[latexrefman-commits] [SCM] latexrefman updated: r641 - trunk

jimhefferon at gnu.org.ua jimhefferon at gnu.org.ua
Wed Jun 6 21:01:02 CEST 2018


Author: jimhefferon
Date: 2018-06-06 22:01:02 +0300 (Wed, 06 Jun 2018)
New Revision: 641

Modified:
   trunk/ChangeLog
   trunk/latex2e.html
   trunk/latex2e.info
   trunk/latex2e.pdf
   trunk/latex2e.texi
Log:
Math spacing, start on Page Styles

Modified: trunk/ChangeLog
===================================================================
--- trunk/ChangeLog	2018-06-05 15:29:46 UTC (rev 640)
+++ trunk/ChangeLog	2018-06-06 19:01:02 UTC (rev 641)
@@ -1,3 +1,22 @@
+2018-06-06  Jim Hefferon  <jhefferon at smcvt.edu>
+
+	* latex2e.texi (Math spacing)  Adjust wording.
+	(Page styles)  Add example, adjust wording.
+
+2018-06-06  Jim Hefferon  <jhefferon at smcvt.edu>
+
+	* latex2e.texi (Math functions)  Make the @math{...} stuff not
+	appear in the HTML.  Add comment about amsmath allowing users to
+	create their own.
+	(Math accents)  Make the @math{...} stuff not
+	appear in the HTML.
+
+2018-06-05  Jim Hefferon  <jhefferon at smcvt.edu>
+
+	* latex2e.texi (Math formulas)  Adjust wording, including a suggestion
+	that new math docs should use the AMS packages.  Add subsection to
+	symbols for Caligraphic, \boldmath, and blackboard bold.
+
 2018-06-04  Jim Hefferon  <jhefferon at smcvt.edu>
 
 	* latex2e.texi (Modes)  Include all six modes, with the vertical ones.

Modified: trunk/latex2e.html
===================================================================
--- trunk/latex2e.html	2018-06-05 15:29:46 UTC (rev 640)
+++ trunk/latex2e.html	2018-06-06 19:01:02 UTC (rev 641)
@@ -341,7 +341,12 @@
   <li><a name="toc-Math-formulas-1" href="#Math-formulas">16 Math formulas</a>
   <ul class="no-bullet">
     <li><a name="toc-Subscripts-_0026-superscripts-1" href="#Subscripts-_0026-superscripts">16.1 Subscripts & superscripts</a></li>
-    <li><a name="toc-Math-symbols-1" href="#Math-symbols">16.2 Math symbols</a></li>
+    <li><a name="toc-Math-symbols-1" href="#Math-symbols">16.2 Math symbols</a>
+    <ul class="no-bullet">
+      <li><a name="toc-Blackboard-bold-1" href="#Blackboard-bold">16.2.1 Blackboard bold</a></li>
+      <li><a name="toc-Caligraphic-1" href="#Caligraphic">16.2.2 Caligraphic</a></li>
+      <li><a name="toc-_005cboldmath-_0026-_005cunboldmath-1" href="#g_t_005cboldmath-_0026-_005cunboldmath">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></a></li>
+    </ul></li>
     <li><a name="toc-Math-functions-1" href="#Math-functions">16.3 Math functions</a></li>
     <li><a name="toc-Math-accents-1" href="#Math-accents">16.4 Math accents</a></li>
     <li><a name="toc-Spacing-in-math-mode-1" href="#Spacing-in-math-mode">16.5 Spacing in math mode</a></li>
@@ -10978,9 +10983,12 @@
 will be placed
 </p>
 <ul>
-<li> in the right margin for one-sided layout (option <code>oneside</code>, see <a href="#Document-class-options">Document class options</a>);
-</li><li> in the outside margin for two-sided layout (option <code>twoside</code>, see <a href="#Document-class-options">Document class options</a>);
-</li><li> in the nearest margin for two-column layout (option <code>twocolumn</code>, see <a href="#Document-class-options">Document class options</a>).
+<li> in the right margin for one-sided layout (option <code>oneside</code>, see
+<a href="#Document-class-options">Document class options</a>);
+</li><li> in the outside margin for two-sided layout (option <code>twoside</code>, see
+<a href="#Document-class-options">Document class options</a>);
+</li><li> in the nearest margin for two-column layout (option <code>twocolumn</code>,
+see <a href="#Document-class-options">Document class options</a>).
 </li></ul>
 
 <a name="index-_005creversemarginpar"></a>
@@ -11049,60 +11057,93 @@
 <a name="index-equation-environment-1"></a>
         
 
-<p>There are three environments that put LaTeX in math mode:
+<p>Produce mathematical text by putting LaTeX into math mode or display
+math mode (see <a href="#Modes">Modes</a>).  This example shows both.
 </p>
-<dl compact="compact">
-<dt><code>math</code></dt>
-<dd><p>For formulas that appear right in the text.
-</p></dd>
-<dt><code>displaymath</code></dt>
-<dd><p>For formulas that appear on their own line.
-</p></dd>
-<dt><code>equation</code></dt>
-<dd><p>The same as the displaymath environment except that it adds an equation
-number in the right margin.
-</p></dd>
-</dl>
-
-<a name="index-_005c_0028"></a>
-<a name="index-_005c_0029"></a>
-<a name="index-_005c_005b"></a>
-<a name="index-_005c_005d"></a>
-<p>The <code>math</code> environment can be used in both paragraph and LR mode,
-but the <code>displaymath</code> and <code>equation</code> environments can be used
-only in paragraph mode.  The <code>math</code> and <code>displaymath</code>
-environments are used so often that they have the following short forms:
-</p>
 <div class="example">
-<pre class="example">\(...\)   <span class="roman">instead of</span>   \begin{math}...\end{math}
-\[...\]   <span class="roman">instead of</span>   \begin{displaymath}...\end{displaymath}
+<pre class="example">The wave equation for \( u \) is
+\begin{displaymath}
+  \frac{\partial^2u}{\partial t^2} = c^2\nabla^2u
+\end{displaymath}
+where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 </pre></div>
 
-<a name="index-_0024"></a>
-<p>In fact, the <code>math</code> environment is so common that it has an even
-shorter form:
+<p>Math mode is for inline mathematics.  It is invoked by the starting
+<code>\(</code> and finished by the matching ending <code>\)</code>.  Display math
+mode is for displayed equations and here is invoked by the
+<code>displaymath</code> environment.  Note that any mathematical text
+whatever, including that consisting of single characters, is handled in
+math mode.
 </p>
+<a name="index-package_002c-amsmath-3"></a>
+<a name="index-amsmath-package-3"></a>
+<a name="index-package_002c-amsfonts"></a>
+<a name="index-amsfonts-package"></a>
+<a name="index-package_002c-mathtools"></a>
+<a name="index-mathtools-package"></a>
+
+<p>The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+<samp>amsmath</samp> and <samp>amssymb</samp> (also be aware of the
+<samp>mathtools</samp> package that is an extension to, and loads,
+<samp>amsmath</samp>).  New documents that will have mathematical text should
+use these packages.  Descriptions of these packages is outside the scope
+of this document; see their documentation on CTAN.
+</p>
+<p>When in math mode or display math mode, LaTeX handles many aspects of
+your input text differently than in other text modes.  For example,
+</p>
 <div class="example">
-<pre class="example">$ ... $   <span class="roman">instead of</span>   \(...\)
+<pre class="example">contrast x+y with \( x+y \).
 </pre></div>
 
-<a name="index-_005cboldmath"></a>
-<a name="index-_005cunboldmath"></a>
-<p>The <code>\boldmath</code> command changes math letters and symbols to be in
-a bold font.  It is used <em>outside</em> of math mode.  Conversely, the
-<code>\unboldmath</code> command changes math glyphs to be in a normal font;
-it too is used <em>outside</em> of math mode.
+<p>in math mode the letters are in italics and the spacing around the plus
+sign is different.
 </p>
+<p>To make inline formulas put LaTeX in math mode with either
+<code>\(<var>mathematical material</var>\)</code>, or <code>$<var>mathematical
+material</var>$</code>, or <code>\begin{math}<var>mathematical
+material\end{math}</var></code>.  The first form is preferred, and the third form
+is very rarely used.  These can be used in paragraph mode or in LR mode
+(see <a href="#Modes">Modes</a>).
+</p>
+<p>To make displayed formulas, put LaTeX into display math mode with
+either <code>\begin{displaymath}<var>mathematical
+material</var>\end{displaymath}</code>, or
+<code>\begin{equation}<var>mathematical material</var>\end{equation}</code>.
+These behave the same way except that with the <code>equation</code>
+environment, LaTeX puts a formula number alongside the formula, which
+by default has the form ‘<samp>(<var>arabic number</var>)</samp>’.  The construct
+<code>\[ <var>math</var> \]</code> is equivalent to <code>\begin{displaymath}
+<var>math</var> \end{displaymath}</code>.  These environments can only be used in
+paragraph mode (see <a href="#Modes">Modes</a>).
+</p>
 <a name="index-_005cdisplaystyle"></a>
-<p>The <code>\displaystyle</code> declaration forces the size and style of the
-formula to be that of <code>displaymath</code>, e.g., with limits above and
-below summations.  For example:
+<p>The two mathematics modes are similar, but there are some differences.
+One involves the placement of subscripts and superscripts; in display
+math mode they are further apart and in inline math mode they are closer
+together.  Sometimes you want the display math treatment to happen in
+the inline math mode.  For this, the <code>\displaystyle</code> declaration
+forces the size and style of the formula to be that of
+<code>displaymath</code>.  Thus <code>\(\displaystyle \sum_{n=0}^\infty
+x_n\)</code> will have the limits above and below the summation sign, not next
+to it.  Another example is that
 </p>
 <div class="example">
-<pre class="example">$\displaystyle \sum_{n=0}^\infty x_n $
+<pre class="example">\begin{tabular}{r|cc}
+  \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
+  Arithmetic     &\( a+(a+b)+(a+2b)+\cdots+(a+(n-1)b) \)
+                   &\( na+(n-1)n\cdot\frac{b}{2}\)  \\
+  Geometric      &\( a+ab+ab^2+\cdots+ab^{n-1} \)
+                   &\(\displaystyle a\cdot\frac{1-b^n}{1-b}\)  \\
+\end{tabular}
 </pre></div>
 
-
+<p>because it has no <code>\displaystyle</code>, the Arithmetic line’s fraction
+will be scrunched.  But, because of its <code>\displaystyle</code>, the
+Geometric line’s fraction will be easy to read, with characters the same
+size as in the rest of the line.
+</p>
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#Subscripts-_0026-superscripts" accesskey="1">Subscripts & superscripts</a>:</td><td>  </td><td align="left" valign="top">Also known as exponent or index.
 </td></tr>
@@ -11112,7 +11153,7 @@
 </td></tr>
 <tr><td align="left" valign="top">• <a href="#Math-accents" accesskey="4">Math accents</a>:</td><td>  </td><td align="left" valign="top">Accents in math.
 </td></tr>
-<tr><td align="left" valign="top">• <a href="#Spacing-in-math-mode" accesskey="5">Spacing in math mode</a>:</td><td>  </td><td align="left" valign="top">Thick, medium, thin and negative spaces.
+<tr><td align="left" valign="top">• <a href="#Spacing-in-math-mode" accesskey="5">Spacing in math mode</a>:</td><td>  </td><td align="left" valign="top">Thick, medium, thin, and negative spaces.
 </td></tr>
 <tr><td align="left" valign="top">• <a href="#Math-miscellany" accesskey="6">Math miscellany</a>:</td><td>  </td><td align="left" valign="top">Stuff that doesn’t fit anywhere else.
 </td></tr>
@@ -11134,43 +11175,79 @@
 <a name="index-_005f"></a>
 <a name="index-_005e"></a>
 
-<p>In math mode, use the caret character <code>^</code> to make the
-<var>exp</var> appear as a superscript: <code>^{<var>exp</var>}</code>.
-Similarly, in math mode, underscore <code>_{<var>exp</var>}</code> makes a
-subscript out of <var>exp</var>.
+<p>Synopsis (in math mode or display math mode):
 </p>
-<p>In this example the <code>0</code> and <code>1</code> appear as subscripts while the
-<code>2</code> is a superscript.
+<div class="example">
+<pre class="example"><var>base</var>^<var>exp</var>
+</pre></div>
+
+<p>or:
 </p>
 <div class="example">
-<pre class="example">\( (x_0+x_1)^2 \)
+<pre class="example"><var>base</var>_<var>exp</var>
 </pre></div>
 
-<p>To have more than one character in <var>exp</var> use curly braces as in
-<code>e^{-2x}</code>.
+<p>Make <var>exp</var> appear as a superscript of <var>base</var> (with the caret
+character, <code>^</code>) or a subscript (with
+underscore, <code>_</code>).
 </p>
-<p>LaTeX handles superscripts on superscripts, and all of that stuff, in
-the natural way, so expressions such as <code>e^{x^2}</code> and
-<code>x_{a_0}</code> will look right.  It also does the right thing when
-something has both a subscript and a superscript.  In this example the
-<code>0</code> appears at the bottom of the integral sign while the <code>10</code>
-appears at the top.
-</p> 
+<p>In this example the <code>0</code>’s and <code>1</code>’s are subscripts while the
+<code>2</code>’s are superscripts.
+</p>
 <div class="example">
-<pre class="example">\int_0^{10} x^2 \,dx
+<pre class="example">\( (x_0+x_1)^2 \leq (x_0)^2+(x_1)^2 \)
 </pre></div>
 
-<p>You can put a superscript or subscript before a symbol with a construct
-such as <code>{}_t K^2</code> in math mode (the initial <code>{}</code> prevents
-the prefixed subscript from being attached to any prior symbols in the
-expression).
+<p>To have the subscript or superscript contain more than one character,
+surround the expression with curly braces, as in <code>e^{-2x}</code>.
+This example’s fourth line shows curly braces used to group an expression
+for the exponent.
 </p>
-<p>Outside of math mode, a construct like <code>A
-test$_\textnormal{subscript}$</code> will produce a subscript typeset in
-text mode, not math mode.  Note that there are packages specialized for
-writing Chemical formulas such as <samp>mhchem</samp>.
+<div class="example">
+<pre class="example">\begin{displaymath}
+  (3^3)^3=27^3=19\,683
+  \qquad
+  3^{(3^3)}=3^{27}=7\,625\,597\,484\,987
+\end{displaymath}
+</pre></div>
+
+<p>LaTeX knows how to handle a superscript on a superscript, or a
+subscript on a subscript, or supers on subs, or subs on supers.  So,
+expressions such as <code>e^{x^2}</code> and <code>x_{i_0}</code> give correct
+output.  Note the use in those expressions of curly braces to give the
+<var>base</var> a determined <var>exp</var>.  If you enter <code>\(3^3^3\)</code> then
+you get ‘<samp>Double superscript</samp>’.
 </p>
+<p>LaTeX does the right thing when something has both a subscript and a
+superscript.  In this example the integral has both.  They come out in
+the correct place without any author intervention.
+</p>
+<div class="example">
+<pre class="example">\begin{displaymath}
+  \int_{x=a}^b f'(x)\,dx = f(b)-f(a)
+\end{displaymath}
+</pre></div>
 
+<p>Note the parentheses around <code>x=a</code> to make the entire
+expression a subscript.
+</p>
+<p>To put a superscript or subscript before a symbol, use a construct like
+<code>{}_t K^2</code>.  The empty curly braces <code>{}</code> give the
+subscript something to attach to and keeps it from accidentally
+attaching to a prior symbols.
+</p>
+<p>Using the subscript or superscript command outside of math mode or
+display math mode, as in <code>the expression x^2</code>, will get you
+the error ‘<samp>Missing $ inserted</samp>’.
+</p>
+<a name="index-package_002c-mhchem"></a>
+<a name="index-mhchem-package"></a>
+
+<p>A common reason to want subscripts outside of a mathematics mode is to
+typeset chemical formulas.  There are packages for that such as
+<samp>mhchem</samp>; see CTAN.
+</p>
+
 <hr>
 <a name="Math-symbols"></a>
 <div class="header">
@@ -11187,13 +11264,21 @@
 <p>LaTeX provides almost any mathematical symbol you’re likely to need.
 For example, if you include <code>$\pi$</code> in your source, you will get
 the pi symbol &#x03C0;.
-</p> 
-<p>Below is a list of commonly-available symbols.  It is by no means an
-exhaustive list.  Each symbol here is described with a short phrase, and
-its symbol class (which determines the spacing around it) is given in
-parenthesis.  Unless said otherwise, the commands for these symbols can
-be used only in math mode.
 </p>
+<a name="index-package_002c-symbols"></a>
+<a name="index-symbols-package"></a>
+
+<p>Virtually any technical symbol anyone has ever used is available for
+use in LaTeX.  See the <samp>Comprehensive LaTeX Symbol List</samp> at
+<a href="https://ctan.org/tex-archive/info/symbols/comprehensive/">https://ctan.org/tex-archive/info/symbols/comprehensive/</a>.  Some
+of these require the use of external packages.
+</p>
+<p>Below is a list of commonly-used symbols that come standard with
+LaTeX.  It is by no means an exhaustive list.  Each symbol here is
+described with a short phrase, and its symbol class (which determines
+the spacing around it) is given in parenthesis.  Unless said otherwise,
+the commands for these symbols can be used only in math mode.
+</p>
 <p>To redefine a command so that it can be used whatever the current mode,
 see <a href="#g_t_005censuremath">\ensuremath</a>.
 </p>
@@ -12695,8 +12780,156 @@
 </dd>
 </dl>
 
+<table class="menu" border="0" cellspacing="0">
+<tr><td align="left" valign="top">• <a href="#Blackboard-bold" accesskey="1">Blackboard bold</a>:</td><td>  </td><td align="left" valign="top">Doublestruck characters.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#Caligraphic" accesskey="2">Caligraphic</a>:</td><td>  </td><td align="left" valign="top">Cursive characters.
+</td></tr>
+<tr><td align="left" valign="top">• <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="3">\boldmath & \unboldmath</a>:</td><td>  </td><td align="left" valign="top">Symbols in boldface.
+</td></tr>
+</table>
 
