4\pi\alpha^2}{3s}\beta \times
         \left[ \frac{Q^2 \BE - 2Q \CV \CPV s \MZs}{\MZs^2 + \MZ \GZ \BE}
              \right.                                        \nonumber \\[-3mm]
                                 &   &                                  \\[-3mm]
                                 & + &
       \left.\frac{(\CV^2 + \CA^2) s^2}%
                   {\MZs^2+\MZ\GZ\left\{\CPV^2 \BE+\CPA^2 \{\beta^2\}\right\}}
         \right]                                             \nonumber
\end{eqnarray}

Bibliography

1 Leslie Lamport. L^{A}TEX—A Document Preparation System—User’s Guide and Reference Manual. Addison-Wesley, Reading, MA, USA, 1985.

2 Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986.

3 Michel Goossens, Frank Mittelbach and Alexander Samarin. The L^{A}TEX Companion Addison-Wesley, Reading, MA, USA, 1993.