+
 <hr>
+<a name="Blackboard-bold"></a>
+<div class="header">
+<p>
+Next: <a href="#Caligraphic" accesskey="n" rel="next">Caligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="Blackboard-bold-1"></a>
+<h4 class="subsection">16.2.1 Blackboard bold</h4>
+
+<a name="index-blackboard-bold"></a>
+<a name="index-doublestruck"></a>
+
+<p>Synopsis:
+</p>
+<div class="example">
+<pre class="example">\usepackage{amssymb}   % in preamble
+  ... 
+\mathbb{<var>uppercase-letter</var>}
+</pre></div>
+
+<p>Provide blackboard bold symbols, sometimes also known as doublestruck
+letters, used to denote number sets such as the natural numbers, the
+integers, etc.
+</p>
+<p>Here 
+</p>
+<div class="example">
+<pre class="example">\( \forall n \in \mathbb{N}, n^2 \geq 0 \)
+</pre></div>
+
+<p>the <code>\mathbb{N}</code> gives blackboard bold symbol &#x2115;
+representing the natural numbers.
+</p>
+<p>If you use other than an upper case letter then you do not get an error
+but you get strange results, including unexpected characters.
+</p>
+<p>There are packages that give access to symbols other than just the
+capital letters; look on CTAN.
+</p>
+
+<hr>
+<a name="Caligraphic"></a>
+<div class="header">
+<p>
+Next: <a href="#g_t_005cboldmath-_0026-_005cunboldmath" accesskey="n" rel="next">\boldmath & \unboldmath</a>, Previous: <a href="#Blackboard-bold" accesskey="p" rel="prev">Blackboard bold</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="Caligraphic-1"></a>
+<h4 class="subsection">16.2.2 Caligraphic</h4>
+
+<a name="index-caligraphic"></a>
+
+<p>Synopsis:
+</p>
+<div class="example">
+<pre class="example">\mathcal{<var>uppercase-letters</var>}
+</pre></div>
+
+<p>Use a script-like font.
+</p>
+<p>In this example the graph identifier is output in a cursive font.
+</p>
+<div class="example">
+<pre class="example">Let the graph be \( \mathcal{G} \).
+</pre></div>
+
+<p>If you use something other than an upper case letter then you do not get
+an error.  Instead you get unexpected output.  For instance,
+<code>\mathcal{g}</code> outputs a close curly brace symbol, while
+<code>\mathcal{+}</code> outputs a plus sign.  
+</p>
+
+<hr>
+<a name="g_t_005cboldmath-_0026-_005cunboldmath"></a>
+<div class="header">
+<p>
+Previous: <a href="#Caligraphic" accesskey="p" rel="prev">Caligraphic</a>, Up: <a href="#Math-symbols" accesskey="u" rel="up">Math symbols</a>   [<a href="#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="#Concept-Index" title="Index" rel="index">Index</a>]</p>
+</div>
+<a name="g_t_005cboldmath-_0026-_005cunboldmath-1"></a>
+<h4 class="subsection">16.2.3 <code>\boldmath</code> & <code>\unboldmath</code></h4>
+
+<a name="index-boldface-mathematics"></a>
+<a name="index-symbols_002c-boldface"></a>
+<a name="index-_005cboldmath"></a>
+<a name="index-_005cunboldmath"></a>
+
+<p>Synopsis (used in paragraph mode or LR mode):
+</p>
+<div class="example">
+<pre class="example">\boldmath \( <var>math</var> \)
+</pre></div>
+
+<p>or
+</p>
+<div class="example">
+<pre class="example">\unboldmath \( <var>math</var> \)
+</pre></div>
+
+
+<a name="index-_005cboldmath-1"></a>
+<a name="index-_005cunboldmath-1"></a>
+<p>Declarations to change the letters and symbols in <var>math</var> to be in a
+bold font, or to countermand that and bring back the unbolded default.
+They must be used when not in math mode or display math mode
+(see <a href="#Modes">Modes</a>).  Both commands are fragile (see <a href="#g_t_005cprotect">\protect</a>).
+</p>
+<p>In this example each <code>\boldmath</code> command takes place inside an
+<code>\mbox</code>,
+</p>
+<div class="example">
+<pre class="example">we have $\mbox{\boldmath \( v \)} = 5\cdot\mbox{\boldmath \( u \)$}$
+</pre></div>
+
+<p>which means <code>\boldmath</code> is only called in a text mode,
+here LR mode, and explains why LaTeX must switch to math mode to set
+<code>v</code> and <code>u</code>.
+</p>
+<p>If you use either command inside math mode, as with <code>Trouble: \(
+\boldmath x \)</code>, then you get something like ‘<samp>LaTeX Font Warning:
+Command \boldmath invalid in math mode on input line 11</samp>’ and ‘<samp>LaTeX
+Font Warning: Command \mathversion invalid in math mode on input line
+11</samp>’.
+</p>
+<a name="index-package_002c-bm"></a>
+<a name="index-bm-package"></a>
+
+<p>There are many issues with <code>\boldmath</code>.  New documents should use
+the <samp>bm</samp> package provided by the LaTeX Project team.  A complete
+description is outside the scope of this document (see the full
+documentation on CTAN) but even this small example
+</p>
+<div class="example">
+<pre class="example">\usepackage{bm}   % in preamble
+...
+we have $\bm{v} = 5\cdot\bm{u}$
+</pre></div>
+
+<p>strongly suggests that it is an improvement over <code>\boldmath</code>.
+</p>
+
+<hr>
 <a name="Math-functions"></a>
 <div class="header">
 <p>
@@ -12715,209 +12948,219 @@
 <dt><code>\arccos</code>
 <a name="index-_005carccos"></a>
 </dt>
-<dd><p><em>\arccos</em>
+<dd><p>Inverse cosine
 </p>
 </dd>
 <dt><code>\arcsin</code>
 <a name="index-_005carcsin"></a>
 </dt>
-<dd><p><em>\arcsin</em>
+<dd><p>Inverse sine
 </p>
 </dd>
 <dt><code>\arctan</code>
 <a name="index-_005carctan"></a>
 </dt>
-<dd><p><em>\arctan</em>
+<dd><p>Inverse tangent
 </p>
 </dd>
 <dt><code>\arg</code>
 <a name="index-_005carg"></a>
 </dt>
-<dd><p><em>\arg</em>
+<dd><p>Angle between the real axis and a point in the complex plane
 </p>
 </dd>
 <dt><code>\bmod</code>
 <a name="index-_005cbmod"></a>
 </dt>
-<dd><p>Binary modulo operator (<em>x \bmod y</em>)
+<dd><p>Binary modulo operator, used as in <code>\( 5\bmod 3=2 \)</code>
 </p>
 </dd>
 <dt><code>\cos</code>
 <a name="index-_005ccos"></a>
 </dt>
-<dd><p><em>\cos</em>
+<dd><p>Cosine
 </p>
 </dd>
 <dt><code>\cosh</code>
 <a name="index-_005ccosh"></a>
 </dt>
-<dd><p><em>\cosh</em>
+<dd><p>Hyperbolic cosine
 </p>
 </dd>
 <dt><code>\cot</code>
 <a name="index-_005ccot"></a>
 </dt>
-<dd><p><em>\cot</em>
+<dd><p>Cotangent
 </p>
 </dd>
 <dt><code>\coth</code>
 <a name="index-_005ccoth"></a>
 </dt>
-<dd><p><em>\coth</em>
+<dd><p>Hyperbolic cotangent
 </p>
 </dd>
 <dt><code>\csc</code>
 <a name="index-_005ccsc"></a>
 </dt>
-<dd><p><em>\csc</em>
+<dd><p>Cosecant
 </p>
 </dd>
 <dt><code>\deg</code>
 <a name="index-_005cdeg"></a>
 </dt>
-<dd><p><em>\deg</em>
+<dd><p>Degrees
 </p>
 </dd>
 <dt><code>\det</code>
 <a name="index-_005cdet"></a>
 </dt>
-<dd><p><em>\det</em>
+<dd><p>Determinant
 </p>
 </dd>
 <dt><code>\dim</code>
 <a name="index-_005cdim"></a>
 </dt>
-<dd><p><em>\dim</em>
+<dd><p>Dimension
 </p>
 </dd>
 <dt><code>\exp</code>
 <a name="index-_005cexp"></a>
 </dt>
-<dd><p><em>\exp</em>
+<dd><p>Exponential
 </p>
 </dd>
 <dt><code>\gcd</code>
 <a name="index-_005cgcd"></a>
 </dt>
-<dd><p><em>\gcd</em>
+<dd><p>Greatest common divisor
 </p>
 </dd>
 <dt><code>\hom</code>
 <a name="index-_005chom"></a>
 </dt>
-<dd><p><em>\hom</em>
+<dd><p>Homomorphisms
 </p>
 </dd>
 <dt><code>\inf</code>
 <a name="index-_005cinf"></a>
 </dt>
-<dd><p><em>\inf</em>
+<dd><p>Infinum
 </p>
 </dd>
 <dt><code>\ker</code>
 <a name="index-_005cker"></a>
 </dt>
-<dd><p><em>\ker</em>
+<dd><p>Kernel
 </p>
 </dd>
 <dt><code>\lg</code>
 <a name="index-_005clg"></a>
 </dt>
-<dd><p><em>\lg</em>
+<dd><p>Base 2 logarithm
 </p>
 </dd>
 <dt><code>\lim</code>
 <a name="index-_005clim"></a>
 </dt>
-<dd><p><em>\lim</em>
+<dd><p>Limit
 </p>
 </dd>
 <dt><code>\liminf</code>
 <a name="index-_005climinf"></a>
 </dt>
-<dd><p><em>\liminf</em>
+<dd><p>Limit inferior
 </p>
 </dd>
 <dt><code>\limsup</code>
 <a name="index-_005climsup"></a>
 </dt>
-<dd><p><em>\limsup</em>
+<dd><p>Limit superior
 </p>
 </dd>
 <dt><code>\ln</code>
 <a name="index-_005cln"></a>
 </dt>
-<dd><p><em>\ln</em>
+<dd><p>Natural logarithm
 </p>
 </dd>
 <dt><code>\log</code>
 <a name="index-_005clog"></a>
 </dt>
-<dd><p><em>\log</em>
+<dd><p>Logarithm
 </p>
 </dd>
 <dt><code>\max</code>
 <a name="index-_005cmax"></a>
 </dt>
-<dd><p><em>\max</em>
+<dd><p>Maximum
 </p>
 </dd>
 <dt><code>\min</code>
 <a name="index-_005cmin"></a>
 </dt>
-<dd><p><em>\min</em>
+<dd><p>Minimum
 </p>
 </dd>
 <dt><code>\pmod</code>
 <a name="index-_005cpmod"></a>
 </dt>
-<dd><p>parenthesized modulus, as in (<em>\pmod 2^n - 1</em>)
+<dd><p>Parenthesized modulus, as used in <code>\( 5\equiv 2\pmod 3 \)</code>
 </p>
 </dd>
 <dt><code>\Pr</code>
 <a name="index-_005cPr"></a>
 </dt>
-<dd><p><em>\Pr</em>
+<dd><p>Probability
 </p>
 </dd>
 <dt><code>\sec</code>
 <a name="index-_005csec"></a>
 </dt>
-<dd><p><em>\sec</em>
+<dd><p>Secant
 </p>
 </dd>
 <dt><code>\sin</code>
 <a name="index-_005csin"></a>
 </dt>
-<dd><p><em>\sin</em>
+<dd><p>Sine
 </p>
 </dd>
 <dt><code>\sinh</code>
 <a name="index-_005csinh"></a>
 </dt>
-<dd><p><em>\sinh</em>
+<dd><p>Hyperbolic sine
 </p>
 </dd>
 <dt><code>\sup</code>
 <a name="index-_005csup"></a>
 </dt>
-<dd><p><em>\sup</em>
+<dd><p>sup
 </p>
 </dd>
 <dt><code>\tan</code>
 <a name="index-_005ctan"></a>
 </dt>
-<dd><p><em>\tan</em>
+<dd><p>Tangent
 </p>
 </dd>
 <dt><code>\tanh</code>
 <a name="index-_005ctanh"></a>
 </dt>
-<dd><p><em>\tanh</em>
+<dd><p>Hyperbolic tangent
 </p>
 </dd>
 </dl>
 
+<a name="index-package_002c-amsmath-4"></a>
+<a name="index-amsmath-package-4"></a>
+<p>The <samp>amsmath</samp> package adds improvements on some
+of these, and also allows you to define your own.  See the full
+documentation on CTAN, but
+<code>\DeclareMathOperator{\identity}{id}</code> creates an operator like
+the ones above but printed as ‘<samp>id</samp>’.  The starred form
+<code>\DeclareMathOperator*{\op}{op}</code> sets any limits above and
+below, as is traditional with <code>\lim</code>, <code>\sup</code>, or <code>\max</code>.
+</p>
 
 <hr>
 <a name="Math-accents"></a>
@@ -12940,7 +13183,7 @@
 <a name="index-_005cacute"></a>
 </dt>
 <dd><a name="index-acute-accent_002c-math"></a>
-<p>Math acute accent: <em>\acute{x}</em>.
+<p>Math acute accent
 </p>
 </dd>
 <dt><code>\bar</code>
@@ -12948,14 +13191,14 @@
 </dt>
 <dd><a name="index-bar_002dover-accent_002c-math"></a>
 <a name="index-macron-accent_002c-math"></a>
-<p>Math bar-over accent: <em>\bar{x}</em>.
+<p>Math bar-over accent
 </p>
 </dd>
 <dt><code>\breve</code>
 <a name="index-_005cbreve"></a>
 </dt>
 <dd><a name="index-breve-accent_002c-math"></a>
-<p>Math breve accent: <em>\breve{x}</em>.
+<p>Math breve accent
 </p>
 </dd>
 <dt><code>\check</code>
@@ -12963,14 +13206,14 @@
 </dt>
 <dd><a name="index-check-accent_002c-math"></a>
 <a name="index-hacek-accent_002c-math"></a>
-<p>Math háček (check) accent: <em>\check{x}</em>.
+<p>Math háček (check) accent
 </p>
 </dd>
 <dt><code>\ddot</code>
 <a name="index-_005cddot"></a>
 </dt>
 <dd><a name="index-double-dot-accent_002c-math"></a>
-<p>Math dieresis accent: <em>\ddot{x}</em>.
+<p>Math dieresis accent
 </p>
 </dd>
 <dt><code>\dot</code>
@@ -12978,14 +13221,14 @@
 </dt>
 <dd><a name="index-overdot-accent_002c-math"></a>
 <a name="index-dot-over-accent_002c-math"></a>
-<p>Math dot accent: <em>\dot{x}</em>.
+<p>Math dot accent
 </p>
 </dd>
 <dt><code>\grave</code>
 <a name="index-_005cgrave"></a>
 </dt>
 <dd><a name="index-grave-accent_002c-math"></a>
-<p>Math grave accent: <em>\grave{x}</em>.
+<p>Math grave accent
 </p>
 </dd>
 <dt><code>\hat</code>
@@ -12993,55 +13236,55 @@
 </dt>
 <dd><a name="index-hat-accent_002c-math"></a>
 <a name="index-circumflex-accent_002c-math"></a>
-<p>Math hat (circumflex) accent: <em>\hat{x}</em>.
+<p>Math hat (circumflex) accent
 </p>
 </dd>
 <dt><code>\imath</code>
 <a name="index-_005cimath"></a>
 </dt>
 <dd><a name="index-dotless-i_002c-math"></a>
-<p>Math dotless i.
+<p>Math dotless i
 </p>
 </dd>
 <dt><code>\jmath</code>
 <a name="index-_005cjmath"></a>
 </dt>
 <dd><a name="index-dotless-j_002c-math"></a>
-<p>Math dotless j.
+<p>Math dotless j
 </p>
 </dd>
 <dt><code>\mathring</code>
 <a name="index-_005cmathring"></a>
 </dt>
 <dd><a name="index-ring-accent_002c-math"></a>
-<p>Math ring accent: x*.  </p>
+<p>Math ring accent  </p>
 </dd>
 <dt><code>\tilde</code>
 <a name="index-_005ctilde"></a>
 </dt>
 <dd><a name="index-tilde-accent_002c-math"></a>
-<p>Math tilde accent: <em>\tilde{x}</em>.
+<p>Math tilde accent
 </p>
 </dd>
 <dt><code>\vec</code>
 <a name="index-_005cvec"></a>
 </dt>
 <dd><a name="index-vector-symbol_002c-math"></a>
-<p>Math vector symbol: <em>\vec{x}</em>.
+<p>Math vector symbol
 </p>
 </dd>
 <dt><code>\widehat</code>
 <a name="index-_005cwidehat"></a>
 </dt>
 <dd><a name="index-wide-hat-accent_002c-math"></a>
-<p>Math wide hat accent: <em>\widehat{x+y}</em>.
+<p>Math wide hat accent
 </p>
 </dd>
 <dt><code>\widetilde</code>
 <a name="index-_005cwidetilde"></a>
 </dt>
 <dd><a name="index-wide-tilde-accent_002c-math"></a>
-<p>Math wide tilde accent: <em>\widetilde{x+y}</em>.
+<p>Math wide tilde accent
 </p>
 </dd>
 </dl>
@@ -13059,21 +13302,29 @@
 <a name="index-spacing-within-math-mode"></a>
 <a name="index-math-mode_002c-spacing"></a>
 
-<p>In a <code>math</code> environment, LaTeX ignores the spaces that you use
-in the source, and instead puts in the spacing according to the normal
-rules for mathematics texts.  
+<p>When typesetting mathematics, LaTeX puts in spacing according to the
+normal rules for mathematics texts.  If you enter <code>y=m x</code> then
+LaTeX ignores the space and in the output the m is next to the x.
 </p>
-<p>Many math mode spacing definitions are expressed in terms of the math unit
-<em>mu</em> given by 1 em = 18 mu, where the em is taken from the current
-math symbols family (see <a href="#Units-of-length">Units of length</a>).
-LaTeX provides the following commands for use in math mode:
+<p>But LaTeX’s rules sometimes need tweaking.  For example, in an
+integral the tradition is to put a small extra space between the
+<code>f(x)</code> and the <code>dx</code>.
 </p>
+<div class="example">
+<pre class="example">\int_0^1 f(x)\,dx
+</pre></div>
+
+<p>LaTeX provides the commands that follow for use in math mode.  Many
+of these spacing definitions are expressed in terms of the math unit
+<em>mu</em>.  It is defined as 1/18 em, where the em is taken from the
+current math symbols family (see <a href="#Units-of-length">Units of length</a>).
+</p>
 <dl compact="compact">
 <dt><code>\;</code></dt>
 <dd><a name="index-_005c_003b"></a>
 <a name="index-_005cthickspace"></a>
-<p>Normally <code>5.0mu plus 5.0mu</code>.  The longer name is
-<code>\thickspace</code>.  Math mode only.
+<p>Synonym: <code>\thickspace</code>.  Normally <code>5.0mu plus 5.0mu</code>.  Math
+mode only.
 </p>
 </dd>
 <dt><code>\:</code></dt>
@@ -13081,15 +13332,16 @@
 <dd><a name="index-_005c_003a"></a>
 <a name="index-_005c_003e-1"></a>
 <a name="index-_005cmedspace"></a>
-<p>Normally <code>4.0mu plus 2.0mu minus 4.0mu</code>.  The longer name is
-<code>\medspace</code>.  Math mode only.
+<p>Synonym: <code>\medspace</code>.  Normally <code>4.0mu plus 2.0mu minus 4.0mu</code>.
+Math mode only.
 </p>
 </dd>
 <dt><code>\,</code></dt>
 <dd><a name="index-_005c_002c"></a>
 <a name="index-_005cthinspace"></a>
-<p>Normally <code>3mu</code>.  The longer name is <code>\thinspace</code>.  This can
-be used in both math mode and text mode. See <a href="#g_t_005cthinspace">\thinspace</a>.
+<p>Synonym: <code>\thinspace</code> (see <a href="#g_t_005cthinspace">\thinspace</a>).
+Normally <code>3mu</code>.
+Can be used in both math mode and text mode. 
 </p>
 </dd>
 <dt><code>\!</code></dt>
@@ -13113,14 +13365,7 @@
 </p></dd>
 </dl>
 
-<p>In this example a thinspace separates the function from the
-infinitesimal.
-</p>
-<div class="example">
-<pre class="example">\int_0^1 f(x)\,dx
-</pre></div>
 
-
 <hr>
 <a name="Math-miscellany"></a>
 <div class="header">
@@ -13203,7 +13448,7 @@
 <dt><code>\mathellipsis</code>
 <a name="index-_005cmathellipsis"></a>
 </dt>
-<dd><p>Ellipsis (spaced for text) in math mode: ….
+<dd><p>Ellipsis (spaced for text) in math mode: …
 </p>
 </dd>
 <dt><code>\mathparagraph</code>
@@ -13265,6 +13510,9 @@
 </dt>
 <dd><p>Generates <var>math</var> with a brace underneath. For example, <code>\underbrace{x+y+z}_{>\,0}</code>
 </p>
+<a name="index-package_002c-ulem"></a>
+<a name="index-ulem-package"></a>
+
 </dd>
 <dt><code>\underline{<var>text</var>}</code>
 <a name="index-_005cunderline_007btext_007d"></a>
@@ -13272,12 +13520,15 @@
 <dd><p>Causes <var>text</var>, which may be either math mode or not, to be
 underlined.  The line is always below the text, taking account of
 descenders.
+(The package <samp>ulem</samp> does underlining and allows line breaking as
+well as a number of other underline-related features.  The documentation
+is on CTAN.)
 </p>
 </dd>
 <dt><code>\vdots</code>
 <a name="index-_005cvdots"></a>
 </dt>
-<dd><p>Produces a vertical ellipsis.
+<dd><p>Vertical ellipsis.
 </p>
 </dd>
 </dl>
@@ -13407,9 +13658,18 @@
 <a name="index-styles_002c-page"></a>
 <a name="index-page-styles"></a>
 
-<p>The <code>\documentclass</code> command determines the size and position of
-the page’s head and foot.  The page style determines what goes in them.
+<p>The style of a page determines where LaTeX places the components of
+that page, such as headers and footers, and the text body.  This
+includes pages in the main part of the document but also includes
+special pages such as the title page of a book, a page from an index, or
+the first page of an article.
 </p>
+<a name="index-package_002c-fancyhdr"></a>
+<a name="index-fancyhdr-package"></a>
+
+<p>The package <samp>fancyhdr</samp> is very helpful for constructing page
+styles.  See its documentation on CTAN.
+</p>
 <table class="menu" border="0" cellspacing="0">
 <tr><td align="left" valign="top">• <a href="#g_t_005cmaketitle" accesskey="1">\maketitle</a>:</td><td>  </td><td align="left" valign="top">Generate a title page.
 </td></tr>
@@ -13434,11 +13694,36 @@
 <a name="index-titles_002c-making"></a>
 <a name="index-_005cmaketitle"></a>
 
-<p>The <code>\maketitle</code> command generates a title on a separate title
-page—except in the <code>article</code> class, where the title is placed
-at the top of the first page.  Information used to produce the title
-is obtained from the following declarations:
+<p>Generate a title.  It is on a separate title page, except in the
+<code>article</code> class where it is at the top of the first page.
 </p>
+<p>This example
+</p>
+<div class="example">
+<pre class="example">\documentclass{article}
+\title{On the Electrodynamics of Moving Bodies}
+\author{A~Einstein\thanks{%
+  Gratefully acknowledged is the support of the Swiss Patent Office.}}
+\date{1905-Jun-30}
+\begin{document}
+\maketitle
+It is known that Maxwell's electrodynamics---as usually understood at the
+present time---when applied to moving bodies, leads to asymmetries which
+do not appear to be inherent in the phenomena.
+   ...
+In conclusion I wish to say that in working at the problem here dealt
+with I have had the loyal assistance of my friend and colleague M~Besso,
+and that I am indebted to him for several valuable suggestions.
+\end{document}
+</pre></div>
+
+<p>shows the <code>\maketitle</code> command appearing immediately after the
+<code>\begin{document}</code>.
+</p>
+<p>Information used to produce the title is obtained from the following
+declarations.  These must come before the <code>\maketitle</code>, either in
+the preamble or in the document body.
+</p>
 <dl compact="compact">
 <dt><code>\author{<var>name</var> \and <var>name2</var>}</code>
 <a name="index-_005cauthor_007bname-_005cand-name2_007d"></a>
@@ -13446,19 +13731,19 @@
 <dd><a name="index-author_002c-for-titlepage"></a>
 <a name="index-_005c_005c-for-_005cauthor"></a>
 <a name="index-_005cand-for-_005cauthor"></a>
-<p>The <code>\author</code> command declares the document author(s), where the
-argument is a list of authors separated by <code>\and</code> commands.  Use
-<code>\\</code> to separate lines within a single author’s entry—for
-example, to give the author’s institution or address.
+<p>Required.  Declare the document author or authors.  The argument is a
+list of authors separated by <code>\and</code> commands.  Use <code>\\</code> to
+separate lines within a single author’s entry—for example, to give the
+author’s institution or address.  If you omit this then you get
+‘<samp>LaTeX Warning: No \author given</samp>’.
 </p>
 </dd>
 <dt><code>\date{<var>text</var>}</code>
 <a name="index-_005cdate_007btext_007d"></a>
 </dt>
 <dd><a name="index-date_002c-for-titlepage"></a>
-<p>The <code>\date</code> command declares <var>text</var> to be the document’s
-date.  With no <code>\date</code> command, the current date (see <a href="#g_t_005ctoday">\today</a>)
-is used.
+<p>Optional.  Declare <var>text</var> to be the document’s date.  If you omit it
+then LaTeX uses the current date (see <a href="#g_t_005ctoday">\today</a>).
 </p>
 </dd>
 <dt><code>\thanks{<var>text</var>}</code>
@@ -13466,8 +13751,8 @@
 </dt>
 <dd><a name="index-thanks_002c-for-titlepage"></a>
 <a name="index-credit-footnote"></a>
-<p>The <code>\thanks</code> command produces a <code>\footnote</code> to the title,
-usually used for credit acknowledgements.
+<p>Optional.  Produce a footnote to the title, usually for
+acknowledgements.
 </p>
 </dd>
 <dt><code>\title{<var>text</var>}</code>
@@ -13475,8 +13760,9 @@
 </dt>
 <dd><a name="index-title_002c-for-titlepage"></a>
 <a name="index-_005c_005c-for-_005ctitle"></a>
-<p>The <code>\title</code> command declares <var>text</var> to be the title of the
-document.  Use <code>\\</code> to force a line break, as usual.
+<p>Required.  Declare <var>text</var> to be the title of the document.  Inside
+<var>text</var>, use <code>\\</code> to get line breaks.  If you omit this command
+then you get ‘<samp>LaTeX Error: No \title given</samp>’.
 </p>
 </dd>
 </dl>
@@ -13911,9 +14197,10 @@
 
 <a name="index-_005cthinspace-1"></a>
 
-<p><code>\thinspace</code> produces an unbreakable and unstretchable space that
-is 1/6 of an em.  This is the proper space to use between nested
-quotes, as in ’”.</p>
+<p>Produce an unbreakable and unstretchable space of 1/6 of an em.  This is
+the proper space to use between nested quotes, as in ’”.Some style guides call for a <code>\thinspace</code> between an ellipsis and a
+sentence ending period.
+</p>
 
 <hr>
 <a name="g_t_005c_002f"></a>
@@ -18337,9 +18624,12 @@
 <tr><td></td><td valign="top"><a href="#index-align-environment_002c-from-amsmath">align <span class="roman">environment, from <code>amsmath</code></span></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-aligning-equations">aligning equations</a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-alignment-via-tabbing">alignment via tabbing</a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsfonts-package"><code>amsfonts</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package-1"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package-2"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-3"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-amsmath-package-4"><code>amsmath</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsmath-package_002c-replacing-eqnarray">amsmath <span class="roman">package, replacing <code>eqnarray</code></span></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-amsthm-package"><code>amsthm</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-appendix_002c-creating">appendix, creating</a>:</td><td> </td><td valign="top"><a href="#Sectioning">Sectioning</a></td></tr>
@@ -18376,9 +18666,12 @@
 <tr><td></td><td valign="top"><a href="#index-Big-point">Big point</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bigfoot-package"><code>bigfoot</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Footnotes-of-footnotes">Footnotes of footnotes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-black-boxes_002c-omitting">black boxes, omitting</a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-blackboard-bold">blackboard bold</a>:</td><td> </td><td valign="top"><a href="#Blackboard-bold">Blackboard bold</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-bm-package"><code>bm</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bold-font">bold font</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bold-math">bold math</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-bold-typewriter_002c-avoiding">bold typewriter, avoiding</a>:</td><td> </td><td valign="top"><a href="#description">description</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-boldface-mathematics">boldface mathematics</a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-box_002c-allocating-new">box, allocating new</a>:</td><td> </td><td valign="top"><a href="#g_t_005cnewsavebox">\newsavebox</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-box_002c-colored">box, colored</a>:</td><td> </td><td valign="top"><a href="#Colored-boxes">Colored boxes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-boxes">boxes</a>:</td><td> </td><td valign="top"><a href="#Boxes">Boxes</a></td></tr>
@@ -18394,6 +18687,7 @@
 <tr><td></td><td valign="top"><a href="#index-bulleted-lists">bulleted lists</a>:</td><td> </td><td valign="top"><a href="#itemize">itemize</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-C">C</a></th><td></td><td></td></tr>
+<tr><td></td><td valign="top"><a href="#index-caligraphic">caligraphic</a>:</td><td> </td><td valign="top"><a href="#Caligraphic">Caligraphic</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-calligraphic-letters-for-math">calligraphic letters for math</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-cap-height">cap height</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-caron-accent">caron accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
@@ -18529,6 +18823,7 @@
 <tr><td></td><td valign="top"><a href="#index-double-right-quote">double right quote</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-spacing">double spacing</a>:</td><td> </td><td valign="top"><a href="#Low_002dlevel-font-commands">Low-level font commands</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-double-vertical-bar_002c-in-text">double vertical bar, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-doublestruck">doublestruck</a>:</td><td> </td><td valign="top"><a href="#Blackboard-bold">Blackboard bold</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-E">E</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-e_002ddash">e-dash</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -18570,6 +18865,7 @@
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-F">F</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-families_002c-of-fonts">families, of fonts</a>:</td><td> </td><td valign="top"><a href="#Low_002dlevel-font-commands">Low-level font commands</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-fancyhdr-package"><code>fancyhdr</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Page-styles">Page styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-fancyvrb-package"><code>fancyvrb</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-fancyvrb-package-1"><code>fancyvrb</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-feminine-ordinal-symbol">feminine ordinal symbol</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -18775,7 +19071,9 @@
 <tr><td></td><td valign="top"><a href="#index-math-mode_002c-spacing">math mode, spacing</a>:</td><td> </td><td valign="top"><a href="#Spacing-in-math-mode">Spacing in math mode</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math-symbols">math symbols</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-math_002c-bold">math, bold</a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-mathtools-package"><code>mathtools</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-mfirstuc-package"><code>mfirstuc</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-mhchem-package"><code>mhchem</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-Millimeter">Millimeter</a>:</td><td> </td><td valign="top"><a href="#Units-of-length">Units of length</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-minipage_002c-creating-a">minipage, creating a</a>:</td><td> </td><td valign="top"><a href="#minipage">minipage</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-minted-package"><code>minted</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
@@ -18835,13 +19133,17 @@
 <tr><td></td><td valign="top"><a href="#index-package-options">package options</a>:</td><td> </td><td valign="top"><a href="#Class-and-package-structure">Class and package structure</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package-options-1">package options</a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-algorithm2e"><span class="roman">package</span>, <code>algorithm2e</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsfonts"><span class="roman">package</span>, <code>amsfonts</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#array">array</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-1"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#displaymath">displaymath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-2"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-3"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-amsmath-4"><span class="roman">package</span>, <code>amsmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-amsthm"><span class="roman">package</span>, <code>amsthm</code></a>:</td><td> </td><td valign="top"><a href="#theorem">theorem</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-babel"><span class="roman">package</span>, <code>babel</code></a>:</td><td> </td><td valign="top"><a href="#thebibliography">thebibliography</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-babel-1"><span class="roman">package</span>, <code>babel</code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-bigfoot"><span class="roman">package</span>, <code>bigfoot</code></a>:</td><td> </td><td valign="top"><a href="#Footnotes-of-footnotes">Footnotes of footnotes</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-bm"><span class="roman">package</span>, <code>bm</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-cleveref"><span class="roman">package</span>, <code>cleveref</code></a>:</td><td> </td><td valign="top"><a href="#Cross-references">Cross references</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-cleveref-1"><span class="roman">package</span>, <code>cleveref</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cfootnotemark">\footnotemark</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-cprotect"><span class="roman">package</span>, <code>cprotect</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
@@ -18850,6 +19152,7 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-enumitem"><span class="roman">package</span>, <code>enumitem</code></a>:</td><td> </td><td valign="top"><a href="#list">list</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-envlab"><span class="roman">package</span>, <code>envlab</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmakelabels">\makelabels</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-etoolbox"><span class="roman">package</span>, <code>etoolbox</code></a>:</td><td> </td><td valign="top"><a href="#Class-and-package-commands">Class and package commands</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-fancyhdr"><span class="roman">package</span>, <code>fancyhdr</code></a>:</td><td> </td><td valign="top"><a href="#Page-styles">Page styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-fancyvrb"><span class="roman">package</span>, <code>fancyvrb</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-fancyvrb-1"><span class="roman">package</span>, <code>fancyvrb</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-flafter"><span class="roman">package</span>, <code>flafter</code></a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
@@ -18862,15 +19165,19 @@
 <tr><td></td><td valign="top"><a href="#index-package_002c-listings-1"><span class="roman">package</span>, <code>listings</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-macros2e"><span class="roman">package</span>, <code>macros2e</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmakeatletter-and-_005cmakeatother">\makeatletter and \makeatother</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-makeidx"><span class="roman">package</span>, <code>makeidx</code></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-mathtools"><span class="roman">package</span>, <code>mathtools</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-mfirstuc"><span class="roman">package</span>, <code>mfirstuc</code></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-mhchem"><span class="roman">package</span>, <code>mhchem</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-minted"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-minted-1"><span class="roman">package</span>, <code>minted</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-multind"><span class="roman">package</span>, <code>multind</code></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-pict2e"><span class="roman">package</span>, <code>pict2e</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cline">\line</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-setspace"><span class="roman">package</span>, <code>setspace</code></a>:</td><td> </td><td valign="top"><a href="#Low_002dlevel-font-commands">Low-level font commands</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-showidx"><span class="roman">package</span>, <code>showidx</code></a>:</td><td> </td><td valign="top"><a href="#Indexes">Indexes</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-symbols"><span class="roman">package</span>, <code>symbols</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-textcase"><span class="roman">package</span>, <code>textcase</code></a>:</td><td> </td><td valign="top"><a href="#Upper-and-lower-case">Upper and lower case</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-textcomp"><span class="roman">package</span>, <code>textcomp</code></a>:</td><td> </td><td valign="top"><a href="#Font-styles">Font styles</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-package_002c-ulem"><span class="roman">package</span>, <code>ulem</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-url"><span class="roman">package</span>, <code>url</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cverb">\verb</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-verbatimbox"><span class="roman">package</span>, <code>verbatimbox</code></a>:</td><td> </td><td valign="top"><a href="#verbatim">verbatim</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-package_002c-xspace"><span class="roman">package</span>, <code>xspace</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_0028SPACE_0029-after-control-sequence">\(SPACE) after control sequence</a></td></tr>
@@ -19024,6 +19331,8 @@
 <tr><td></td><td valign="top"><a href="#index-styles_002c-page">styles, page</a>:</td><td> </td><td valign="top"><a href="#Page-styles">Page styles</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-subscript">subscript</a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-superscript">superscript</a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-symbols-package"><code>symbols</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-symbols_002c-boldface">symbols, boldface</a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-symbols_002c-math">symbols, math</a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-symbols_002c-text">symbols, text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
@@ -19075,6 +19384,7 @@
 <tr><td></td><td valign="top"><a href="#index-typewriter-labels-in-lists">typewriter labels in lists</a>:</td><td> </td><td valign="top"><a href="#description">description</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Concept-Index_cp_letter-U">U</a></th><td></td><td></td></tr>
+<tr><td></td><td valign="top"><a href="#index-ulem-package"><code>ulem</code> <span class="roman">package</span></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-umlaut-accent">umlaut accent</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-underbar">underbar</a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-underscore_002c-in-text">underscore, in text</a>:</td><td> </td><td valign="top"><a href="#Text-symbols">Text symbols</a></td></tr>
@@ -19184,26 +19494,24 @@
 <a name="Command-Index-1"></a>
 <h2 class="unnumbered">Command Index</h2>
 
-<table><tr><th valign="top">Jump to:   </th><td><a class="summary-letter" href="#Command-Index_fn_symbol-1"><b>$</b></a>
+<table><tr><th valign="top">Jump to:   </th><td><a class="summary-letter" href="#Command-Index_fn_symbol-1"><b>&</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-2"><b>&</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-2"><b>-</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-3"><b>-</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-3"><b>.</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>.</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>1</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>1</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>[</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>[</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>\</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>\</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>^</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>^</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>_</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>_</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>{</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-10"><b>{</b></a>
-   
 <br>
 <a class="summary-letter" href="#Command-Index_fn_letter-A"><b>A</b></a>
    
@@ -19249,16 +19557,13 @@
 <table class="index-fn" border="0">
 <tr><td></td><th align="left">Index Entry</th><td> </td><th align="left"> Section</th></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-1">$</a></th><td></td><td></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_0024"><code>$</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
-<tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-2">&</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-1">&</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_0026"><code>&</code></a>:</td><td> </td><td valign="top"><a href="#tabular">tabular</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-3">-</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-2">-</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002d_002dhelp-command_002dline-option"><code>--help <span class="roman">command-line option</span></code></a>:</td><td> </td><td valign="top"><a href="#Command-line">Command line</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-4">.</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-3">.</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002eaux-file"><code>.aux <span class="roman">file</span></code></a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002edvi-file"><code>.dvi <span class="roman">file</span></code></a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002elof-file"><code>.lof <span class="roman">file</span></code></a>:</td><td> </td><td valign="top"><a href="#Output-files">Output files</a></td></tr>
@@ -19272,15 +19577,15 @@
 <tr><td></td><td valign="top"><a href="#index-_002etoc-file-1"><code>.toc <span class="roman">file</span></code></a>:</td><td> </td><td valign="top"><a href="#Tables-of-contents">Tables of contents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_002exdv-file"><code>.xdv <span class="roman">file</span></code></a>:</td><td> </td><td valign="top"><a href="#TeX-engines">TeX engines</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-5">1</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-4">1</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-10pt-option"><code>10pt <span class="roman">option</span></code></a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-11pt-option"><code>11pt <span class="roman">option</span></code></a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-12pt-option"><code>12pt <span class="roman">option</span></code></a>:</td><td> </td><td valign="top"><a href="#Document-class-options">Document class options</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-6">[</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-5">[</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005b_002e_002e_002e_005d-for-optional-arguments"><code>[...] <span class="roman">for optional arguments</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-7">\</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-6">\</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c-character-starting-commands"><code>\ <span class="roman">character starting commands</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0021"><code>\!</code></a>:</td><td> </td><td valign="top"><a href="#Spacing-in-math-mode">Spacing in math mode</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0022-_0028umlaut-accent_0029"><code>\" <span class="roman">(umlaut accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
@@ -19290,9 +19595,7 @@
 <tr><td></td><td valign="top"><a href="#index-_005c_0026"><code>\&</code></a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0027-_0028acute-accent_0029"><code>\' <span class="roman">(acute accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0027-_0028tabbing_0029"><code>\' <span class="roman">(tabbing)</span></code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005c_0028"><code>\(</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_0028SPACE_0029"><code>\(SPACE)</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_0028SPACE_0029-and-_005c_0040">\(SPACE) and \@</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005c_0029"><code>\)</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002a"><code>\*</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002b"><code>\+</code></a>:</td><td> </td><td valign="top"><a href="#tabbing">tabbing</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_002c"><code>\,</code></a>:</td><td> </td><td valign="top"><a href="#Spacing-in-math-mode">Spacing in math mode</a></td></tr>
@@ -19384,7 +19687,8 @@
 <tr><td></td><td valign="top"><a href="#index-_005cbigvee"><code>\bigvee</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cbigwedge"><code>\bigwedge</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cbmod"><code>\bmod</code></a>:</td><td> </td><td valign="top"><a href="#Math-functions">Math functions</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cboldmath"><code>\boldmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cboldmath"><code>\boldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cboldmath-1"><code>\boldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cbot"><code>\bot</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cbottomfraction"><code>\bottomfraction</code></a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cbottomfraction-1"><code>\bottomfraction</code></a>:</td><td> </td><td valign="top"><a href="#Floats">Floats</a></td></tr>
@@ -20096,7 +20400,8 @@
 <tr><td></td><td valign="top"><a href="#index-_005ctypein"><code>\typein</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ctypein">\typein</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005ctypeout"><code>\typeout</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005ctypeout">\typeout</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cu-_0028breve-accent_0029"><code>\u <span class="roman">(breve accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005cunboldmath"><code>\unboldmath</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cunboldmath"><code>\unboldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
+<tr><td></td><td valign="top"><a href="#index-_005cunboldmath-1"><code>\unboldmath</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cboldmath-_0026-_005cunboldmath">\boldmath & \unboldmath</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunderbar"><code>\underbar</code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunderbrace_007bmath_007d"><code>\underbrace{<var>math</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cunderline_007btext_007d"><code>\underline{<var>text</var>}</code></a>:</td><td> </td><td valign="top"><a href="#Math-miscellany">Math miscellany</a></td></tr>
@@ -20146,7 +20451,6 @@
 <tr><td></td><td valign="top"><a href="#index-_005cxi"><code>\xi</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005cyear"><code>\year</code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cday-_005cmonth-_005cyear">\day \month \year</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005czeta"><code>\zeta</code></a>:</td><td> </td><td valign="top"><a href="#Math-symbols">Math symbols</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005c_005b"><code>\[</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005c-_0028for-center_0029"><code>\\ <span class="roman">(for <code>center</code>)</span></code></a>:</td><td> </td><td valign="top"><a href="#center">center</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005c-_0028for-eqnarray_0029"><code>\\ <span class="roman">(for <code>eqnarray</code>)</span></code></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005c-_0028for-flushright_0029"><code>\\ (for <code>flushright</code>)</code></a>:</td><td> </td><td valign="top"><a href="#flushright">flushright</a></td></tr>
@@ -20160,7 +20464,6 @@
 <tr><td></td><td valign="top"><a href="#index-_005c_005c-for-_005ctitle"><code>\\ <span class="roman">for <code>\title</code></span></code></a>:</td><td> </td><td valign="top"><a href="#g_t_005cmaketitle">\maketitle</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005c-force-line-break"><code>\\ <span class="roman">force line break</span></code></a>:</td><td> </td><td valign="top"><a href="#g_t_005c_005c">\\</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005c_002a-_0028for-eqnarray_0029"><code>\\* <span class="roman">(for <code>eqnarray</code>)</span></code></a>:</td><td> </td><td valign="top"><a href="#eqnarray">eqnarray</a></td></tr>
-<tr><td></td><td valign="top"><a href="#index-_005c_005d"><code>\]</code></a>:</td><td> </td><td valign="top"><a href="#Math-formulas">Math formulas</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005e"><code>\^</code></a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005e-_0028circumflex-accent_0029"><code>\^ <span class="roman">(circumflex accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_005f"><code>\_</code></a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
@@ -20172,13 +20475,13 @@
 <tr><td></td><td valign="top"><a href="#index-_005c_007e"><code>\~</code></a>:</td><td> </td><td valign="top"><a href="#Reserved-characters">Reserved characters</a></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005c_007e-_0028tilde-accent_0029"><code>\~ <span class="roman">(tilde accent)</span></code></a>:</td><td> </td><td valign="top"><a href="#Accents">Accents</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-8">^</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-7">^</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005e"><code>^</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-9">_</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-8">_</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_005f"><code>_</code></a>:</td><td> </td><td valign="top"><a href="#Subscripts-_0026-superscripts">Subscripts & superscripts</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
-<tr><th><a name="Command-Index_fn_symbol-10">{</a></th><td></td><td></td></tr>
+<tr><th><a name="Command-Index_fn_symbol-9">{</a></th><td></td><td></td></tr>
 <tr><td></td><td valign="top"><a href="#index-_007b_002e_002e_002e_007d-for-required-arguments"><code>{...} <span class="roman">for required arguments</span></code></a>:</td><td> </td><td valign="top"><a href="#LaTeX-command-syntax">LaTeX command syntax</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 <tr><th><a name="Command-Index_fn_letter-A">A</a></th><td></td><td></td></tr>
@@ -20357,26 +20660,24 @@
 <tr><td></td><td valign="top"><a href="#index-xelatex-command"><code>xelatex <span class="roman">command</span></code></a>:</td><td> </td><td valign="top"><a href="#TeX-engines">TeX engines</a></td></tr>
 <tr><td colspan="4"> <hr></td></tr>
 </table>
-<table><tr><th valign="top">Jump to:   </th><td><a class="summary-letter" href="#Command-Index_fn_symbol-1"><b>$</b></a>
+<table><tr><th valign="top">Jump to:   </th><td><a class="summary-letter" href="#Command-Index_fn_symbol-1"><b>&</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-2"><b>&</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-2"><b>-</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-3"><b>-</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-3"><b>.</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>.</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-4"><b>1</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>1</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-5"><b>[</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>[</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-6"><b>\</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>\</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-7"><b>^</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>^</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-8"><b>_</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>_</b></a>
+<a class="summary-letter" href="#Command-Index_fn_symbol-9"><b>{</b></a>
    
-<a class="summary-letter" href="#Command-Index_fn_symbol-10"><b>{</b></a>
-   
 <br>
 <a class="summary-letter" href="#Command-Index_fn_letter-A"><b>A</b></a>
    

Modified: trunk/latex2e.info
===================================================================
--- trunk/latex2e.info	2018-06-05 15:29:46 UTC (rev 640)
+++ trunk/latex2e.info	2018-06-06 19:01:02 UTC (rev 641)
@@ -7544,47 +7544,82 @@
 16 Math formulas
 ****************
 
-There are three environments that put LaTeX in math mode:
+Produce mathematical text by putting LaTeX into math mode or display
+math mode (*note Modes::).  This example shows both.
 
-'math'
-     For formulas that appear right in the text.
-'displaymath'
-     For formulas that appear on their own line.
-'equation'
-     The same as the displaymath environment except that it adds an
-     equation number in the right margin.
+     The wave equation for \( u \) is
+     \begin{displaymath}
+       \frac{\partial^2u}{\partial t^2} = c^2\nabla^2u
+     \end{displaymath}
+     where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 
-   The 'math' environment can be used in both paragraph and LR mode, but
-the 'displaymath' and 'equation' environments can be used only in
-paragraph mode.  The 'math' and 'displaymath' environments are used so
-often that they have the following short forms:
+   Math mode is for inline mathematics.  It is invoked by the starting
+'\(' and finished by the matching ending '\)'.  Display math mode is for
+displayed equations and here is invoked by the 'displaymath'
+environment.  Note that any mathematical text whatever, including that
+consisting of single characters, is handled in math mode.
 
-     \(...\)   instead of   \begin{math}...\end{math}
-     \[...\]   instead of   \begin{displaymath}...\end{displaymath}
+   The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+'amsmath' and 'amssymb' (also be aware of the 'mathtools' package that
+is an extension to, and loads, 'amsmath').  New documents that will have
+mathematical text should use these packages.  Descriptions of these
+packages is outside the scope of this document; see their documentation
+on CTAN.
 
-   In fact, the 'math' environment is so common that it has an even
-shorter form:
+   When in math mode or display math mode, LaTeX handles many aspects of
+your input text differently than in other text modes.  For example,
 
-     $ ... $   instead of   \(...\)
+     contrast x+y with \( x+y \).
 
-   The '\boldmath' command changes math letters and symbols to be in a
-bold font.  It is used _outside_ of math mode.  Conversely, the
-'\unboldmath' command changes math glyphs to be in a normal font; it too
-is used _outside_ of math mode.
+   in math mode the letters are in italics and the spacing around the
+plus sign is different.
 
-   The '\displaystyle' declaration forces the size and style of the
-formula to be that of 'displaymath', e.g., with limits above and below
-summations.  For example:
+   To make inline formulas put LaTeX in math mode with either
+'\(MATHEMATICAL MATERIAL\)', or '$MATHEMATICAL MATERIAL$', or
+'\begin{math}MATHEMATICAL MATERIAL\END{MATH}'.  The first form is
+preferred, and the third form is very rarely used.  These can be used in
+paragraph mode or in LR mode (*note Modes::).
 
-     $\displaystyle \sum_{n=0}^\infty x_n $
+   To make displayed formulas, put LaTeX into display math mode with
+either '\begin{displaymath}MATHEMATICAL MATERIAL\end{displaymath}', or
+'\begin{equation}MATHEMATICAL MATERIAL\end{equation}'.  These behave the
+same way except that with the 'equation' environment, LaTeX puts a
+formula number alongside the formula, which by default has the form
+'(ARABIC NUMBER)'.  The construct '\[ MATH \]' is equivalent to
+'\begin{displaymath} MATH \end{displaymath}'.  These environments can
+only be used in paragraph mode (*note Modes::).
 
+   The two mathematics modes are similar, but there are some
+differences.  One involves the placement of subscripts and superscripts;
+in display math mode they are further apart and in inline math mode they
+are closer together.  Sometimes you want the display math treatment to
+happen in the inline math mode.  For this, the '\displaystyle'
+declaration forces the size and style of the formula to be that of
+'displaymath'.  Thus '\(\displaystyle \sum_{n=0}^\infty x_n\)' will have
+the limits above and below the summation sign, not next to it.  Another
+example is that
+
+     \begin{tabular}{r|cc}
+       \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
+       Arithmetic     &\( a+(a+b)+(a+2b)+\cdots+(a+(n-1)b) \)
+                        &\( na+(n-1)n\cdot\frac{b}{2}\)  \\
+       Geometric      &\( a+ab+ab^2+\cdots+ab^{n-1} \)
+                        &\(\displaystyle a\cdot\frac{1-b^n}{1-b}\)  \\
+     \end{tabular}
+
+   because it has no '\displaystyle', the Arithmetic line's fraction
+will be scrunched.  But, because of its '\displaystyle', the Geometric
+line's fraction will be easy to read, with characters the same size as
+in the rest of the line.
+
 * Menu:
 
 * Subscripts & superscripts::   Also known as exponent or index.
 * Math symbols::                Various mathematical squiggles.
 * Math functions::              Math function names like sin and exp.
 * Math accents::                Accents in math.
-* Spacing in math mode::        Thick, medium, thin and negative spaces.
+* Spacing in math mode::        Thick, medium, thin, and negative spaces.
 * Math miscellany::             Stuff that doesn't fit anywhere else.
 
 
@@ -7593,36 +7628,64 @@
 16.1 Subscripts & superscripts
 ==============================
 
-In math mode, use the caret character '^' to make the EXP appear as a
-superscript: '^{EXP}'.  Similarly, in math mode, underscore '_{EXP}'
-makes a subscript out of EXP.
+Synopsis (in math mode or display math mode):
 
-   In this example the '0' and '1' appear as subscripts while the '2' is
-a superscript.
+     BASE^EXP
 
-     \( (x_0+x_1)^2 \)
+   or:
 
-   To have more than one character in EXP use curly braces as in
-'e^{-2x}'.
+     BASE_EXP
 
-   LaTeX handles superscripts on superscripts, and all of that stuff, in
-the natural way, so expressions such as 'e^{x^2}' and 'x_{a_0}' will
-look right.  It also does the right thing when something has both a
-subscript and a superscript.  In this example the '0' appears at the
-bottom of the integral sign while the '10' appears at the top.
+   Make EXP appear as a superscript of BASE (with the caret
+character, '^') or a subscript (with underscore, '_').
 
-     \int_0^{10} x^2 \,dx
+   In this example the '0''s and '1''s are subscripts while the '2''s
+are superscripts.
 
-   You can put a superscript or subscript before a symbol with a
-construct such as '{}_t K^2' in math mode (the initial '{}' prevents the
-prefixed subscript from being attached to any prior symbols in the
-expression).
+     \( (x_0+x_1)^2 \leq (x_0)^2+(x_1)^2 \)
 
-   Outside of math mode, a construct like 'A
-test$_\textnormal{subscript}$' will produce a subscript typeset in text
-mode, not math mode.  Note that there are packages specialized for
-writing Chemical formulas such as 'mhchem'.
+   To have the subscript or superscript contain more than one character,
+surround the expression with curly braces, as in 'e^{-2x}'.  This
+example's fourth line shows curly braces used to group an expression for
+the exponent.
 
+     \begin{displaymath}
+       (3^3)^3=27^3=19\,683
+       \qquad
+       3^{(3^3)}=3^{27}=7\,625\,597\,484\,987
+     \end{displaymath}
+
+   LaTeX knows how to handle a superscript on a superscript, or a
+subscript on a subscript, or supers on subs, or subs on supers.  So,
+expressions such as 'e^{x^2}' and 'x_{i_0}' give correct output.  Note
+the use in those expressions of curly braces to give the BASE a
+determined EXP.  If you enter '\(3^3^3\)' then you get 'Double
+superscript'.
+
+   LaTeX does the right thing when something has both a subscript and a
+superscript.  In this example the integral has both.  They come out in
+the correct place without any author intervention.
+
+     \begin{displaymath}
+       \int_{x=a}^b f'(x)\,dx = f(b)-f(a)
+     \end{displaymath}
+
+Note the parentheses around 'x=a' to make the entire expression a
+subscript.
+
+   To put a superscript or subscript before a symbol, use a construct
+like '{}_t K^2'.  The empty curly braces '{}' give the subscript
+something to attach to and keeps it from accidentally attaching to a
+prior symbols.
+
+   Using the subscript or superscript command outside of math mode or
+display math mode, as in 'the expression x^2', will get you the error
+'Missing $ inserted'.
+
+   A common reason to want subscripts outside of a mathematics mode is
+to typeset chemical formulas.  There are packages for that such as
+'mhchem'; see CTAN.
+
 
 File: latex2e.info,  Node: Math symbols,  Next: Math functions,  Prev: Subscripts & superscripts,  Up: Math formulas
 
@@ -7633,12 +7696,17 @@
 For example, if you include '$\pi$' in your source, you will get the pi
 symbol U+03C0.
 
-   Below is a list of commonly-available symbols.  It is by no means an
-exhaustive list.  Each symbol here is described with a short phrase, and
-its symbol class (which determines the spacing around it) is given in
-parenthesis.  Unless said otherwise, the commands for these symbols can
-be used only in math mode.
+   Virtually any technical symbol anyone has ever used is available for
+use in LaTeX.  See the 'Comprehensive LaTeX Symbol List' at
+<https://ctan.org/tex-archive/info/symbols/comprehensive/>.  Some of
+these require the use of external packages.
 
+   Below is a list of commonly-used symbols that come standard with
+LaTeX.  It is by no means an exhaustive list.  Each symbol here is
+described with a short phrase, and its symbol class (which determines
+the spacing around it) is given in parenthesis.  Unless said otherwise,
+the commands for these symbols can be used only in math mode.
+
    To redefine a command so that it can be used whatever the current
 mode, see *note \ensuremath::.
 
@@ -8487,7 +8555,106 @@
 '\zeta'
      U+03B6 Lower case Greek letter (ordinary).
 
+* Menu:
+
+* Blackboard bold::            Doublestruck characters.
+* Caligraphic::                Cursive characters.
+* \boldmath & \unboldmath::    Symbols in boldface.
+
 
+File: latex2e.info,  Node: Blackboard bold,  Next: Caligraphic,  Up: Math symbols
+
+16.2.1 Blackboard bold
+----------------------
+
+Synopsis:
+
+     \usepackage{amssymb}   % in preamble
+       ...
+     \mathbb{UPPERCASE-LETTER}
+
+   Provide blackboard bold symbols, sometimes also known as doublestruck
+letters, used to denote number sets such as the natural numbers, the
+integers, etc.
+
+   Here
+
+     \( \forall n \in \mathbb{N}, n^2 \geq 0 \)
+
+   the '\mathbb{N}' gives blackboard bold symbol U+2115 representing the
+natural numbers.
+
+   If you use other than an upper case letter then you do not get an
+error but you get strange results, including unexpected characters.
+
+   There are packages that give access to symbols other than just the
+capital letters; look on CTAN.
+
+
+File: latex2e.info,  Node: Caligraphic,  Next: \boldmath & \unboldmath,  Prev: Blackboard bold,  Up: Math symbols
+
+16.2.2 Caligraphic
+------------------
+
+Synopsis:
+
+     \mathcal{UPPERCASE-LETTERS}
+
+   Use a script-like font.
+
+   In this example the graph identifier is output in a cursive font.
+
+     Let the graph be \( \mathcal{G} \).
+
+   If you use something other than an upper case letter then you do not
+get an error.  Instead you get unexpected output.  For instance,
+'\mathcal{g}' outputs a close curly brace symbol, while '\mathcal{+}'
+outputs a plus sign.
+
+
+File: latex2e.info,  Node: \boldmath & \unboldmath,  Prev: Caligraphic,  Up: Math symbols
+
+16.2.3 '\boldmath' & '\unboldmath'
+----------------------------------
+
+Synopsis (used in paragraph mode or LR mode):
+
+     \boldmath \( MATH \)
+
+   or
+
+     \unboldmath \( MATH \)
+
+   Declarations to change the letters and symbols in MATH to be in a
+bold font, or to countermand that and bring back the unbolded default.
+They must be used when not in math mode or display math mode (*note
+Modes::).  Both commands are fragile (*note \protect::).
+
+   In this example each '\boldmath' command takes place inside an
+'\mbox',
+
+     we have $\mbox{\boldmath \( v \)} = 5\cdot\mbox{\boldmath \( u \)$}$
+
+which means '\boldmath' is only called in a text mode, here LR mode, and
+explains why LaTeX must switch to math mode to set 'v' and 'u'.
+
+   If you use either command inside math mode, as with 'Trouble: \(
+\boldmath x \)', then you get something like 'LaTeX Font Warning:
+Command \boldmath invalid in math mode on input line 11' and 'LaTeX Font
+Warning: Command \mathversion invalid in math mode on input line 11'.
+
+   There are many issues with '\boldmath'.  New documents should use the
+'bm' package provided by the LaTeX Project team.  A complete description
+is outside the scope of this document (see the full documentation on
+CTAN) but even this small example
+
+     \usepackage{bm}   % in preamble
+     ...
+     we have $\bm{v} = 5\cdot\bm{u}$
+
+   strongly suggests that it is an improvement over '\boldmath'.
+
+
 File: latex2e.info,  Node: Math functions,  Next: Math accents,  Prev: Math symbols,  Up: Math formulas
 
 16.3 Math functions
@@ -8497,107 +8664,114 @@
 spacing.
 
 '\arccos'
-     \arccos
+     Inverse cosine
 
 '\arcsin'
-     \arcsin
+     Inverse sine
 
 '\arctan'
-     \arctan
+     Inverse tangent
 
 '\arg'
-     \arg
+     Angle between the real axis and a point in the complex plane
 
 '\bmod'
-     Binary modulo operator (x \bmod y)
+     Binary modulo operator, used as in '\( 5\bmod 3=2 \)'
 
 '\cos'
-     \cos
+     Cosine
 
 '\cosh'
-     \cosh
+     Hyperbolic cosine
 
 '\cot'
-     \cot
+     Cotangent
 
 '\coth'
-     \coth
+     Hyperbolic cotangent
 
 '\csc'
-     \csc
+     Cosecant
 
 '\deg'
-     \deg
+     Degrees
 
 '\det'
-     \det
+     Determinant
 
 '\dim'
-     \dim
+     Dimension
 
 '\exp'
-     \exp
+     Exponential
 
 '\gcd'
-     \gcd
+     Greatest common divisor
 
 '\hom'
-     \hom
+     Homomorphisms
 
 '\inf'
-     \inf
+     Infinum
 
 '\ker'
-     \ker
+     Kernel
 
 '\lg'
-     \lg
+     Base 2 logarithm
 
 '\lim'
-     \lim
+     Limit
 
 '\liminf'
-     \liminf
+     Limit inferior
 
 '\limsup'
-     \limsup
+     Limit superior
 
 '\ln'
-     \ln
+     Natural logarithm
 
 '\log'
-     \log
+     Logarithm
 
 '\max'
-     \max
+     Maximum
 
 '\min'
-     \min
+     Minimum
 
 '\pmod'
-     parenthesized modulus, as in (\pmod 2^n - 1)
+     Parenthesized modulus, as used in '\( 5\equiv 2\pmod 3 \)'
 
 '\Pr'
-     \Pr
+     Probability
 
 '\sec'
-     \sec
+     Secant
 
 '\sin'
-     \sin
+     Sine
 
 '\sinh'
-     \sinh
+     Hyperbolic sine
 
 '\sup'
-     \sup
+     sup
 
 '\tan'
-     \tan
+     Tangent
 
 '\tanh'
-     \tanh
+     Hyperbolic tangent
 
+   The 'amsmath' package adds improvements on some of these, and also
+allows you to define your own.  See the full documentation on CTAN, but
+'\DeclareMathOperator{\identity}{id}' creates an operator like the ones
+above but printed as 'id'.  The starred form
+'\DeclareMathOperator*{\op}{op}' sets any limits above and below, as is
+traditional with '\lim', '\sup', or '\max'.
+
 
 File: latex2e.info,  Node: Math accents,  Next: Spacing in math mode,  Prev: Math functions,  Up: Math formulas
 
@@ -8609,49 +8783,49 @@
 Accents::).
 
 '\acute'
-     Math acute accent: \acute{x}.
+     Math acute accent
 
 '\bar'
-     Math bar-over accent: \bar{x}.
+     Math bar-over accent
 
 '\breve'
-     Math breve accent: \breve{x}.
+     Math breve accent
 
 '\check'
-     Math ha'c<ek (check) accent: \check{x}.
+     Math ha'c<ek (check) accent
 
 '\ddot'
-     Math dieresis accent: \ddot{x}.
+     Math dieresis accent
 
 '\dot'
-     Math dot accent: \dot{x}.
+     Math dot accent
 
 '\grave'
-     Math grave accent: \grave{x}.
+     Math grave accent
 
 '\hat'
-     Math hat (circumflex) accent: \hat{x}.
+     Math hat (circumflex) accent
 
 '\imath'
-     Math dotless i.
+     Math dotless i
 
 '\jmath'
-     Math dotless j.
+     Math dotless j
 
 '\mathring'
-     Math ring accent: x*.
+     Math ring accent
 
 '\tilde'
-     Math tilde accent: \tilde{x}.
+     Math tilde accent
 
 '\vec'
-     Math vector symbol: \vec{x}.
+     Math vector symbol
 
 '\widehat'
-     Math wide hat accent: \widehat{x+y}.
+     Math wide hat accent
 
 '\widetilde'
-     Math wide tilde accent: \widetilde{x+y}.
+     Math wide tilde accent
 
 
 File: latex2e.info,  Node: Spacing in math mode,  Next: Math miscellany,  Prev: Math accents,  Up: Math formulas
@@ -8659,27 +8833,33 @@
 16.5 Spacing in math mode
 =========================
 
-In a 'math' environment, LaTeX ignores the spaces that you use in the
-source, and instead puts in the spacing according to the normal rules
-for mathematics texts.
+When typesetting mathematics, LaTeX puts in spacing according to the
+normal rules for mathematics texts.  If you enter 'y=m x' then LaTeX
+ignores the space and in the output the m is next to the x.
 
-   Many math mode spacing definitions are expressed in terms of the math
-unit "mu" given by 1 em = 18 mu, where the em is taken from the current
-math symbols family (*note Units of length::).  LaTeX provides the
-following commands for use in math mode:
+   But LaTeX's rules sometimes need tweaking.  For example, in an
+integral the tradition is to put a small extra space between the 'f(x)'
+and the 'dx'.
 
+     \int_0^1 f(x)\,dx
+
+   LaTeX provides the commands that follow for use in math mode.  Many
+of these spacing definitions are expressed in terms of the math unit
+"mu".  It is defined as 1/18 em, where the em is taken from the current
+math symbols family (*note Units of length::).
+
 '\;'
-     Normally '5.0mu plus 5.0mu'.  The longer name is '\thickspace'.
-     Math mode only.
+     Synonym: '\thickspace'.  Normally '5.0mu plus 5.0mu'.  Math mode
+     only.
 
 '\:'
 '\>'
-     Normally '4.0mu plus 2.0mu minus 4.0mu'.  The longer name is
-     '\medspace'.  Math mode only.
+     Synonym: '\medspace'.  Normally '4.0mu plus 2.0mu minus 4.0mu'.
+     Math mode only.
 
 '\,'
-     Normally '3mu'.  The longer name is '\thinspace'.  This can be used
-     in both math mode and text mode.  *Note \thinspace::.
+     Synonym: '\thinspace' (*note \thinspace::).  Normally '3mu'.  Can
+     be used in both math mode and text mode.
 
 '\!'
      A negative thin space.  Normally '-3mu'.  Math mode only.
@@ -8694,11 +8874,6 @@
      A length of 2 quads, that is, 36mu = 2em.  It is available in both
      text and math mode.
 
-   In this example a thinspace separates the function from the
-infinitesimal.
-
-     \int_0^1 f(x)\,dx
-
 
 File: latex2e.info,  Node: Math miscellany,  Prev: Spacing in math mode,  Up: Math formulas
 
@@ -8743,7 +8918,7 @@
      Dollar sign in math mode: $.
 
 '\mathellipsis'
-     Ellipsis (spaced for text) in math mode: ....
+     Ellipsis (spaced for text) in math mode: ...
 
 '\mathparagraph'
      Paragraph sign (pilcrow) in math mode: U+00B6.
@@ -8781,10 +8956,12 @@
 '\underline{TEXT}'
      Causes TEXT, which may be either math mode or not, to be
      underlined.  The line is always below the text, taking account of
-     descenders.
+     descenders.  (The package 'ulem' does underlining and allows line
+     breaking as well as a number of other underline-related features.
+     The documentation is on CTAN.)
 
 '\vdots'
-     Produces a vertical ellipsis.
+     Vertical ellipsis.
 
 
 File: latex2e.info,  Node: Modes,  Next: Page styles,  Prev: Math formulas,  Up: Top
@@ -8876,9 +9053,15 @@
 18 Page styles
 **************
 
-The '\documentclass' command determines the size and position of the
-page's head and foot.  The page style determines what goes in them.
+The style of a page determines where LaTeX places the components of that
+page, such as headers and footers, and the text body.  This includes
+pages in the main part of the document but also includes special pages
+such as the title page of a book, a page from an index, or the first
+page of an article.
 
+   The package 'fancyhdr' is very helpful for constructing page styles.
+See its documentation on CTAN.
+
 * Menu:
 
 * \maketitle::          Generate a title page.
@@ -8892,28 +9075,53 @@
 18.1 '\maketitle'
 =================
 
-The '\maketitle' command generates a title on a separate title
-page--except in the 'article' class, where the title is placed at the
-top of the first page.  Information used to produce the title is
-obtained from the following declarations:
+Generate a title.  It is on a separate title page, except in the
+'article' class where it is at the top of the first page.
 
+   This example
+
+     \documentclass{article}
+     \title{On the Electrodynamics of Moving Bodies}
+     \author{A~Einstein\thanks{%
+       Gratefully acknowledged is the support of the Swiss Patent Office.}}
+     \date{1905-Jun-30}
+     \begin{document}
+     \maketitle
+     It is known that Maxwell's electrodynamics---as usually understood at the
+     present time---when applied to moving bodies, leads to asymmetries which
+     do not appear to be inherent in the phenomena.
+        ...
+     In conclusion I wish to say that in working at the problem here dealt
+     with I have had the loyal assistance of my friend and colleague M~Besso,
+     and that I am indebted to him for several valuable suggestions.
+     \end{document}
+
+   shows the '\maketitle' command appearing immediately after the
+'\begin{document}'.
+
+   Information used to produce the title is obtained from the following
+declarations.  These must come before the '\maketitle', either in the
+preamble or in the document body.
+
 '\author{NAME \and NAME2}'
-     The '\author' command declares the document author(s), where the
-     argument is a list of authors separated by '\and' commands.  Use
-     '\\' to separate lines within a single author's entry--for example,
-     to give the author's institution or address.
+     Required.  Declare the document author or authors.  The argument is
+     a list of authors separated by '\and' commands.  Use '\\' to
+     separate lines within a single author's entry--for example, to give
+     the author's institution or address.  If you omit this then you get
+     'LaTeX Warning: No \author given'.
 
 '\date{TEXT}'
-     The '\date' command declares TEXT to be the document's date.  With
-     no '\date' command, the current date (*note \today::) is used.
+     Optional.  Declare TEXT to be the document's date.  If you omit it
+     then LaTeX uses the current date (*note \today::).
 
 '\thanks{TEXT}'
-     The '\thanks' command produces a '\footnote' to the title, usually
-     used for credit acknowledgements.
+     Optional.  Produce a footnote to the title, usually for
+     acknowledgements.
 
 '\title{TEXT}'
-     The '\title' command declares TEXT to be the title of the document.
-     Use '\\' to force a line break, as usual.
+     Required.  Declare TEXT to be the title of the document.  Inside
+     TEXT, use '\\' to get line breaks.  If you omit this command then
+     you get 'LaTeX Error: No \title given'.
 
 
 File: latex2e.info,  Node: \pagenumbering,  Next: \pagestyle,  Prev: \maketitle,  Up: Page styles
@@ -9205,9 +9413,10 @@
 19.5 '\thinspace': Insert 1/6em
 ===============================
 
-'\thinspace' produces an unbreakable and unstretchable space that is 1/6
-of an em.  This is the proper space to use between nested quotes, as in
-'".
+Produce an unbreakable and unstretchable space of 1/6 of an em.  This is
+the proper space to use between nested quotes, as in '".Some style
+guides call for a '\thinspace' between an ellipsis and a sentence ending
+period.
 
 
 File: latex2e.info,  Node: \/,  Next: \hrulefill \dotfill,  Prev: \thinspace,  Up: Spaces
@@ -12121,9 +12330,12 @@
 * align environment, from amsmath:       eqnarray.            (line   6)
 * aligning equations:                    eqnarray.            (line   6)
 * alignment via tabbing:                 tabbing.             (line   6)
+* amsfonts package:                      Math formulas.       (line  21)
 * amsmath package:                       array.               (line  42)
 * amsmath package <1>:                   displaymath.         (line  22)
 * amsmath package <2>:                   theorem.             (line  28)
+* amsmath package <3>:                   Math formulas.       (line  21)
+* amsmath package <4>:                   Math functions.      (line 111)
 * amsmath package, replacing eqnarray:   eqnarray.            (line   6)
 * amsthm package:                        theorem.             (line  28)
 * appendix, creating:                    Sectioning.          (line  37)
@@ -12137,7 +12349,7 @@
 * ASCII tilde, in text:                  Text symbols.        (line  67)
 * asterisk, centered, in text:           Text symbols.        (line  70)
 * at clause, in font definitions:        \newfont.            (line  19)
-* author, for titlepage:                 \maketitle.          (line  12)
+* author, for titlepage:                 \maketitle.          (line  35)
 * auxiliary file:                        Output files.        (line  33)
 * babel package:                         thebibliography.     (line  53)
 * babel package <1>:                     Accents.             (line   6)
@@ -12162,9 +12374,14 @@
                                                               (line   6)
 * black boxes, omitting:                 Document class options.
                                                               (line  53)
+* blackboard bold:                       Blackboard bold.     (line   6)
+* bm package:                            \boldmath & \unboldmath.
+                                                              (line  32)
 * bold font:                             Font styles.         (line  71)
 * bold math:                             Font styles.         (line 130)
 * bold typewriter, avoiding:             description.         (line  34)
+* boldface mathematics:                  \boldmath & \unboldmath.
+                                                              (line   6)
 * box, allocating new:                   \newsavebox.         (line   6)
 * box, colored:                          Colored boxes.       (line   6)
 * boxes:                                 Boxes.               (line   6)
@@ -12175,9 +12392,10 @@
 * breve accent:                          Accents.             (line  86)
 * breve accent, math:                    Math accents.        (line  17)
 * bug reporting:                         About this document. (line  21)
-* bullet symbol:                         Math symbols.        (line 114)
+* bullet symbol:                         Math symbols.        (line 119)
 * bullet, in text:                       Text symbols.        (line  91)
 * bulleted lists:                        itemize.             (line   6)
+* caligraphic:                           Caligraphic.         (line   6)
 * calligraphic letters for math:         Font styles.         (line  74)
 * cap height:                            Text symbols.        (line  99)
 * caron accent:                          Accents.             (line  97)
@@ -12280,7 +12498,7 @@
 * cprotect package <1>:                  \verb.               (line  34)
 * creating pictures:                     picture.             (line   6)
 * creating tables:                       table.               (line   6)
-* credit footnote:                       \maketitle.          (line  22)
+* credit footnote:                       \maketitle.          (line  46)
 * cross references:                      Cross references.    (line   6)
 * cross references, resolving:           Output files.        (line  33)
 * cross referencing with page number:    \pageref.            (line   6)
@@ -12290,7 +12508,7 @@
 * dagger, double, in text:               Text symbols.        (line 107)
 * dagger, in text:                       Text symbols.        (line  15)
 * dagger, in text <1>:                   Text symbols.        (line 104)
-* date, for titlepage:                   \maketitle.          (line  18)
+* date, for titlepage:                   \maketitle.          (line  42)
 * date, today's:                         \today.              (line   6)
 * datetime package:                      \today.              (line  22)
 * define color:                          Define colors.       (line   6)
@@ -12343,6 +12561,7 @@
 * double spacing:                        Low-level font commands.
                                                               (line 118)
 * double vertical bar, in text:          Text symbols.        (line  79)
+* doublestruck:                          Blackboard bold.     (line   6)
 * e-dash:                                Text symbols.        (line 116)
 * e-TeX:                                 TeX engines.         (line  12)
 * ellipsis:                              Text symbols.        (line  36)
@@ -12390,6 +12609,7 @@
 * external files, writing:               filecontents.        (line   6)
 * families, of fonts:                    Low-level font commands.
                                                               (line  21)
+* fancyhdr package:                      Page styles.         (line  12)
 * fancyvrb package:                      tabbing.             (line 145)
 * fancyvrb package <1>:                  verbatim.            (line  37)
 * feminine ordinal symbol:               Text symbols.        (line 135)
@@ -12617,8 +12837,11 @@
                                                               (line   6)
 * math symbols:                          Math symbols.        (line   6)
 * math, bold:                            Font styles.         (line 130)
+* mathtools package:                     Math formulas.       (line  21)
 * mfirstuc package:                      Upper and lower case.
                                                               (line  45)
+* mhchem package:                        Subscripts & superscripts.
+                                                              (line  60)
 * Millimeter:                            Units of length.     (line  27)
 * minipage, creating a:                  minipage.            (line   6)
 * minted package:                        tabbing.             (line 145)
@@ -12692,14 +12915,19 @@
 * package options <1>:                   Class and package commands.
                                                               (line  66)
 * package, algorithm2e:                  tabbing.             (line 145)
+* package, amsfonts:                     Math formulas.       (line  21)
 * package, amsmath:                      array.               (line  42)
 * package, amsmath <1>:                  displaymath.         (line  22)
 * package, amsmath <2>:                  theorem.             (line  28)
+* package, amsmath <3>:                  Math formulas.       (line  21)
+* package, amsmath <4>:                  Math functions.      (line 111)
 * package, amsthm:                       theorem.             (line  28)
 * package, babel:                        thebibliography.     (line  53)
 * package, babel <1>:                    Accents.             (line   6)
 * package, bigfoot:                      Footnotes of footnotes.
                                                               (line   6)
+* package, bm:                           \boldmath & \unboldmath.
+                                                              (line  32)
 * package, cleveref:                     Cross references.    (line  38)
 * package, cleveref <1>:                 \footnotemark.       (line  48)
 * package, cprotect:                     verbatim.            (line  26)
@@ -12709,6 +12937,7 @@
 * package, envlab:                       \makelabels.         (line  49)
 * package, etoolbox:                     Class and package commands.
                                                               (line 110)
+* package, fancyhdr:                     Page styles.         (line  12)
 * package, fancyvrb:                     tabbing.             (line 145)
 * package, fancyvrb <1>:                 verbatim.            (line  37)
 * package, flafter:                      Floats.              (line  82)
@@ -12724,8 +12953,11 @@
 * package, macros2e:                     \makeatletter and \makeatother.
                                                               (line  39)
 * package, makeidx:                      Indexes.             (line  28)
+* package, mathtools:                    Math formulas.       (line  21)
 * package, mfirstuc:                     Upper and lower case.
                                                               (line  45)
+* package, mhchem:                       Subscripts & superscripts.
+                                                              (line  60)
 * package, minted:                       tabbing.             (line 145)
 * package, minted <1>:                   verbatim.            (line  31)
 * package, multind:                      Indexes.             (line  39)
@@ -12733,9 +12965,11 @@
 * package, setspace:                     Low-level font commands.
                                                               (line 118)
 * package, showidx:                      Indexes.             (line  35)
+* package, symbols:                      Math symbols.        (line  10)
 * package, textcase:                     Upper and lower case.
                                                               (line  42)
 * package, textcomp:                     Font styles.         (line 134)
+* package, ulem:                         Math miscellany.     (line  79)
 * package, url:                          \verb.               (line  30)
 * package, verbatimbox:                  verbatim.            (line  37)
 * package, xspace:                       \(SPACE) after control sequence.
@@ -12797,7 +13031,7 @@
 * prompt, *:                             Command line.        (line  18)
 * pronunciation:                         Overview.            (line  24)
 * quad:                                  Spacing in math mode.
-                                                              (line  32)
+                                                              (line  38)
 * question mark, upside-down:            Text symbols.        (line 141)
 * quotation marks, French:               Text symbols.        (line  30)
 * quote, single straight:                Text symbols.        (line 156)
@@ -12913,6 +13147,9 @@
                                                               (line   6)
 * superscript:                           Subscripts & superscripts.
                                                               (line   6)
+* symbols package:                       Math symbols.        (line  10)
+* symbols, boldface:                     \boldmath & \unboldmath.
+                                                              (line   6)
 * symbols, math:                         Math symbols.        (line   6)
 * symbols, text:                         Text symbols.        (line   6)
 * tab stops, using:                      tabbing.             (line   6)
@@ -12937,7 +13174,7 @@
 * textcase package:                      Upper and lower case.
                                                               (line  42)
 * textcomp package:                      Font styles.         (line 134)
-* thanks, for titlepage:                 \maketitle.          (line  22)
+* thanks, for titlepage:                 \maketitle.          (line  46)
 * theorem-like environment:              \newtheorem.         (line   6)
 * theorems, defining:                    \newtheorem.         (line   6)
 * theorems, typesetting:                 theorem.             (line   6)
@@ -12951,7 +13188,7 @@
 * title page, separate or run-in:        Document class options.
                                                               (line  71)
 * title pages, creating:                 titlepage.           (line   6)
-* title, for titlepage:                  \maketitle.          (line  26)
+* title, for titlepage:                  \maketitle.          (line  50)
 * titles, making:                        \maketitle.          (line   6)
 * trademark symbol:                      Text symbols.        (line 172)
 * transcript file:                       Output files.        (line  28)
@@ -12965,6 +13202,7 @@
 * typefaces:                             Fonts.               (line   6)
 * typewriter font:                       Font styles.         (line  92)
 * typewriter labels in lists:            description.         (line  34)
+* ulem package:                          Math miscellany.     (line  79)
 * umlaut accent:                         Accents.             (line  16)
 * underbar:                              Accents.             (line  89)
 * underscore, in text:                   Text symbols.        (line 178)
@@ -13015,7 +13253,6 @@
  * Menu:
 
-* $:                                     Math formulas.       (line  24)
 * &:                                     tabular.             (line  32)
 * --help command-line option:            Command line.        (line  14)
 * .aux file:                             Output files.        (line  33)
@@ -13041,7 +13278,7 @@
 * \ character starting commands:         LaTeX command syntax.
                                                               (line   6)
 * \!:                                    Spacing in math mode.
-                                                              (line  29)
+                                                              (line  35)
 * \" (umlaut accent):                    Accents.             (line  16)
 * \#:                                    Reserved characters. (line  13)
 * \$:                                    Reserved characters. (line  13)
@@ -13049,27 +13286,25 @@
 * \&:                                    Reserved characters. (line  13)
 * \' (acute accent):                     Accents.             (line  20)
 * \' (tabbing):                          tabbing.             (line  87)
-* \(:                                    Math formulas.       (line  16)
 * \(SPACE):                              \(SPACE) and \@.     (line   6)
-* \):                                    Math formulas.       (line  16)
 * \*:                                    Math miscellany.     (line   6)
 * \+:                                    tabbing.             (line  79)
 * \,:                                    Spacing in math mode.
-                                                              (line  25)
+                                                              (line  31)
 * \-:                                    tabbing.             (line  83)
 * \- (hyphenation):                      \- (hyphenation).    (line   6)
 * \. (dot-over accent):                  Accents.             (line  25)
 * \/:                                    \/.                  (line   6)
 * \::                                    Spacing in math mode.
-                                                              (line  21)
+                                                              (line  27)
 * \;:                                    Spacing in math mode.
-                                                              (line  16)
+                                                              (line  22)
 * \<:                                    tabbing.             (line  75)
 * \= (macron accent):                    Accents.             (line  29)
 * \= (tabbing):                          tabbing.             (line  69)
 * \>:                                    tabbing.             (line  73)
 * \> <1>:                                Spacing in math mode.
-                                                              (line  21)
+                                                              (line  27)
 * \> (tabbing):                          tabbing.             (line  72)
 * \@:                                    \(SPACE) and \@.     (line   6)
 * \@beginparpenalty:                     list.                (line 236)
@@ -13096,19 +13331,19 @@
                                                               (line  16)
 * \AE (AE):                              Additional Latin letters.
                                                               (line  16)
-* \aleph:                                Math symbols.        (line  22)
+* \aleph:                                Math symbols.        (line  27)
 * \Alph example:                         enumerate.           (line  61)
-* \alpha:                                Math symbols.        (line  25)
+* \alpha:                                Math symbols.        (line  30)
 * \alph{COUNTER}:                        \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                               (line  14)
 * \Alph{COUNTER}:                        \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                               (line  19)
 * \alsoname:                             Indexes.             (line  20)
-* \amalg:                                Math symbols.        (line  28)
-* \and for \author:                      \maketitle.          (line  12)
-* \angle:                                Math symbols.        (line  31)
+* \amalg:                                Math symbols.        (line  33)
+* \and for \author:                      \maketitle.          (line  35)
+* \angle:                                Math symbols.        (line  36)
 * \appendix:                             Sectioning.          (line  37)
-* \approx:                               Math symbols.        (line  36)
+* \approx:                               Math symbols.        (line  41)
 * \arabic{COUNTER}:                      \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                               (line  24)
 * \arccos:                               Math functions.      (line   9)
@@ -13118,8 +13353,8 @@
 * \arraycolsep:                          array.               (line  39)
 * \arrayrulewidth:                       tabular.             (line 157)
 * \arraystretch:                         tabular.             (line 163)
-* \ast:                                  Math symbols.        (line  39)
-* \asymp:                                Math symbols.        (line  48)
+* \ast:                                  Math symbols.        (line  44)
+* \asymp:                                Math symbols.        (line  53)
 * \AtBeginDocument:                      \AtBeginDocument.    (line   6)
 * \AtBeginDvi:                           Class and package commands.
                                                               (line   9)
@@ -13128,50 +13363,53 @@
                                                               (line  14)
 * \AtEndOfPackage:                       Class and package commands.
                                                               (line  14)
-* \author{NAME \and NAME2}:              \maketitle.          (line  11)
+* \author{NAME \and NAME2}:              \maketitle.          (line  34)
 * \a` (grave accent in tabbing):         tabbing.             (line 103)
 * \b (bar-under accent):                 Accents.             (line  46)
-* \backslash:                            Math symbols.        (line  51)
+* \backslash:                            Math symbols.        (line  56)
 * \bar:                                  Math accents.        (line  13)
 * \baselineskip:                         Low-level font commands.
                                                               (line 101)
 * \baselinestretch:                      Low-level font commands.
                                                               (line 111)
 * \begin:                                Environments.        (line   6)
-* \beta:                                 Math symbols.        (line  55)
+* \beta:                                 Math symbols.        (line  60)
 * \bf:                                   Font styles.         (line  70)
 * \bfseries:                             Font styles.         (line  39)
 * \bibitem:                              \bibitem.            (line   6)
 * \bibliography:                         Using BibTeX.        (line   6)
 * \bibliographystyle:                    Using BibTeX.        (line   6)
-* \bigcap:                               Math symbols.        (line  58)
-* \bigcirc:                              Math symbols.        (line  62)
-* \bigcup:                               Math symbols.        (line  66)
-* \bigodot:                              Math symbols.        (line  70)
-* \bigoplus:                             Math symbols.        (line  73)
-* \bigotimes:                            Math symbols.        (line  76)
+* \bigcap:                               Math symbols.        (line  63)
+* \bigcirc:                              Math symbols.        (line  67)
+* \bigcup:                               Math symbols.        (line  71)
+* \bigodot:                              Math symbols.        (line  75)
+* \bigoplus:                             Math symbols.        (line  78)
+* \bigotimes:                            Math symbols.        (line  81)
 * \bigskip:                              \bigskip \medskip \smallskip.
                                                               (line   9)
 * \bigskipamount:                        \bigskip \medskip \smallskip.
                                                               (line  10)
-* \bigsqcup:                             Math symbols.        (line  87)
-* \bigtriangledown:                      Math symbols.        (line  79)
-* \bigtriangleup:                        Math symbols.        (line  83)
-* \biguplus:                             Math symbols.        (line  90)
-* \bigvee:                               Math symbols.        (line  94)
-* \bigwedge:                             Math symbols.        (line  97)
+* \bigsqcup:                             Math symbols.        (line  92)
+* \bigtriangledown:                      Math symbols.        (line  84)
+* \bigtriangleup:                        Math symbols.        (line  88)
+* \biguplus:                             Math symbols.        (line  95)
+* \bigvee:                               Math symbols.        (line  99)
+* \bigwedge:                             Math symbols.        (line 102)
 * \bmod:                                 Math functions.      (line  21)
-* \boldmath:                             Math formulas.       (line  29)
-* \bot:                                  Math symbols.        (line 100)
+* \boldmath:                             \boldmath & \unboldmath.
+                                                              (line   6)
+* \boldmath <1>:                         \boldmath & \unboldmath.
+                                                              (line  14)
+* \bot:                                  Math symbols.        (line 105)
 * \bottomfraction:                       Floats.              (line  94)
 * \bottomfraction <1>:                   Floats.              (line  95)
-* \bowtie:                               Math symbols.        (line 105)
-* \Box:                                  Math symbols.        (line 108)
+* \bowtie:                               Math symbols.        (line 110)
+* \Box:                                  Math symbols.        (line 113)
 * \breve:                                Math accents.        (line  16)
-* \bullet:                               Math symbols.        (line 113)
+* \bullet:                               Math symbols.        (line 118)
 * \c (cedilla accent):                   Accents.             (line  51)
 * \cal:                                  Font styles.         (line  73)
-* \cap:                                  Math symbols.        (line 116)
+* \cap:                                  Math symbols.        (line 121)
 * \capitalacute:                         Accents.             (line  20)
 * \capitalbreve:                         Accents.             (line  86)
 * \capitalcaron:                         Accents.             (line  97)
@@ -13190,7 +13428,7 @@
 * \caption:                              figure.              (line  42)
 * \caption <1>:                          table.               (line  47)
 * \cc:                                   \cc.                 (line   6)
-* \cdot:                                 Math symbols.        (line 121)
+* \cdot:                                 Math symbols.        (line 126)
 * \cdots:                                Math miscellany.     (line  25)
 * \centering:                            \centering.          (line   6)
 * \chapter:                              Sectioning.          (line   9)
@@ -13199,8 +13437,8 @@
                                                               (line  21)
 * \CheckCommand*:                        Class and package commands.
                                                               (line  21)
-* \chi:                                  Math symbols.        (line 124)
-* \circ:                                 Math symbols.        (line 127)
+* \chi:                                  Math symbols.        (line 129)
+* \circ:                                 Math symbols.        (line 132)
 * \circle:                               \circle.             (line   6)
 * \cite:                                 \cite.               (line   6)
 * \ClassError:                           Class and package commands.
@@ -13219,7 +13457,7 @@
                                                               (line   6)
 * \cline:                                \cline.              (line   6)
 * \closing:                              \closing.            (line   6)
-* \clubsuit:                             Math symbols.        (line 132)
+* \clubsuit:                             Math symbols.        (line 137)
 * \columnsep:                            \twocolumn.          (line  22)
 * \columnsep <1>:                        Page layout parameters.
                                                               (line   6)
@@ -13235,25 +13473,25 @@
                                                               (line   8)
 * \columnwidth <2>:                      Page layout parameters.
                                                               (line   9)
-* \complement:                           Math symbols.        (line 135)
-* \cong:                                 Math symbols.        (line 141)
+* \complement:                           Math symbols.        (line 140)
+* \cong:                                 Math symbols.        (line 146)
 * \contentsline:                         \addcontentsline.    (line  33)
-* \coprod:                               Math symbols.        (line 144)
+* \coprod:                               Math symbols.        (line 149)
 * \copyright:                            Text symbols.        (line  10)
 * \cos:                                  Math functions.      (line  24)
 * \cosh:                                 Math functions.      (line  27)
 * \cot:                                  Math functions.      (line  30)
 * \coth:                                 Math functions.      (line  33)
 * \csc:                                  Math functions.      (line  36)
-* \cup:                                  Math symbols.        (line 147)
+* \cup:                                  Math symbols.        (line 152)
 * \CurrentOption:                        Class and package commands.
                                                               (line  60)
 * \d (dot-under accent):                 Accents.             (line  55)
 * \dag:                                  Text symbols.        (line  14)
-* \dagger:                               Math symbols.        (line 152)
+* \dagger:                               Math symbols.        (line 157)
 * \dashbox:                              \dashbox.            (line   6)
-* \dashv:                                Math symbols.        (line 155)
-* \date{TEXT}:                           \maketitle.          (line  17)
+* \dashv:                                Math symbols.        (line 160)
+* \date{TEXT}:                           \maketitle.          (line  41)
 * \day:                                  \day \month \year.   (line   6)
 * \dblfloatpagefraction:                 \twocolumn.          (line  69)
 * \dblfloatsep:                          \twocolumn.          (line  75)
@@ -13261,7 +13499,7 @@
 * \dbltopfraction:                       \twocolumn.          (line  47)
 * \dbltopnumber:                         \twocolumn.          (line  87)
 * \ddag:                                 Text symbols.        (line  17)
-* \ddagger:                              Math symbols.        (line 159)
+* \ddagger:                              Math symbols.        (line 164)
 * \ddot:                                 Math accents.        (line  22)
 * \ddots:                                Math miscellany.     (line  29)
 * \DeclareGraphicsExtensions:            \DeclareGraphicsExtensions.
@@ -13277,35 +13515,35 @@
 * \DeclareRobustCommand*:                Class and package commands.
                                                               (line  96)
 * \deg:                                  Math functions.      (line  39)
-* \Delta:                                Math symbols.        (line 162)
-* \delta:                                Math symbols.        (line 165)
+* \Delta:                                Math symbols.        (line 167)
+* \delta:                                Math symbols.        (line 170)
 * \depth:                                Predefined lengths.  (line  10)
 * \det:                                  Math functions.      (line  42)
 * \dh (d):                               Additional Latin letters.
                                                               (line  20)
 * \DH (D):                               Additional Latin letters.
                                                               (line  20)
-* \Diamond:                              Math symbols.        (line 168)
-* \diamond:                              Math symbols.        (line 172)
-* \diamondsuit:                          Math symbols.        (line 176)
+* \Diamond:                              Math symbols.        (line 173)
+* \diamond:                              Math symbols.        (line 177)
+* \diamondsuit:                          Math symbols.        (line 181)
 * \dim:                                  Math functions.      (line  45)
-* \displaystyle:                         Math formulas.       (line  34)
-* \div:                                  Math symbols.        (line 179)
+* \displaystyle:                         Math formulas.       (line  52)
+* \div:                                  Math symbols.        (line 184)
 * \dj:                                   Additional Latin letters.
                                                               (line  26)
 * \DJ:                                   Additional Latin letters.
                                                               (line  26)
 * \documentclass:                        Document classes.    (line   6)
 * \dot:                                  Math accents.        (line  25)
-* \doteq:                                Math symbols.        (line 182)
+* \doteq:                                Math symbols.        (line 187)
 * \dotfill:                              \hrulefill \dotfill. (line   6)
 * \dots:                                 Text symbols.        (line  34)
 * \doublerulesep:                        tabular.             (line 168)
-* \downarrow:                            Math symbols.        (line 186)
-* \Downarrow:                            Math symbols.        (line 190)
-* \ell:                                  Math symbols.        (line 194)
+* \downarrow:                            Math symbols.        (line 191)
+* \Downarrow:                            Math symbols.        (line 195)
+* \ell:                                  Math symbols.        (line 199)
 * \emph:                                 Font styles.         (line  59)
-* \emptyset:                             Math symbols.        (line 197)
+* \emptyset:                             Math symbols.        (line 202)
 * \encl:                                 \encl.               (line   6)
 * \end:                                  Environments.        (line   6)
 * \endinput:                             \endinput.           (line   6)
@@ -13314,9 +13552,9 @@
 * \enumii:                               enumerate.           (line  47)
 * \enumiii:                              enumerate.           (line  47)
 * \enumiv:                               enumerate.           (line  47)
-* \epsilon:                              Math symbols.        (line 201)
-* \equiv:                                Math symbols.        (line 207)
-* \eta:                                  Math symbols.        (line 210)
+* \epsilon:                              Math symbols.        (line 206)
+* \equiv:                                Math symbols.        (line 212)
+* \eta:                                  Math symbols.        (line 215)
 * \evensidemargin:                       Document class options.
                                                               (line  84)
 * \evensidemargin <1>:                   Page layout parameters.
@@ -13325,7 +13563,7 @@
                                                               (line  68)
 * \ExecuteOptions:                       Class and package commands.
                                                               (line 166)
-* \exists:                               Math symbols.        (line 213)
+* \exists:                               Math symbols.        (line 218)
 * \exp:                                  Math functions.      (line  48)
 * \extracolsep:                          tabular.             (line 115)
 * \fbox:                                 \fbox and \framebox. (line   6)
@@ -13334,7 +13572,7 @@
 * \fboxsep:                              \framebox (picture). (line  13)
 * \fboxsep <1>:                          \fbox and \framebox. (line  18)
 * \fill:                                 \hfill.              (line   9)
-* \flat:                                 Math symbols.        (line 216)
+* \flat:                                 Math symbols.        (line 221)
 * \floatpagefraction:                    Floats.              (line  98)
 * \floatpagefraction <1>:                Floats.              (line  99)
 * \floatsep:                             Floats.              (line 114)
@@ -13363,22 +13601,22 @@
                                                               (line  26)
 * \footskip <1>:                         Page layout parameters.
                                                               (line  27)
-* \forall:                               Math symbols.        (line 219)
+* \forall:                               Math symbols.        (line 224)
 * \frac:                                 Math miscellany.     (line  33)
 * \frac{NUM}{DEN}:                       Math miscellany.     (line  32)
 * \frame:                                \frame.              (line   6)
 * \framebox:                             \framebox (picture). (line   6)
 * \framebox <1>:                         \fbox and \framebox. (line   6)
 * \frenchspacing:                        \frenchspacing.      (line   6)
-* \frown:                                Math symbols.        (line 222)
+* \frown:                                Math symbols.        (line 227)
 * \fussy:                                \fussy & \sloppy.    (line   6)
-* \Gamma:                                Math symbols.        (line 225)
-* \gamma:                                Math symbols.        (line 228)
+* \Gamma:                                Math symbols.        (line 230)
+* \gamma:                                Math symbols.        (line 233)
 * \gcd:                                  Math functions.      (line  51)
-* \ge:                                   Math symbols.        (line 231)
-* \geq:                                  Math symbols.        (line 235)
-* \gets:                                 Math symbols.        (line 239)
-* \gg:                                   Math symbols.        (line 242)
+* \ge:                                   Math symbols.        (line 236)
+* \geq:                                  Math symbols.        (line 240)
+* \gets:                                 Math symbols.        (line 244)
+* \gg:                                   Math symbols.        (line 247)
 * \glossary:                             Glossaries.          (line   8)
 * \glossaryentry:                        Glossaries.          (line  11)
 * \graphicspath:                         \graphicspath.       (line   6)
@@ -13390,7 +13628,7 @@
 * \guilsinglright (>):                   Text symbols.        (line  29)
 * \H (Hungarian umlaut accent):          Accents.             (line  59)
 * \hat:                                  Math accents.        (line  31)
-* \hbar:                                 Math symbols.        (line 246)
+* \hbar:                                 Math symbols.        (line 251)
 * \headheight:                           Page layout parameters.
                                                               (line  14)
 * \headheight <1>:                       Page layout parameters.
@@ -13399,13 +13637,13 @@
                                                               (line  19)
 * \headsep <1>:                          Page layout parameters.
                                                               (line  20)
-* \heartsuit:                            Math symbols.        (line 249)
+* \heartsuit:                            Math symbols.        (line 254)
 * \height:                               Predefined lengths.  (line   8)
 * \hfill:                                \hfill.              (line   6)
 * \hline:                                \hline.              (line   6)
 * \hom:                                  Math functions.      (line  54)
-* \hookleftarrow:                        Math symbols.        (line 252)
-* \hookrightarrow:                       Math symbols.        (line 255)
+* \hookleftarrow:                        Math symbols.        (line 257)
+* \hookrightarrow:                       Math symbols.        (line 260)
 * \hrulefill:                            \hrulefill \dotfill. (line   6)
 * \hsize:                                Page layout parameters.
                                                               (line 119)
@@ -13416,7 +13654,7 @@
 * \Huge:                                 Font sizes.          (line  11)
 * \hyphenation:                          \hyphenation.        (line   6)
 * \i (dotless i):                        Accents.             (line  63)
-* \iff:                                  Math symbols.        (line 258)
+* \iff:                                  Math symbols.        (line 263)
 * \IfFileExists:                         Class and package commands.
                                                               (line 127)
 * \ignorespaces:                         \ignorespaces & \ignorespacesafterend.
@@ -13427,9 +13665,9 @@
                                                               (line  32)
 * \IJ (IJ):                              Additional Latin letters.
                                                               (line  32)
-* \Im:                                   Math symbols.        (line 262)
+* \Im:                                   Math symbols.        (line 267)
 * \imath:                                Math accents.        (line  34)
-* \in:                                   Math symbols.        (line 265)
+* \in:                                   Math symbols.        (line 270)
 * \include:                              \include & \includeonly.
                                                               (line   6)
 * \includegraphics:                      \includegraphics.    (line   6)
@@ -13440,14 +13678,14 @@
 * \indexentry:                           Indexes.             (line  12)
 * \indexspace:                           Indexes.             (line  32)
 * \inf:                                  Math functions.      (line  57)
-* \infty:                                Math symbols.        (line 271)
+* \infty:                                Math symbols.        (line 276)
 * \input:                                \input.              (line   6)
 * \InputIfFileExists:                    Class and package commands.
                                                               (line 127)
-* \int:                                  Math symbols.        (line 274)
+* \int:                                  Math symbols.        (line 279)
 * \intextsep:                            Floats.              (line 118)
 * \intextsep <1>:                        Floats.              (line 119)
-* \iota:                                 Math symbols.        (line 277)
+* \iota:                                 Math symbols.        (line 282)
 * \it:                                   Font styles.         (line  76)
 * \item:                                 description.         (line  29)
 * \item <1>:                             enumerate.           (line  29)
@@ -13458,9 +13696,9 @@
 * \itshape:                              Font styles.         (line  33)
 * \j (dotless j):                        Accents.             (line  66)
 * \jmath:                                Math accents.        (line  37)
-* \Join:                                 Math symbols.        (line 280)
+* \Join:                                 Math symbols.        (line 285)
 * \k (ogonek):                           Accents.             (line  70)
-* \kappa:                                Math symbols.        (line 284)
+* \kappa:                                Math symbols.        (line 289)
 * \ker:                                  Math functions.      (line  60)
 * \kill:                                 tabbing.             (line 107)
 * \l (/l):                               Additional Latin letters.
@@ -13478,27 +13716,27 @@
 * \labelitemiv:                          itemize.             (line  34)
 * \labelsep:                             list.                (line  94)
 * \labelwidth:                           list.                (line  99)
-* \Lambda:                               Math symbols.        (line 287)
-* \lambda:                               Math symbols.        (line 290)
-* \land:                                 Math symbols.        (line 293)
-* \langle:                               Math symbols.        (line 298)
+* \Lambda:                               Math symbols.        (line 292)
+* \lambda:                               Math symbols.        (line 295)
+* \land:                                 Math symbols.        (line 298)
+* \langle:                               Math symbols.        (line 303)
 * \large:                                Font sizes.          (line  11)
 * \Large:                                Font sizes.          (line  11)
 * \LARGE:                                Font sizes.          (line  11)
 * \LaTeX:                                Text symbols.        (line  20)
 * \LaTeXe:                               Text symbols.        (line  23)
-* \lbrace:                               Math symbols.        (line 303)
-* \lbrack:                               Math symbols.        (line 307)
-* \lceil:                                Math symbols.        (line 311)
+* \lbrace:                               Math symbols.        (line 308)
+* \lbrack:                               Math symbols.        (line 312)
+* \lceil:                                Math symbols.        (line 316)
 * \ldots:                                Text symbols.        (line  33)
-* \le:                                   Math symbols.        (line 315)
-* \leadsto:                              Math symbols.        (line 319)
+* \le:                                   Math symbols.        (line 320)
+* \leadsto:                              Math symbols.        (line 324)
 * \left DELIM1 ... \right DELIM2:        Math miscellany.     (line  35)
-* \Leftarrow:                            Math symbols.        (line 326)
-* \leftarrow:                            Math symbols.        (line 331)
+* \Leftarrow:                            Math symbols.        (line 331)
+* \leftarrow:                            Math symbols.        (line 336)
 * \lefteqn:                              eqnarray.            (line  46)
-* \leftharpoondown:                      Math symbols.        (line 335)
-* \leftharpoonup:                        Math symbols.        (line 338)
+* \leftharpoondown:                      Math symbols.        (line 340)
+* \leftharpoonup:                        Math symbols.        (line 343)
 * \leftmargin:                           itemize.             (line  53)
 * \leftmargin <1>:                       list.                (line 119)
 * \leftmargini:                          itemize.             (line  53)
@@ -13507,12 +13745,12 @@
 * \leftmarginiv:                         itemize.             (line  53)
 * \leftmarginv:                          itemize.             (line  53)
 * \leftmarginvi:                         itemize.             (line  53)
-* \Leftrightarrow:                       Math symbols.        (line 341)
-* \leftrightarrow:                       Math symbols.        (line 346)
-* \leq:                                  Math symbols.        (line 351)
-* \lfloor:                               Math symbols.        (line 355)
+* \Leftrightarrow:                       Math symbols.        (line 346)
+* \leftrightarrow:                       Math symbols.        (line 351)
+* \leq:                                  Math symbols.        (line 356)
+* \lfloor:                               Math symbols.        (line 360)
 * \lg:                                   Math functions.      (line  63)
-* \lhd:                                  Math symbols.        (line 358)
+* \lhd:                                  Math symbols.        (line 363)
 * \lim:                                  Math functions.      (line  66)
 * \liminf:                               Math functions.      (line  69)
 * \limsup:                               Math functions.      (line  72)
@@ -13529,20 +13767,20 @@
 * \listoffigures:                        Tables of contents.  (line  16)
 * \listoftables:                         Tables of contents.  (line  16)
 * \listparindent:                        list.                (line 136)
-* \ll:                                   Math symbols.        (line 366)
+* \ll:                                   Math symbols.        (line 371)
 * \ln:                                   Math functions.      (line  75)
-* \lnot:                                 Math symbols.        (line 370)
+* \lnot:                                 Math symbols.        (line 375)
 * \LoadClass:                            Class and package commands.
                                                               (line 144)
 * \LoadClassWithOptions:                 Class and package commands.
                                                               (line 144)
 * \location:                             \location.           (line   6)
 * \log:                                  Math functions.      (line  78)
-* \longleftarrow:                        Math symbols.        (line 373)
-* \longleftrightarrow:                   Math symbols.        (line 378)
-* \longmapsto:                           Math symbols.        (line 382)
-* \longrightarrow:                       Math symbols.        (line 387)
-* \lor:                                  Math symbols.        (line 392)
+* \longleftarrow:                        Math symbols.        (line 378)
+* \longleftrightarrow:                   Math symbols.        (line 383)
+* \longmapsto:                           Math symbols.        (line 387)
+* \longrightarrow:                       Math symbols.        (line 392)
+* \lor:                                  Math symbols.        (line 397)
 * \lq:                                   Text symbols.        (line  39)
 * \makebox:                              \makebox.            (line   6)
 * \makebox (for picture):                \makebox (picture).  (line   6)
@@ -13551,7 +13789,7 @@
 * \makelabel:                            list.                (line  55)
 * \makelabels:                           \makelabels.         (line   6)
 * \maketitle:                            \maketitle.          (line   6)
-* \mapsto:                               Math symbols.        (line 395)
+* \mapsto:                               Math symbols.        (line 400)
 * \marginpar:                            Marginal notes.      (line   6)
 * \marginparpush:                        Page layout parameters.
                                                               (line  40)
@@ -13592,25 +13830,25 @@
 * \medskipamount:                        \bigskip \medskip \smallskip.
                                                               (line  15)
 * \medspace:                             Spacing in math mode.
-                                                              (line  21)
-* \mho:                                  Math symbols.        (line 399)
-* \mid:                                  Math symbols.        (line 404)
+                                                              (line  27)
+* \mho:                                  Math symbols.        (line 404)
+* \mid:                                  Math symbols.        (line 409)
 * \min:                                  Math functions.      (line  84)
-* \models:                               Math symbols.        (line 414)
+* \models:                               Math symbols.        (line 419)
 * \month:                                \day \month \year.   (line   6)
-* \mp:                                   Math symbols.        (line 419)
-* \mu:                                   Math symbols.        (line 422)
+* \mp:                                   Math symbols.        (line 424)
+* \mu:                                   Math symbols.        (line 427)
 * \multicolumn:                          \multicolumn.        (line   6)
 * \multiput:                             \multiput.           (line   6)
-* \nabla:                                Math symbols.        (line 425)
+* \nabla:                                Math symbols.        (line 430)
 * \name:                                 \name.               (line   6)
-* \natural:                              Math symbols.        (line 428)
-* \ne:                                   Math symbols.        (line 431)
-* \nearrow:                              Math symbols.        (line 434)
+* \natural:                              Math symbols.        (line 433)
+* \ne:                                   Math symbols.        (line 436)
+* \nearrow:                              Math symbols.        (line 439)
 * \NeedsTeXFormat:                       Class and package commands.
                                                               (line 176)
-* \neg:                                  Math symbols.        (line 437)
-* \neq:                                  Math symbols.        (line 441)
+* \neg:                                  Math symbols.        (line 442)
+* \neq:                                  Math symbols.        (line 446)
 * \newcommand:                           \newcommand & \renewcommand.
                                                               (line   6)
 * \newcounter:                           \newcounter.         (line   6)
@@ -13628,7 +13866,7 @@
                                                               (line  40)
 * \NG:                                   Additional Latin letters.
                                                               (line  40)
-* \ni:                                   Math symbols.        (line 444)
+* \ni:                                   Math symbols.        (line 449)
 * \nocite:                               \nocite.             (line   6)
 * \nocorr:                               Font styles.         (line  21)
 * \nocorrlist:                           Font styles.         (line  21)
@@ -13644,10 +13882,10 @@
 * \normalmarginpar:                      Marginal notes.      (line  23)
 * \normalsfcodes:                        \normalsfcodes.      (line   6)
 * \normalsize:                           Font sizes.          (line  11)
-* \not:                                  Math symbols.        (line 449)
-* \notin:                                Math symbols.        (line 457)
-* \nu:                                   Math symbols.        (line 461)
-* \nwarrow:                              Math symbols.        (line 464)
+* \not:                                  Math symbols.        (line 454)
+* \notin:                                Math symbols.        (line 462)
+* \nu:                                   Math symbols.        (line 466)
+* \nwarrow:                              Math symbols.        (line 469)
 * \o (/o):                               Additional Latin letters.
                                                               (line  44)
 * \O (/O):                               Additional Latin letters.
@@ -13660,27 +13898,27 @@
                                                               (line  66)
 * \oddsidemargin <2>:                    Page layout parameters.
                                                               (line  68)
-* \odot:                                 Math symbols.        (line 467)
+* \odot:                                 Math symbols.        (line 472)
 * \oe (oe):                              Additional Latin letters.
                                                               (line  48)
 * \OE (OE):                              Additional Latin letters.
                                                               (line  48)
-* \oint:                                 Math symbols.        (line 472)
+* \oint:                                 Math symbols.        (line 477)
 * \oldstylenums:                         Font styles.         (line 134)
-* \Omega:                                Math symbols.        (line 476)
-* \omega:                                Math symbols.        (line 479)
-* \ominus:                               Math symbols.        (line 482)
+* \Omega:                                Math symbols.        (line 481)
+* \omega:                                Math symbols.        (line 484)
+* \ominus:                               Math symbols.        (line 487)
 * \onecolumn:                            \onecolumn.          (line   6)
 * \opening:                              \opening.            (line   6)
-* \oplus:                                Math symbols.        (line 485)
+* \oplus:                                Math symbols.        (line 490)
 * \OptionNotUsed:                        Class and package commands.
                                                               (line 192)
-* \oslash:                               Math symbols.        (line 489)
-* \otimes:                               Math symbols.        (line 492)
+* \oslash:                               Math symbols.        (line 494)
+* \otimes:                               Math symbols.        (line 497)
 * \oval:                                 \oval.               (line   6)
 * \overbrace{MATH}:                      Math miscellany.     (line  58)
 * \overline{TEXT}:                       Math miscellany.     (line  62)
-* \owns:                                 Math symbols.        (line 497)
+* \owns:                                 Math symbols.        (line 502)
 * \P:                                    Text symbols.        (line  42)
 * \PackageError:                         Class and package commands.
                                                               (line  41)
@@ -13707,7 +13945,7 @@
                                                               (line  86)
 * \par:                                  \par.                (line   6)
 * \paragraph:                            Sectioning.          (line  14)
-* \parallel:                             Math symbols.        (line 502)
+* \parallel:                             Math symbols.        (line 507)
 * \parbox:                               \parbox.             (line   6)
 * \parindent:                            minipage.            (line 108)
 * \parindent <1>:                        \indent & \noindent. (line   6)
@@ -13718,7 +13956,7 @@
                                                               (line   6)
 * \parskip example:                      itemize.             (line  72)
 * \part:                                 Sectioning.          (line   8)
-* \partial:                              Math symbols.        (line 505)
+* \partial:                              Math symbols.        (line 510)
 * \partopsep:                            list.                (line 151)
 * \PassOptionsToClass:                   Class and package commands.
                                                               (line 198)
@@ -13728,26 +13966,26 @@
                                                               (line  40)
 * \pdfpagewidth:                         Document class options.
                                                               (line  40)
-* \perp:                                 Math symbols.        (line 508)
-* \phi:                                  Math symbols.        (line 513)
-* \Pi:                                   Math symbols.        (line 517)
-* \pi:                                   Math symbols.        (line 520)
-* \pm:                                   Math symbols.        (line 524)
+* \perp:                                 Math symbols.        (line 513)
+* \phi:                                  Math symbols.        (line 518)
+* \Pi:                                   Math symbols.        (line 522)
+* \pi:                                   Math symbols.        (line 525)
+* \pm:                                   Math symbols.        (line 529)
 * \pmod:                                 Math functions.      (line  87)
 * \poptabs:                              tabbing.             (line 113)
 * \poptabs <1>:                          tabbing.             (line 114)
 * \pounds:                               Text symbols.        (line  46)
 * \Pr:                                   Math functions.      (line  90)
-* \prec:                                 Math symbols.        (line 527)
-* \preceq:                               Math symbols.        (line 530)
-* \prime:                                Math symbols.        (line 535)
+* \prec:                                 Math symbols.        (line 532)
+* \preceq:                               Math symbols.        (line 535)
+* \prime:                                Math symbols.        (line 540)
 * \printindex:                           Indexes.             (line  28)
 * \ProcessOptions:                       Class and package commands.
                                                               (line 232)
 * \ProcessOptions*:                      Class and package commands.
                                                               (line 232)
-* \prod:                                 Math symbols.        (line 544)
-* \propto:                               Math symbols.        (line 547)
+* \prod:                                 Math symbols.        (line 549)
+* \propto:                               Math symbols.        (line 552)
 * \protect:                              \protect.            (line   6)
 * \providecommand:                       \providecommand.     (line   6)
 * \ProvidesClass:                        Class and package commands.
@@ -13757,15 +13995,15 @@
 * \ProvidesPackage:                      Class and package commands.
                                                               (line 270)
 * \ps:                                   \ps.                 (line   6)
-* \Psi:                                  Math symbols.        (line 550)
-* \psi:                                  Math symbols.        (line 553)
+* \Psi:                                  Math symbols.        (line 555)
+* \psi:                                  Math symbols.        (line 558)
 * \pushtabs:                             tabbing.             (line 116)
 * \put:                                  \put.                (line   6)
 * \qbezier:                              \qbezier.            (line   6)
 * \qquad:                                Spacing in math mode.
+                                                              (line  44)
+* \quad:                                 Spacing in math mode.
                                                               (line  38)
-* \quad:                                 Spacing in math mode.
-                                                              (line  32)
 * \quotedblbase (,,):                    Text symbols.        (line  50)
 * \quotesinglbase (,):                   Text symbols.        (line  51)
 * \r (ring accent):                      Accents.             (line  75)
@@ -13773,11 +14011,11 @@
 * \raggedleft:                           \raggedleft.         (line   6)
 * \raggedright:                          \raggedright.        (line   6)
 * \raisebox:                             \raisebox.           (line   6)
-* \rangle:                               Math symbols.        (line 556)
-* \rbrace:                               Math symbols.        (line 560)
-* \rbrack:                               Math symbols.        (line 564)
-* \rceil:                                Math symbols.        (line 568)
-* \Re:                                   Math symbols.        (line 571)
+* \rangle:                               Math symbols.        (line 561)
+* \rbrace:                               Math symbols.        (line 565)
+* \rbrack:                               Math symbols.        (line 569)
+* \rceil:                                Math symbols.        (line 573)
+* \Re:                                   Math symbols.        (line 576)
 * \ref:                                  \ref.                (line   6)
 * \reflectbox:                           \scalebox.           (line   6)
 * \refstepcounter:                       \refstepcounter.     (line   6)
@@ -13790,18 +14028,18 @@
 * \resizebox:                            \resizebox.          (line   6)
 * \restorecr:                            \obeycr & \restorecr.
                                                               (line   6)
-* \restriction:                          Math symbols.        (line 576)
-* \revemptyset:                          Math symbols.        (line 581)
+* \restriction:                          Math symbols.        (line 581)
+* \revemptyset:                          Math symbols.        (line 586)
 * \reversemarginpar:                     Marginal notes.      (line  23)
-* \rfloor:                               Math symbols.        (line 586)
-* \rhd:                                  Math symbols.        (line 590)
-* \rho:                                  Math symbols.        (line 597)
+* \rfloor:                               Math symbols.        (line 591)
+* \rhd:                                  Math symbols.        (line 595)
+* \rho:                                  Math symbols.        (line 602)
 * \right:                                Math miscellany.     (line  36)
-* \Rightarrow:                           Math symbols.        (line 601)
-* \rightarrow:                           Math symbols.        (line 605)
-* \rightharpoondown:                     Math symbols.        (line 610)
-* \rightharpoonup:                       Math symbols.        (line 613)
-* \rightleftharpoons:                    Math symbols.        (line 616)
+* \Rightarrow:                           Math symbols.        (line 606)
+* \rightarrow:                           Math symbols.        (line 610)
+* \rightharpoondown:                     Math symbols.        (line 615)
+* \rightharpoonup:                       Math symbols.        (line 618)
+* \rightleftharpoons:                    Math symbols.        (line 621)
 * \rightmargin:                          list.                (line 166)
 * \rm:                                   Font styles.         (line  79)
 * \rmfamily:                             Font styles.         (line  30)
@@ -13819,7 +14057,7 @@
 * \scalebox:                             \scalebox.           (line   6)
 * \scriptsize:                           Font sizes.          (line  11)
 * \scshape:                              Font styles.         (line  51)
-* \searrow:                              Math symbols.        (line 619)
+* \searrow:                              Math symbols.        (line 624)
 * \sec:                                  Math functions.      (line  93)
 * \section:                              Sectioning.          (line  11)
 * \seename:                              Indexes.             (line  20)
@@ -13827,62 +14065,62 @@
                                                               (line 131)
 * \setcounter:                           \setcounter.         (line   6)
 * \setlength:                            \setlength.          (line   6)
-* \setminus:                             Math symbols.        (line 622)
+* \setminus:                             Math symbols.        (line 627)
 * \settodepth:                           \settodepth.         (line   6)
 * \settoheight:                          \settoheight.        (line   6)
 * \settowidth:                           \settowidth.         (line   6)
 * \sf:                                   Font styles.         (line  85)
 * \sffamily:                             Font styles.         (line  48)
-* \sharp:                                Math symbols.        (line 628)
+* \sharp:                                Math symbols.        (line 633)
 * \shortstack:                           \shortstack.         (line   6)
-* \Sigma:                                Math symbols.        (line 631)
-* \sigma:                                Math symbols.        (line 634)
+* \Sigma:                                Math symbols.        (line 636)
+* \sigma:                                Math symbols.        (line 639)
 * \signature:                            \signature.          (line  11)
-* \sim:                                  Math symbols.        (line 638)
-* \simeq:                                Math symbols.        (line 641)
+* \sim:                                  Math symbols.        (line 643)
+* \simeq:                                Math symbols.        (line 646)
 * \sin:                                  Math functions.      (line  96)
 * \sinh:                                 Math functions.      (line  99)
 * \sl:                                   Font styles.         (line  88)
 * \sloppy:                               \fussy & \sloppy.    (line   6)
 * \slshape:                              Font styles.         (line  45)
 * \small:                                Font sizes.          (line  11)
-* \smallint:                             Math symbols.        (line 644)
+* \smallint:                             Math symbols.        (line 649)
 * \smallskip:                            \bigskip \medskip \smallskip.
                                                               (line  19)
 * \smallskipamount:                      \bigskip \medskip \smallskip.
                                                               (line  20)
-* \smile:                                Math symbols.        (line 648)
+* \smile:                                Math symbols.        (line 653)
 * \spacefactor:                          \spacefactor.        (line  10)
-* \spadesuit:                            Math symbols.        (line 651)
-* \sqcap:                                Math symbols.        (line 654)
-* \sqcup:                                Math symbols.        (line 658)
+* \spadesuit:                            Math symbols.        (line 656)
+* \sqcap:                                Math symbols.        (line 659)
+* \sqcup:                                Math symbols.        (line 663)
 * \sqrt[ROOT]{ARG}:                      Math miscellany.     (line  66)
-* \sqsubset:                             Math symbols.        (line 662)
-* \sqsubseteq:                           Math symbols.        (line 667)
-* \sqsupset:                             Math symbols.        (line 672)
-* \sqsupseteq:                           Math symbols.        (line 677)
+* \sqsubset:                             Math symbols.        (line 667)
+* \sqsubseteq:                           Math symbols.        (line 672)
+* \sqsupset:                             Math symbols.        (line 677)
+* \sqsupseteq:                           Math symbols.        (line 682)
 * \ss (ss):                              Additional Latin letters.
                                                               (line  52)
 * \SS (SS):                              Additional Latin letters.
                                                               (line  52)
 * \stackrel{TEXT}{RELATION}:             Math miscellany.     (line  71)
-* \star:                                 Math symbols.        (line 681)
+* \star:                                 Math symbols.        (line 686)
 * \stepcounter:                          \stepcounter.        (line   6)
 * \stop:                                 Command line.        (line  18)
 * \subparagraph:                         Sectioning.          (line  15)
 * \subsection:                           Sectioning.          (line  12)
-* \subset:                               Math symbols.        (line 688)
-* \subseteq:                             Math symbols.        (line 691)
+* \subset:                               Math symbols.        (line 693)
+* \subseteq:                             Math symbols.        (line 696)
 * \subsubsection:                        Sectioning.          (line  13)
-* \succ:                                 Math symbols.        (line 694)
-* \succeq:                               Math symbols.        (line 698)
-* \sum:                                  Math symbols.        (line 703)
+* \succ:                                 Math symbols.        (line 699)
+* \succeq:                               Math symbols.        (line 703)
+* \sum:                                  Math symbols.        (line 708)
 * \sup:                                  Math functions.      (line 102)
 * \suppressfloats:                       Floats.              (line  87)
-* \supset:                               Math symbols.        (line 707)
-* \supseteq:                             Math symbols.        (line 710)
-* \surd:                                 Math symbols.        (line 713)
-* \swarrow:                              Math symbols.        (line 718)
+* \supset:                               Math symbols.        (line 712)
+* \supseteq:                             Math symbols.        (line 715)
+* \surd:                                 Math symbols.        (line 718)
+* \swarrow:                              Math symbols.        (line 723)
 * \symbol:                               Symbols by font position.
                                                               (line   6)
 * \t (tie-after accent):                 Accents.             (line  81)
@@ -13892,7 +14130,7 @@
 * \tableofcontents:                      Tables of contents.  (line   6)
 * \tan:                                  Math functions.      (line 105)
 * \tanh:                                 Math functions.      (line 108)
-* \tau:                                  Math symbols.        (line 721)
+* \tau:                                  Math symbols.        (line 726)
 * \telephone:                            \telephone.          (line   6)
 * \TeX:                                  Text symbols.        (line  60)
 * \textascendercompwordmark:             Text symbols.        (line  98)
@@ -13968,23 +14206,23 @@
                                                               (line  56)
 * \TH (TH):                              Additional Latin letters.
                                                               (line  56)
-* \thanks{TEXT}:                         \maketitle.          (line  21)
-* \theta:                                Math symbols.        (line 724)
+* \thanks{TEXT}:                         \maketitle.          (line  45)
+* \theta:                                Math symbols.        (line 729)
 * \thicklines:                           \thicklines.         (line   6)
 * \thickspace:                           Spacing in math mode.
-                                                              (line  16)
+                                                              (line  22)
 * \thinlines:                            \thinlines.          (line   6)
 * \thinspace:                            Spacing in math mode.
-                                                              (line  25)
+                                                              (line  31)
 * \thinspace <1>:                        \thinspace.          (line   6)
 * \thispagestyle:                        \thispagestyle.      (line   6)
 * \tilde:                                Math accents.        (line  43)
-* \times:                                Math symbols.        (line 728)
+* \times:                                Math symbols.        (line 733)
 * \tiny:                                 Font sizes.          (line  11)
-* \title{TEXT}:                          \maketitle.          (line  25)
-* \to:                                   Math symbols.        (line 732)
+* \title{TEXT}:                          \maketitle.          (line  49)
+* \to:                                   Math symbols.        (line 737)
 * \today:                                \today.              (line   6)
-* \top:                                  Math symbols.        (line 736)
+* \top:                                  Math symbols.        (line 741)
 * \topfraction:                          Floats.              (line 107)
 * \topfraction <1>:                      Floats.              (line 108)
 * \topmargin:                            Page layout parameters.
@@ -13995,31 +14233,34 @@
 * \topskip <1>:                          Page layout parameters.
                                                               (line 131)
 * \totalheight:                          Predefined lengths.  (line  12)
-* \triangle:                             Math symbols.        (line 741)
-* \triangleleft:                         Math symbols.        (line 744)
-* \triangleright:                        Math symbols.        (line 750)
+* \triangle:                             Math symbols.        (line 746)
+* \triangleleft:                         Math symbols.        (line 749)
+* \triangleright:                        Math symbols.        (line 755)
 * \tt:                                   Font styles.         (line  91)
 * \ttfamily:                             Font styles.         (line  54)
 * \twocolumn:                            \twocolumn.          (line   6)
 * \typein:                               \typein.             (line   6)
 * \typeout:                              \typeout.            (line   6)
 * \u (breve accent):                     Accents.             (line  86)
-* \unboldmath:                           Math formulas.       (line  29)
+* \unboldmath:                           \boldmath & \unboldmath.
+                                                              (line   6)
+* \unboldmath <1>:                       \boldmath & \unboldmath.
+                                                              (line  14)
 * \underbar:                             Accents.             (line  89)
 * \underbrace{MATH}:                     Math miscellany.     (line  75)
 * \underline{TEXT}:                      Math miscellany.     (line  79)
 * \unitlength:                           picture.             (line  25)
-* \unlhd:                                Math symbols.        (line 756)
-* \unrhd:                                Math symbols.        (line 763)
-* \Uparrow:                              Math symbols.        (line 770)
-* \uparrow:                              Math symbols.        (line 774)
-* \Updownarrow:                          Math symbols.        (line 778)
-* \updownarrow:                          Math symbols.        (line 783)
-* \upharpoonright:                       Math symbols.        (line 788)
-* \uplus:                                Math symbols.        (line 793)
+* \unlhd:                                Math symbols.        (line 761)
+* \unrhd:                                Math symbols.        (line 768)
+* \Uparrow:                              Math symbols.        (line 775)
+* \uparrow:                              Math symbols.        (line 779)
+* \Updownarrow:                          Math symbols.        (line 783)
+* \updownarrow:                          Math symbols.        (line 788)
+* \upharpoonright:                       Math symbols.        (line 793)
+* \uplus:                                Math symbols.        (line 798)
 * \upshape:                              Font styles.         (line  42)
-* \Upsilon:                              Math symbols.        (line 800)
-* \upsilon:                              Math symbols.        (line 803)
+* \Upsilon:                              Math symbols.        (line 805)
+* \upsilon:                              Math symbols.        (line 808)
 * \usebox:                               \usebox.             (line   6)
 * \usecounter:                           \usecounter.         (line   6)
 * \usefont:                              Low-level font commands.
@@ -14027,35 +14268,34 @@
 * \usepackage:                           Additional packages. (line   6)
 * \v (breve accent):                     Accents.             (line  97)
 * \value:                                \value.              (line   6)
-* \vanothing:                            Math symbols.        (line 811)
-* \varepsilon:                           Math symbols.        (line 806)
-* \varphi:                               Math symbols.        (line 816)
-* \varpi:                                Math symbols.        (line 820)
-* \varrho:                               Math symbols.        (line 824)
-* \varsigma:                             Math symbols.        (line 828)
-* \vartheta:                             Math symbols.        (line 832)
-* \vdash:                                Math symbols.        (line 836)
-* \vdots:                                Math miscellany.     (line  84)
+* \vanothing:                            Math symbols.        (line 816)
+* \varepsilon:                           Math symbols.        (line 811)
+* \varphi:                               Math symbols.        (line 821)
+* \varpi:                                Math symbols.        (line 825)
+* \varrho:                               Math symbols.        (line 829)
+* \varsigma:                             Math symbols.        (line 833)
+* \vartheta:                             Math symbols.        (line 837)
+* \vdash:                                Math symbols.        (line 841)
+* \vdots:                                Math miscellany.     (line  86)
 * \vec:                                  Math accents.        (line  46)
 * \vector:                               \vector.             (line   6)
-* \vee:                                  Math symbols.        (line 840)
+* \vee:                                  Math symbols.        (line 845)
 * \verb:                                 \verb.               (line   6)
-* \Vert:                                 Math symbols.        (line 845)
-* \vert:                                 Math symbols.        (line 861)
+* \Vert:                                 Math symbols.        (line 850)
+* \vert:                                 Math symbols.        (line 866)
 * \vfill:                                \vfill.              (line   6)
 * \vline:                                \vline.              (line   6)
 * \vspace:                               \vspace.             (line   6)
-* \wedge:                                Math symbols.        (line 879)
+* \wedge:                                Math symbols.        (line 884)
 * \widehat:                              Math accents.        (line  49)
 * \widetilde:                            Math accents.        (line  52)
 * \width:                                Predefined lengths.  (line   6)
-* \wp:                                   Math symbols.        (line 883)
-* \wr:                                   Math symbols.        (line 886)
-* \Xi:                                   Math symbols.        (line 889)
-* \xi:                                   Math symbols.        (line 892)
+* \wp:                                   Math symbols.        (line 888)
+* \wr:                                   Math symbols.        (line 891)
+* \Xi:                                   Math symbols.        (line 894)
+* \xi:                                   Math symbols.        (line 897)
 * \year:                                 \day \month \year.   (line   6)
-* \zeta:                                 Math symbols.        (line 895)
-* \[:                                    Math formulas.       (line  16)
+* \zeta:                                 Math symbols.        (line 900)
 * \\ (for center):                       center.              (line  22)
 * \\ (for eqnarray):                     eqnarray.            (line  29)
 * \\ (for flushright):                   flushright.          (line  12)
@@ -14065,18 +14305,17 @@
 * \\ for letters:                        Letters.             (line  49)
 * \\ for tabular:                        tabular.             (line  34)
 * \\ for verse:                          verse.               (line  21)
-* \\ for \author:                        \maketitle.          (line  12)
-* \\ for \title:                         \maketitle.          (line  26)
+* \\ for \author:                        \maketitle.          (line  35)
+* \\ for \title:                         \maketitle.          (line  50)
 * \\ force line break:                   \\.                  (line   6)
 * \\* (for eqnarray):                    eqnarray.            (line  37)
-* \]:                                    Math formulas.       (line  16)
 * \^:                                    Reserved characters. (line  20)
 * \^ (circumflex accent):                Accents.             (line  33)
 * \_:                                    Reserved characters. (line  13)
 * \` (grave accent):                     Accents.             (line  37)
 * \` (tabbing):                          tabbing.             (line  93)
 * \{:                                    Reserved characters. (line  13)
-* \|:                                    Math symbols.        (line  19)
+* \|:                                    Math symbols.        (line  24)
 * \}:                                    Reserved characters. (line  13)
 * \~:                                    Reserved characters. (line  20)
 * \~ (tilde accent):                     Accents.             (line  43)
@@ -14408,105 +14647,108 @@
 Node: \parindent & \parskip281200
 Node: Marginal notes282239
 Node: Math formulas284038
-Node: Subscripts & superscripts285822
-Node: Math symbols287160
-Node: Math functions312489
-Node: Math accents313432
-Node: Spacing in math mode314404
-Node: Math miscellany315871
-Node: Modes318421
-Node: \ensuremath321035
-Node: Page styles321752
-Node: \maketitle322246
-Node: \pagenumbering323316
-Node: \pagestyle323812
-Node: \thispagestyle324953
-Node: Spaces325259
-Node: \hspace326129
-Node: \hfill327084
-Node: \spacefactor327476
-Node: \(SPACE) and \@330188
-Ref: \AT330331
-Node: \frenchspacing331808
-Node: \normalsfcodes332424
-Node: \(SPACE) after control sequence332613
-Node: \thinspace333524
-Node: \/333844
-Node: \hrulefill \dotfill335026
-Node: \addvspace336019
-Node: \bigskip \medskip \smallskip337065
-Node: \vfill337957
-Node: \vspace338826
-Node: Boxes339819
-Node: \mbox340531
-Node: \fbox and \framebox340818
-Node: lrbox341622
-Node: \makebox341980
-Node: \parbox342700
-Node: \raisebox344811
-Node: \savebox345424
-Node: \sbox345839
-Node: \usebox346288
-Node: Color346549
-Node: Color package options347393
-Node: Color models349039
-Node: Commands for color351348
-Node: Define colors351763
-Node: Colored text352478
-Node: Colored boxes354853
-Node: Colored pages356292
-Node: Graphics356985
-Node: Graphics package options359112
-Node: Graphics package configuration361868
-Node: \graphicspath362670
-Node: \DeclareGraphicsExtensions365593
-Node: \DeclareGraphicsRule367390
-Node: Commands for graphics370579
-Node: \includegraphics371084
-Node: \rotatebox384053
-Node: \scalebox386848
-Node: \resizebox387900
-Node: Special insertions389092
-Node: Reserved characters389896
-Node: Upper and lower case391097
-Node: Symbols by font position393012
-Node: Text symbols393632
-Node: Accents397080
-Node: Additional Latin letters399622
-Ref: Non-English characters399793
-Node: \rule400810
-Node: \today401239
-Node: Splitting the input401993
-Node: \endinput403370
-Node: \include & \includeonly404637
-Node: \input408673
-Node: Front/back matter409381
-Node: Tables of contents409586
-Node: \addcontentsline410647
-Node: \addtocontents411665
-Node: Glossaries412198
-Node: Indexes412717
-Node: Letters414350
-Node: \address418016
-Node: \cc418827
-Node: \closing419245
-Node: \encl419522
-Node: \location419937
-Node: \makelabels420201
-Node: \name422353
-Node: \opening422594
-Node: \ps422875
-Node: \signature423164
-Node: \telephone424381
-Node: Terminal input/output424746
-Node: \typein425011
-Node: \typeout425596
-Node: Command line426219
-Node: Document templates427171
-Node: beamer template427578
-Node: book template428229
-Node: tugboat template428597
-Node: Concept Index430961
-Node: Command Index496668
+Node: Subscripts & superscripts287959
+Node: Math symbols290072
+Node: Blackboard bold315841
+Node: Caligraphic316616
+Node: \boldmath & \unboldmath317186
+Node: Math functions318693
+Node: Math accents320302
+Node: Spacing in math mode321122
+Node: Math miscellany322669
+Node: Modes325368
+Node: \ensuremath327982
+Node: Page styles328699
+Node: \maketitle329462
+Node: \pagenumbering331502
+Node: \pagestyle331998
+Node: \thispagestyle333139
+Node: Spaces333445
+Node: \hspace334315
+Node: \hfill335270
+Node: \spacefactor335662
+Node: \(SPACE) and \@338374
+Ref: \AT338517
+Node: \frenchspacing339994
+Node: \normalsfcodes340610
+Node: \(SPACE) after control sequence340799
+Node: \thinspace341710
+Node: \/342102
+Node: \hrulefill \dotfill343284
+Node: \addvspace344277
+Node: \bigskip \medskip \smallskip345323
+Node: \vfill346215
+Node: \vspace347084
+Node: Boxes348077
+Node: \mbox348789
+Node: \fbox and \framebox349076
+Node: lrbox349880
+Node: \makebox350238
+Node: \parbox350958
+Node: \raisebox353069
+Node: \savebox353682
+Node: \sbox354097
+Node: \usebox354546
+Node: Color354807
+Node: Color package options355651
+Node: Color models357297
+Node: Commands for color359606
+Node: Define colors360021
+Node: Colored text360736
+Node: Colored boxes363111
+Node: Colored pages364550
+Node: Graphics365243
+Node: Graphics package options367370
+Node: Graphics package configuration370126
+Node: \graphicspath370928
+Node: \DeclareGraphicsExtensions373851
+Node: \DeclareGraphicsRule375648
+Node: Commands for graphics378837
+Node: \includegraphics379342
+Node: \rotatebox392311
+Node: \scalebox395106
+Node: \resizebox396158
+Node: Special insertions397350
+Node: Reserved characters398154
+Node: Upper and lower case399355
+Node: Symbols by font position401270
+Node: Text symbols401890
+Node: Accents405338
+Node: Additional Latin letters407880
+Ref: Non-English characters408051
+Node: \rule409068
+Node: \today409497
+Node: Splitting the input410251
+Node: \endinput411628
+Node: \include & \includeonly412895
+Node: \input416931
+Node: Front/back matter417639
+Node: Tables of contents417844
+Node: \addcontentsline418905
+Node: \addtocontents419923
+Node: Glossaries420456
+Node: Indexes420975
+Node: Letters422608
+Node: \address426274
+Node: \cc427085
+Node: \closing427503
+Node: \encl427780
+Node: \location428195
+Node: \makelabels428459
+Node: \name430611
+Node: \opening430852
+Node: \ps431133
+Node: \signature431422
+Node: \telephone432639
+Node: Terminal input/output433004
+Node: \typein433269
+Node: \typeout433854
+Node: Command line434477
+Node: Document templates435429
+Node: beamer template435836
+Node: book template436487
+Node: tugboat template436855
+Node: Concept Index439219
+Node: Command Index507005
 
 End Tag Table

Modified: trunk/latex2e.pdf
===================================================================
(Binary files differ)

Modified: trunk/latex2e.texi
===================================================================
--- trunk/latex2e.texi	2018-06-05 15:29:46 UTC (rev 640)
+++ trunk/latex2e.texi	2018-06-06 19:01:02 UTC (rev 641)
@@ -9195,11 +9195,14 @@
 
 @itemize @bullet
 @item
-in the right margin for one-sided layout (option @code{oneside}, see @ref{Document class options});
+in the right margin for one-sided layout (option @code{oneside}, see
+ at ref{Document class options});
 @item
-in the outside margin for two-sided layout (option @code{twoside}, see @ref{Document class options});
+in the outside margin for two-sided layout (option @code{twoside}, see
+ at ref{Document class options});
 @item
-in the nearest margin for two-column layout (option @code{twocolumn}, see @ref{Document class options}).
+in the nearest margin for two-column layout (option @code{twocolumn},
+see @ref{Document class options}).
 @end itemize
 
 @findex \reversemarginpar
@@ -9250,65 +9253,93 @@
 @EnvIndex{displaymath}
 @EnvIndex{equation}
 
-There are three environments that put @LaTeX{} in math mode:
+Produce mathematical text by putting @LaTeX{} into math mode or display
+math mode (@pxref{Modes}).  This example shows both.
 
- at table @code
- at item math
-For formulas that appear right in the text.
- at item displaymath
-For formulas that appear on their own line.
- at item equation
-The same as the displaymath environment except that it adds an equation
-number in the right margin.
- at end table
-
- at findex \(
- at findex \)
- at findex \[
- at findex \]
-The @code{math} environment can be used in both paragraph and LR mode,
-but the @code{displaymath} and @code{equation} environments can be used
-only in paragraph mode.  The @code{math} and @code{displaymath}
-environments are used so often that they have the following short forms:
-
 @example
-\(...\)   @r{instead of}   \begin@{math@}...\end@{math@}
-\[...\]   @r{instead of}   \begin@{displaymath@}...\end@{displaymath@}
+The wave equation for \( u \) is
+\begin@{displaymath@}
+  \frac@{\partial^2u@}@{\partial t^2@} = c^2\nabla^2u
+\end@{displaymath@}
+where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.
 @end example
 
- at findex $
-In fact, the @code{math} environment is so common that it has an even
-shorter form:
+Math mode is for inline mathematics.  It is invoked by the starting
+ at code{\(} and finished by the matching ending @code{\)}.  Display math
+mode is for displayed equations and here is invoked by the
+ at code{displaymath} environment.  Note that any mathematical text
+whatever, including that consisting of single characters, is handled in
+math mode.
 
+ at PkgIndex{amsmath} @PkgIndex{amsfonts} @PkgIndex{mathtools}
+The American Mathematical Society has made freely available a set of
+packages that greatly expand your options for writing mathematics,
+ at file{amsmath} and @file{amssymb} (also be aware of the
+ at file{mathtools} package that is an extension to, and loads,
+ at file{amsmath}).  New documents that will have mathematical text should
+use these packages.  Descriptions of these packages is outside the scope
+of this document; see their documentation on CTAN.
+
+When in math mode or display math mode, @LaTeX{} handles many aspects of
+your input text differently than in other text modes.  For example,
+
 @example
-$ ... $   @r{instead of}   \(...\)
+contrast x+y with \( x+y \).
 @end example
 
- at findex \boldmath
- at findex \unboldmath
-The @code{\boldmath} command changes math letters and symbols to be in
-a bold font.  It is used @emph{outside} of math mode.  Conversely, the
- at code{\unboldmath} command changes math glyphs to be in a normal font;
-it too is used @emph{outside} of math mode.
+in math mode the letters are in italics and the spacing around the plus
+sign is different.
 
- at c xx own section? Math fonts?
+To make inline formulas put @LaTeX{} in math mode with either
+ at code{\(@var{mathematical material}\)}, or @code{$@var{mathematical
+material}$}, or @code{\begin@{math@}@var{mathematical
+material\end@{math@}}}.  The first form is preferred, and the third form
+is very rarely used.  These can be used in paragraph mode or in LR mode
+(@pxref{Modes}).
+
+To make displayed formulas, put @LaTeX{} into display math mode with
+either @code{\begin@{displaymath@}@var{mathematical
+material}\end@{displaymath@}}, or
+ at code{\begin@{equation@}@var{mathematical material}\end@{equation@}}.
+These behave the same way except that with the @code{equation}
+environment, @LaTeX{} puts a formula number alongside the formula, which
+by default has the form @samp{(@var{arabic number})}.  The construct
+ at code{\[ @var{math} \]} is equivalent to @code{\begin@{displaymath@}
+ at var{math} \end@{displaymath@}}.  These environments can only be used in
+paragraph mode (@pxref{Modes}).
+
 @findex \displaystyle
-The @code{\displaystyle} declaration forces the size and style of the
-formula to be that of @code{displaymath}, e.g., with limits above and
-below summations.  For example:
+The two mathematics modes are similar, but there are some differences.
+One involves the placement of subscripts and superscripts; in display
+math mode they are further apart and in inline math mode they are closer
+together.  Sometimes you want the display math treatment to happen in
+the inline math mode.  For this, the @code{\displaystyle} declaration
+forces the size and style of the formula to be that of
+ at code{displaymath}.  Thus @code{\(\displaystyle \sum_@{n=0@}^\infty
+x_n\)} will have the limits above and below the summation sign, not next
+to it.  Another example is that
 
 @example
-$\displaystyle \sum_@{n=0@}^\infty x_n $
+\begin@{tabular@}@{r|cc@}
+  \textsc@{Name@}  &\textsc@{Series@}  &\textsc@{Sum@}  \\  \hline
+  Arithmetic     &\( a+(a+b)+(a+2b)+\cdots+(a+(n-1)b) \)
+                   &\( na+(n-1)n\cdot\frac@{b@}@{2@}\)  \\
+  Geometric      &\( a+ab+ab^2+\cdots+ab^@{n-1@} \)
+                   &\(\displaystyle a\cdot\frac@{1-b^n@}@{1-b@}\)  \\
+\end@{tabular@}
 @end example
 
- at c xx see also \cal, \mathcal
+because it has no @code{\displaystyle}, the Arithmetic line's fraction
+will be scrunched.  But, because of its @code{\displaystyle}, the
+Geometric line's fraction will be easy to read, with characters the same
+size as in the rest of the line.
 
 @menu
 * Subscripts & superscripts::   Also known as exponent or index.
 * Math symbols::                Various mathematical squiggles.
 * Math functions::              Math function names like sin and exp.
 * Math accents::                Accents in math.
-* Spacing in math mode::        Thick, medium, thin and negative spaces.
+* Spacing in math mode::        Thick, medium, thin, and negative spaces.
 * Math miscellany::             Stuff that doesn't fit anywhere else.
 @end menu
 
@@ -9322,44 +9353,77 @@
 @findex _
 @findex ^
 
-In math mode, use the caret character at tie{}@code{^} to make the
- at var{exp} appear as a superscript: @code{^@{@var{exp}@}}.
-Similarly, in math mode, underscore at tie{}@code{_@{@var{exp}@}} makes a
-subscript out of @var{exp}.
+Synopsis (in math mode or display math mode):
 
-In this example the @code{0} and @code{1} appear as subscripts while the
- at code{2} is a superscript.
+ at example
+ at var{base}^@var{exp}
+ at end example
 
+or:
+
 @example
-\( (x_0+x_1)^2 \)
+ at var{base}_ at var{exp}
 @end example 
 
-To have more than one character in @var{exp} use curly braces as in
- at code{e^@{-2x@}}.
+Make @var{exp} appear as a superscript of @var{base} (with the caret
+character, at tie{}@code{^}) or a subscript (with
+underscore, at tie{}@code{_}).
 
- at LaTeX{} handles superscripts on superscripts, and all of that stuff, in
-the natural way, so expressions such as @code{e^@{x^2@}} and
- at code{x_@{a_0@}} will look right.  It also does the right thing when
-something has both a subscript and a superscript.  In this example the
- at code{0} appears at the bottom of the integral sign while the @code{10}
-appears at the top.
- 
+In this example the @code{0}'s and @code{1}'s are subscripts while the
+ at code{2}'s are superscripts.
+
 @example
-\int_0^@{10@} x^2 \,dx
+\( (x_0+x_1)^2 \leq (x_0)^2+(x_1)^2 \)
+ at end example 
+
+To have the subscript or superscript contain more than one character,
+surround the expression with curly braces, as in @code{e^@{-2x@}}.
+This example's fourth line shows curly braces used to group an expression
+for the exponent.
+
+ at example
+\begin@{displaymath@}
+  (3^3)^3=27^3=19\,683
+  \qquad
+  3^@{(3^3)@}=3^@{27@}=7\,625\,597\,484\,987
+\end@{displaymath@}
 @end example
 
-You can put a superscript or subscript before a symbol with a construct
-such as @code{@{@}_t K^2} in math mode (the initial @code{@{@}} prevents
-the prefixed subscript from being attached to any prior symbols in the
-expression).
+ at LaTeX{} knows how to handle a superscript on a superscript, or a
+subscript on a subscript, or supers on subs, or subs on supers.  So,
+expressions such as @code{e^@{x^2@}} and @code{x_@{i_0@}} give correct
+output.  Note the use in those expressions of curly braces to give the
+ at var{base} a determined @var{exp}.  If you enter @code{\(3^3^3\)} then
+you get @samp{Double superscript}.
 
-Outside of math mode, a construct like @code{A
-test$_\textnormal@{subscript@}$} will produce a subscript typeset in
-text mode, not math mode.  Note that there are packages specialized for
-writing Chemical formulas such as @file{mhchem}.
- at c xx display mode
+ at LaTeX{} does the right thing when something has both a subscript and a
+superscript.  In this example the integral has both.  They come out in
+the correct place without any author intervention.
 
+ at example
+\begin@{displaymath@}
+  \int_@{x=a@}^b f'(x)\,dx = f(b)-f(a)
+\end@{displaymath@}
+ at end example
 
+ at noindent Note the parentheses around @code{x=a} to make the entire
+expression a subscript.
+
+To put a superscript or subscript before a symbol, use a construct like
+ at code{@{@}_t K^2}.  The empty curly braces @code{@{@}} give the
+subscript something to attach to and keeps it from accidentally
+attaching to a prior symbols.
+
+Using the subscript or superscript command outside of math mode or
+display math mode, as in @code{the expression x^2}, will get you
+the error @samp{Missing $ inserted}.
+
+ at PkgIndex{mhchem}
+A common reason to want subscripts outside of a mathematics mode is to
+typeset chemical formulas.  There are packages for that such as
+ at file{mhchem}; see CTAN.
+
+
 @node Math symbols
 @section Math symbols
 
@@ -9370,13 +9434,19 @@
 @LaTeX{} provides almost any mathematical symbol you're likely to need.
 For example, if you include @code{$\pi$} in your source, you will get
 the pi symbol @BES{03C0,\pi}.
- 
-Below is a list of commonly-available symbols.  It is by no means an
-exhaustive list.  Each symbol here is described with a short phrase, and
-its symbol class (which determines the spacing around it) is given in
-parenthesis.  Unless said otherwise, the commands for these symbols can
-be used only in math mode.
 
+ at PkgIndex{symbols}
+Virtually any technical symbol anyone has ever used is available for
+use in @LaTeX{}.  See the @file{Comprehensive @LaTeX{} Symbol List} at
+ at url{https://ctan.org/tex-archive/info/symbols/comprehensive/}.  Some
+of these require the use of external packages.
+
+Below is a list of commonly-used symbols that come standard with
+ at LaTeX{}.  It is by no means an exhaustive list.  Each symbol here is
+described with a short phrase, and its symbol class (which determines
+the spacing around it) is given in parenthesis.  Unless said otherwise,
+the commands for these symbols can be used only in math mode.
+
 To redefine a command so that it can be used whatever the current mode,
 see @ref{\ensuremath}.
 
@@ -10243,7 +10313,133 @@
 
 @end ftable
 
+ at menu
+* Blackboard bold::            Doublestruck characters.
+* Caligraphic::                Cursive characters.
+* \boldmath & \unboldmath::    Symbols in boldface.
+ at end menu
 
+
+ at node Blackboard bold
+ at subsection Blackboard bold
+
+ at cindex blackboard bold
+ at cindex doublestruck
+
+Synopsis:
+
+ at example
+\usepackage@{amssymb@}   % in preamble
+  ... 
+\mathbb@{@var{uppercase-letter}@}
+ at end example
+
+Provide blackboard bold symbols, sometimes also known as doublestruck
+letters, used to denote number sets such as the natural numbers, the
+integers, etc.
+
+Here 
+
+ at example
+\( \forall n \in \mathbb@{N@}, n^2 \geq 0 \)
+ at end example
+
+the @code{\mathbb@{N@}} gives blackboard bold symbol @BES{2115,}
+representing the natural numbers.
+
+If you use other than an upper case letter then you do not get an error
+but you get strange results, including unexpected characters.
+
+There are packages that give access to symbols other than just the
+capital letters; look on CTAN.
+
+
+ at node Caligraphic
+ at subsection Caligraphic
+
+ at cindex caligraphic
+
+Synopsis:
+
+ at example
+\mathcal@{@var{uppercase-letters}@}
+ at end example
+
+Use a script-like font.
+
+In this example the graph identifier is output in a cursive font.
+
+ at example
+Let the graph be \( \mathcal@{G@} \).
+ at end example
+
+If you use something other than an upper case letter then you do not get
+an error.  Instead you get unexpected output.  For instance,
+ at code{\mathcal@{g@}} outputs a close curly brace symbol, while
+ at code{\mathcal@{+@}} outputs a plus sign.  
+
+
+ at node \boldmath & \unboldmath
+ at subsection @code{\boldmath} & @code{\unboldmath}
+
+ at cindex boldface mathematics
+ at cindex symbols, boldface
+ at findex \boldmath
+ at findex \unboldmath
+
+Synopsis (used in paragraph mode or LR mode):
+
+ at example
+\boldmath \( @var{math} \)
+ at end example
+
+or
+
+ at example
+\unboldmath \( @var{math} \)
+ at end example
+
+
+ at findex \boldmath
+ at findex \unboldmath
+ at c xx Refer to package bm: https://tex.stackexchange.com/q/595/121234
+Declarations to change the letters and symbols in @var{math} to be in a
+bold font, or to countermand that and bring back the unbolded default.
+They must be used when not in math mode or display math mode
+(@pxref{Modes}).  Both commands are fragile (@pxref{\protect}).
+
+In this example each @code{\boldmath} command takes place inside an
+ at code{\mbox},
+
+ at example
+we have $\mbox@{\boldmath \( v \)@} = 5\cdot\mbox@{\boldmath \( u \)$@}$
+ at end example
+
+ at noindent which means @code{\boldmath} is only called in a text mode,
+here LR mode, and explains why @LaTeX{} must switch to math mode to set
+ at code{v} and @code{u}.
+
+If you use either command inside math mode, as with @code{Trouble: \(
+\boldmath x \)}, then you get something like @samp{LaTeX Font Warning:
+Command \boldmath invalid in math mode on input line 11} and @samp{LaTeX
+Font Warning: Command \mathversion invalid in math mode on input line
+11}.
+
+ at PkgIndex{bm}
+There are many issues with @code{\boldmath}.  New documents should use
+the @file{bm} package provided by the @LaTeX{} Project team.  A complete
+description is outside the scope of this document (see the full
+documentation on CTAN) but even this small example
+
+ at example
+\usepackage@{bm@}   % in preamble
+...
+we have $\bm@{v@} = 5\cdot\bm@{u@}$
+ at end example
+
+strongly suggests that it is an improvement over @code{\boldmath}.
+
+
 @node Math functions
 @section Math functions
 
@@ -10255,118 +10451,227 @@
 
 @ftable @code
 @item \arccos
+Inverse cosine
+ at iftex
 @math{\arccos}
+ at end iftex
 
 @item \arcsin
+Inverse sine
+ at iftex
 @math{\arcsin}
+ at end iftex
 
 @item \arctan
+Inverse tangent
+ at iftex
 @math{\arctan}
+ at end iftex
 
 @item \arg
+Angle between the real axis and a point in the complex plane
+ at iftex
 @math{\arg}
+ at end iftex
 
 @item \bmod
-Binary modulo operator (@math{x \bmod y})
+Binary modulo operator, used as in @code{\( 5\bmod 3=2 \)}
+ at iftex
+ at math{5 \bmod 3}
+ at end iftex
 
 @item \cos
+Cosine
+ at iftex
 @math{\cos}
+ at end iftex
 
 @item \cosh
+Hyperbolic cosine
+ at iftex
 @math{\cosh}
+ at end iftex
 
 @item \cot
+Cotangent
+ at iftex
 @math{\cot}
+ at end iftex
 
 @item \coth
+Hyperbolic cotangent
+ at iftex
 @math{\coth}
+ at end iftex
 
 @item \csc
+Cosecant
+ at iftex
 @math{\csc}
+ at end iftex
 
 @item \deg
+Degrees
+ at iftex
 @math{\deg}
+ at end iftex
 
 @item \det
+Determinant
+ at iftex
 @math{\det}
+ at end iftex
 
 @item \dim
+Dimension
+ at iftex
 @math{\dim}
+ at end iftex
 
 @item \exp
+Exponential
+ at iftex
 @math{\exp}
+ at end iftex
 
 @item \gcd
+Greatest common divisor
+ at iftex
 @math{\gcd}
+ at end iftex
 
 @item \hom
+Homomorphisms
+ at iftex
 @math{\hom}
+ at end iftex
 
 @item \inf
+Infinum
+ at iftex
 @math{\inf}
+ at end iftex
 
 @item \ker
+Kernel
+ at iftex
 @math{\ker}
+ at end iftex
 
 @item \lg
+Base 2 logarithm
+ at iftex
 @math{\lg}
+ at end iftex
 
 @item \lim
+Limit
+ at iftex
 @math{\lim}
+ at end iftex
 
 @item \liminf
+Limit inferior
+ at iftex
 @math{\liminf}
+ at end iftex
 
 @item \limsup
+Limit superior
+ at iftex
 @math{\limsup}
+ at end iftex
 
 @item \ln
+Natural logarithm
+ at iftex
 @math{\ln}
+ at end iftex
 
 @item \log
+Logarithm
+ at iftex
 @math{\log}
+ at end iftex
 
 @item \max
+Maximum
+ at iftex
 @math{\max}
+ at end iftex
 
 @item \min
+Minimum
+ at iftex
 @math{\min}
+ at end iftex
 
 @item \pmod
-parenthesized modulus, as in (@math{\pmod 2^n - 1})
+Parenthesized modulus, as used in @code{\( 5\equiv 2\pmod 3 \)}
+ at iftex
+ at math{5\equiv 2\pmod 3}
+ at end iftex
 
 @item \Pr
+Probability
+ at iftex
 @math{\Pr}
+ at end iftex
 
 @item \sec
+Secant
+ at iftex
 @math{\sec}
+ at end iftex
 
 @item \sin
+Sine
+ at iftex
 @math{\sin}
+ at end iftex
 
 @item \sinh
+Hyperbolic sine
+ at iftex
 @math{\sinh}
+ at end iftex
 
 @item \sup
 @iftex
+Supremum
+ at iftex
 @math{\mathop {\rm sup}}
 @end iftex
 @ifnottex
- at math{\sup}
+sup
 @end ifnottex
 @c don't try to use \sup with dvi/pdf output since that turned into a
 @c Texinfo command and it's not worth hassling with different versions
 @c when it's just three roman letters anyway.
 
 @item \tan
+Tangent
+ at iftex
 @math{\tan}
+ at end iftex
 
 @item \tanh
+Hyperbolic tangent
+ at iftex
 @math{\tanh}
+ at end iftex
 
 @end ftable
 
+ at PkgIndex{amsmath} The @file{amsmath} package adds improvements on some
+of these, and also allows you to define your own.  See the full
+documentation on CTAN, but
+ at code{\DeclareMathOperator@{\identity@}@{id@}} creates an operator like
+the ones above but printed as @samp{id}.  The starred form
+ at code{\DeclareMathOperator*@{\op@}@{op@}} sets any limits above and
+below, as is traditional with @code{\lim}, @code{\sup}, or @code{\max}.
 
+
 @node Math accents
 @section Math accents
 
@@ -10380,67 +10685,106 @@
 @ftable @code
 @item \acute
 @cindex acute accent, math
-Math acute accent: @math{\acute{x}}.
+Math acute accent
+ at iftex
+ at math{\acute{x}}.
+ at end iftex
 
 @item \bar
 @cindex bar-over accent, math
 @cindex macron accent, math
-Math bar-over accent: @math{\bar{x}}.
+Math bar-over accent
+ at iftex
+ at math{\bar{x}}
+ at end iftex
 
 @item \breve
 @cindex breve accent, math
-Math breve accent: @math{\breve{x}}.
+Math breve accent
+ at iftex
+ at math{\breve{x}}
+ at end iftex
 
 @item \check
 @cindex check accent, math
 @cindex h@'a at v{c}ek accent, math
-Math h@'a at v{c}ek (check) accent: @math{\check{x}}.
+Math h@'a at v{c}ek (check) accent
+ at iftex
+ at math{\check{x}}
+ at end iftex
 
 @item \ddot
 @cindex double dot accent, math
-Math dieresis accent: @math{\ddot{x}}.
+Math dieresis accent
+ at iftex
+ at math{\ddot{x}}
+ at end iftex
 
 @item \dot
 @cindex overdot accent, math
 @cindex dot over accent, math
-Math dot accent: @math{\dot{x}}.
+Math dot accent
+ at iftex
+ at math{\dot{x}}
+ at end iftex
 
 @item \grave
 @cindex grave accent, math
-Math grave accent: @math{\grave{x}}.
+Math grave accent
+ at iftex
+ at math{\grave{x}}
+ at end iftex
 
 @item \hat
 @cindex hat accent, math
 @cindex circumflex accent, math
-Math hat (circumflex) accent: @math{\hat{x}}.
+Math hat (circumflex) accent
+ at iftex
+ at math{\hat{x}}
+ at end iftex
 
 @item \imath
 @cindex dotless i, math
-Math dotless i.
+Math dotless i
 
 @item \jmath
 @cindex dotless j, math
-Math dotless j.
+Math dotless j
 
 @item \mathring
 @cindex ring accent, math
-Math ring accent: @ringaccent{x}.  @c don't bother implementing in texinfo
+Math ring accent  @c don't bother implementing in texinfo
+ at iftex
+ at ringaccent{x}
+ at end iftex
 
 @item \tilde
 @cindex tilde accent, math
-Math tilde accent: @math{\tilde{x}}.
+Math tilde accent
+ at iftex
+ at math{\tilde{x}}
+ at end iftex
 
 @item \vec
 @cindex vector symbol, math
-Math vector symbol: @math{\vec{x}}.
+Math vector symbol
+ at iftex
+ at math{\vec{x}}
+ at end iftex
 
 @item \widehat
 @cindex wide hat accent, math
-Math wide hat accent: @math{\widehat{x+y}}.
+Math wide hat accent
+ at iftex
+ at math{\widehat{x+y}}
+ at end iftex
 
 @item \widetilde
 @cindex wide tilde accent, math
-Math wide tilde accent: @math{\widetilde{x+y}}.
+Math wide tilde accent
+ at iftex
+ at math{\widetilde{x+y}}
+ at end iftex
 
 @end ftable
 
@@ -10451,35 +10795,44 @@
 @cindex spacing within math mode
 @cindex math mode, spacing
 
-In a @code{math} environment, @LaTeX{} ignores the spaces that you use
-in the source, and instead puts in the spacing according to the normal
-rules for mathematics texts.  
+When typesetting mathematics, @LaTeX{} puts in spacing according to the
+normal rules for mathematics texts.  If you enter @code{y=m x} then
+ at LaTeX{} ignores the space and in the output the m is next to the x.
 
-Many math mode spacing definitions are expressed in terms of the math unit
- at dfn{mu} given by 1 em = 18 mu, where the em is taken from the current
-math symbols family (@pxref{Units of length}).
- at LaTeX{} provides the following commands for use in math mode:
+But @LaTeX{}'s rules sometimes need tweaking.  For example, in an
+integral the tradition is to put a small extra space between the
+ at code{f(x)} and the @code{dx}.
 
+ at example
+\int_0^1 f(x)\,dx
+ at end example
+
+ at LaTeX{} provides the commands that follow for use in math mode.  Many
+of these spacing definitions are expressed in terms of the math unit
+ at dfn{mu}.  It is defined as 1/18 em, where the em is taken from the
+current math symbols family (@pxref{Units of length}).
+
 @table @code
 @item \;
 @findex \;
 @findex \thickspace
-Normally @code{5.0mu plus 5.0mu}.  The longer name is
- at code{\thickspace}.  Math mode only.
+Synonym: @code{\thickspace}.  Normally @code{5.0mu plus 5.0mu}.  Math
+mode only.
 
 @item \:
 @itemx \>
 @findex \:
 @findex \>
 @findex \medspace
-Normally @code{4.0mu plus 2.0mu minus 4.0mu}.  The longer name is
- at code{\medspace}.  Math mode only.
+Synonym: @code{\medspace}.  Normally @code{4.0mu plus 2.0mu minus 4.0mu}.
+Math mode only.
 
 @item \,
 @findex \,
 @findex \thinspace
-Normally @code{3mu}.  The longer name is @code{\thinspace}.  This can
-be used in both math mode and text mode. @xref{\thinspace}.
+Synonym: @code{\thinspace} (@pxref{\thinspace}).
+Normally @code{3mu}.
+Can be used in both math mode and text mode. 
 
 @item \!
 @findex \!
@@ -10499,14 +10852,7 @@
 both text and math mode.
 @end table
 
-In this example a thinspace separates the function from the
-infinitesimal.
 
- at example
-\int_0^1 f(x)\,dx
- at end example
-
-
 @node Math miscellany
 @section Math miscellany
 
@@ -10578,7 +10924,7 @@
 Dollar sign in math mode: $.
 
 @item \mathellipsis
-Ellipsis (spaced for text) in math mode: @dots{}.
+Ellipsis (spaced for text) in math mode: @dots{}
 
 @item \mathparagraph
 Paragraph sign (pilcrow) in math mode: @BES{00B6,\P}.
@@ -10628,6 +10974,7 @@
 The result looks like this: @math{\underbrace{x+y+z}_{>\,0}}.
 @end ifset
 
+ at PkgIndex{ulem}
 @item \underline@{@var{text}@}
 Causes @var{text}, which may be either math mode or not, to be
 underlined.  The line is always below the text, taking account of
@@ -10635,9 +10982,12 @@
 @ifset HAS-MATH
 The result looks like this: @math{\underline{xyz}}
 @end ifset
+(The package @file{ulem} does underlining and allows line breaking as
+well as a number of other underline-related features.  The documentation
+is on CTAN.)
 
 @item \vdots
-Produces a vertical ellipsis.
+Vertical ellipsis.
 @ifset HAS-MATH
 The result looks like this: @math{\vdots}.
 @end ifset
@@ -10753,9 +11103,16 @@
 @cindex styles, page
 @cindex page styles
 
-The @code{\documentclass} command determines the size and position of
-the page's head and foot.  The page style determines what goes in them.
+The style of a page determines where @LaTeX{} places the components of
+that page, such as headers and footers, and the text body.  This
+includes pages in the main part of the document but also includes
+special pages such as the title page of a book, a page from an index, or
+the first page of an article.
 
+ at PkgIndex{fancyhdr}
+The package @file{fancyhdr} is very helpful for constructing page
+styles.  See its documentation on CTAN.
+
 @menu
 * \maketitle::          Generate a title page.
 * \pagenumbering::      Set the style used for page numbers.
@@ -10770,38 +11127,64 @@
 @cindex titles, making
 @findex \maketitle
 
-The @code{\maketitle} command generates a title on a separate title
-page---except in the @code{article} class, where the title is placed
-at the top of the first page.  Information used to produce the title
-is obtained from the following declarations:
+Generate a title.  It is on a separate title page, except in the
+ at code{article} class where it is at the top of the first page.
 
+This example
+
+ at example
+\documentclass@{article@}
+\title@{On the Electrodynamics of Moving Bodies@}
+\author@{A~Einstein\thanks@{%
+  Gratefully acknowledged is the support of the Swiss Patent Office.@}@}
+\date@{1905-Jun-30@}
+\begin@{document@}
+\maketitle
+It is known that Maxwell's electrodynamics---as usually understood at the
+present time---when applied to moving bodies, leads to asymmetries which
+do not appear to be inherent in the phenomena.
+   ...
+In conclusion I wish to say that in working at the problem here dealt
+with I have had the loyal assistance of my friend and colleague M~Besso,
+and that I am indebted to him for several valuable suggestions.
+\end@{document@}
+ at end example
+
+shows the @code{\maketitle} command appearing immediately after the
+ at code{\begin@{document@}}.
+
+Information used to produce the title is obtained from the following
+declarations.  These must come before the @code{\maketitle}, either in
+the preamble or in the document body.
+
 @ftable @code
 @item \author@{@var{name} \and @var{name2}@}
 @cindex author, for titlepage
 @findex \\ @r{for @code{\author}}
 @findex \and @r{for @code{\author}}
-The @code{\author} command declares the document author(s), where the
-argument is a list of authors separated by @code{\and} commands.  Use
- at code{\\} to separate lines within a single author's entry---for
-example, to give the author's institution or address.
+Required.  Declare the document author or authors.  The argument is a
+list of authors separated by @code{\and} commands.  Use @code{\\} to
+separate lines within a single author's entry---for example, to give the
+author's institution or address.  If you omit this then you get
+ at samp{LaTeX Warning: No \author given}.
 
 @item \date@{@var{text}@}
 @cindex date, for titlepage
-The @code{\date} command declares @var{text} to be the document's
-date.  With no @code{\date} command, the current date (@pxref{\today})
-is used.
+Optional.  Declare @var{text} to be the document's date.  If you omit it
+then @LaTeX{} uses the current date (@pxref{\today}).
 
 @item \thanks@{@var{text}@}
 @cindex thanks, for titlepage
 @cindex credit footnote
-The @code{\thanks} command produces a @code{\footnote} to the title,
-usually used for credit acknowledgements.
+Optional.  Produce a footnote to the title, usually for
+acknowledgements.
 
 @item \title@{@var{text}@}
 @cindex title, for titlepage
 @findex \\ @r{for @code{\title}}
-The @code{\title} command declares @var{text} to be the title of the
-document.  Use @code{\\} to force a line break, as usual.
+Required.  Declare @var{text} to be the title of the document.  Inside
+ at var{text}, use @code{\\} to get line breaks.  If you omit this command
+then you get @samp{LaTeX Error: No \title given}.
 
 @end ftable
 
@@ -11131,9 +11514,10 @@
 
 @findex \thinspace
 
- at code{\thinspace} produces an unbreakable and unstretchable space that
-is 1/6 of an em.  This is the proper space to use between nested
-quotes, as in '@dmn{}''. at c Abuse @dmn, which is a thin space in Texinfo.
+Produce an unbreakable and unstretchable space of 1/6 of an em.  This is
+the proper space to use between nested quotes, as in '@dmn{}''. at c Abuse @dmn, which is a thin space in Texinfo.
+Some style guides call for a @code{\thinspace} between an ellipsis and a
+sentence ending period.
 
 
 @node \/



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