LaTeX:Layout

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This article outlines some of the basics of layout in LaTeX.

Note: Rather than typing up all the examples, you can copy-paste the examples into your TeXnicCenter files. We highly recommend opening up your TeXnicCenter and trying out each of the examples as you go. It takes almost no time at all to just copy-paste, compile, and view the results.

Source File Format

The source file of a LaTeX broadly consists of two parts, the preamble and the document itself. The preamble consists of everything before the \begin{document} command. Things like margin settings, document style definitions, paragraph spacing settings, custom function definition and page numeration style are items that are set in the preamble. Often, much of the preamble is placed in a separate file and included using the \usepackage statement. This allows you to use the same code in many source files by just including a single line in each source file.

Our next three sections deal primarily with preamble items, while the rest cover tools you might use within your document.

The Preamble

Document Class

The first line of the file sets the document class with the \documentclass[options]{class} command. For typical use the document class should be article. (Other supported classes are book, report, and letter.) There are several options that can be set with \documentclass, but generally they can be left to their defaults. One option that might need modification is the font size, which is 10pt by default but can be increased to 11pt or 12pt. A reference on other options for this command can be found here.

Packages

Packages are included after the \documentclass statement using \usepackage[options]{packagename}. Two common packages are amsmath, which allows you to write math formulas in your document, and graphicx with the pdftex option, which allows you to include images in your document.

Page Setup

LaTeX automatically sets reasonable values for the page dimensions, orientation, etc. However, in some cases customization may be required. There are two ways to do this: the easy way, using several packages which do all the work for you, and the hard way, which involves doing all the work yourself.

The Easy Way

The easy way involves using certain packages to do the heavy lifting. For example, to set the margins using the geometry package, use the line \usepackage[margin=2.5cm]{geometry}. Check out the geometry package user manual for more detailed possibilities. As another example, if you want a layout where paragraphs are separated by some space, but not indented (like in most HTML pages), use the parskip package: \usepackage{parskip}.

The Hard Way

The hard way involves setting all the desired values manually. Here are some values that can be set:

\pdfpageheight, \pdfpagewidth Dimensions of the PDF file.
\topmargin Length of margin at top of page above all printing. 1 inch is added to this value.
\evensidemargin Left margin on even numbered pages. 1 inch is added to this value.
\oddsidemargin Left margin on odd numbered pages. 1 inch is added to this value.
\headheight Height of the page header.
\headsep Distance from bottom of header to the body of text on a page.
\topskip Distance from top of main text box to the baseline of the first line of text in the main text box.
\textheight, \textwidth Height and width of main text box.
\footskip Distance from bottom of body to the bottom of the footer.
\parskip Distance between paragraphs.
\parindent Amount of indentation at the first line of a paragraph.

The \setlength{length}{value} command is used to set these lengths. Units include inches (in), centimeters (cm) and points (pt). Note that these lengths can be negative. Here is an example:

\setlength{\topmargin}{0in}
\setlength{\headheight}{0in}
\setlength{\headsep}{0in}
\setlength{\textheight}{7.7in}
\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\parindent}{0.25in}
\setlength{\parskip}{0.25in}

Note that the right margin of a page is automatically set based on the left margin (with \oddsidemargin and \evensidemargin) and the width of the text (with \textwidth).

There are many other parameters that you can set in the preamble, such as the title of the document, the header style, the footer style, page numbering, etc. You can consult books or Google for more information on these areas.

Document Formatting

The document begins after the preamble. Use the command \begin{document} to start the document and \end{document} at the end.

This section will cover techniques to format material in the document you create.

Paragraphs

Any time LaTeX sees a blank line, it treats the next line as the start of a new paragraph. For example, try the following text:

Fourscore and seven years ago our fathers brought forth on this continent a new nation, 
conceived in liberty and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation or any nation so
conceived and so dedicated can long endure. We are met on a great battlefield of 
that war. We have come to dedicate a portion of it as a final resting place for those
who died here that the nation might live. This we may, in all propriety do.
But in a larger sense, we cannot dedicate, we cannot consecrate, we cannot hallow 
this ground. The brave men, living and dead who struggled here have hallowed it
far above our poor power to add or detract. The world will little note nor long 
remember what we say here, but it can never forget what they did here.

It is rather for us the living, we here be dedicated to the great task remaining before 
us--that from these honored dead we take increased devotion to that cause for 
which they here gave the last full measure of devotion--that we here highly 
resolve that these dead shall not have died in vain, that this nation shall 
have a new birth of freedom, and that government of the people, by the people, 
for the people shall not perish from the earth.

When you typeset this, you should find that each of the three sections above is indented and is its own paragraph. Moreover, you should see that if you don't have a full empty line between two lines in your source file, there is not only no new paragraph, but there is no line break, either. To end one paragraph and start another it is not enough to simply hit return and start typing on the next line - you must hit return twice and create an empty line for LaTeX to know to start a new paragraph.

You can also create indents wherever you want in text by adding the \indent command, and you can suppress the automatic indent caused by a new paragraph by using \noindent. For example, try typesetting this:

Fourscore and seven years ago our fathers brought forth on this continent a 
new nation, conceived in liberty and dedicated to the proposition that all men are 
created equal.

\indent \indent Now \indent we \indent are engaged in a great civil war, testing 
whether that nation or any nation so conceived and so dedicated can long endure. 
We are met on a great battlefield of that war. We have come to dedicate a portion of 
it as a final resting place for those who died here that the nation might live. 
This we may, in all propriety do. But in a larger sense, we cannot dedicate, 
we cannot consecrate, we cannot hallow this ground. The brave men, living and 
dead who struggled here have hallowed it far above our poor power to add or 
detract. The world will little note nor long remember what we say here, but it 
can never forget what they did here.

\noindent It is rather for us the living, we here be dedicated to the great task 
remaining before us--that from these honored dead we take increased devotion 
to that cause for which they here gave the last full measure of devotion--that 
we here highly resolve that these dead shall not have died in vain, that this 
nation shall have a new birth of freedom, and that government of the people, by 
the people, for the people shall not perish from the earth.

Note the effects of \indent and \noindent. Finally, understanding paragraphing rules in LaTeX is very important when using display math. Notice the difference in the following:

Now, if we can prove
\[ \Big(2\sqrt{\frac{a}{b}}\Big)^m + \Big(2\sqrt{\frac{b}{a}}\Big)^m
\ge 2^{m+1} \]
then we will be done. Dividing both sides of this inequality by $2^m$ yields
\[ \Big(\frac{a}{b}\Big)^m + \Big(\frac{b}{a}\Big)^m \ge 2, \]
which we can verify easily by AM-GM on the reciprocals that make up the LHS,
thus we have our desired
\[ \Big(1 + \frac{a}{b}\Big)^m + \Big(1 + \frac{b}{a}\Big)^m \ge
\Big(2\sqrt{\frac{a}{b}}\Big)^m + \Big(2\sqrt{\frac{b}{a}}\Big)^m \ge 2^{m+1}. \]

and

Now, if we can prove
\[ \Big(2\sqrt{\frac{a}{b}}\Big)^m + \Big(2\sqrt{\frac{b}{a}}\Big)^m
\ge 2^{m+1} \]

then we will be done. Dividing both sides of this inequality by $2^m$ yields
\[ \Big(\frac{a}{b}\Big)^m + \Big(\frac{b}{a}\Big)^m \ge 2, \]

which we can verify easily by AM-GM on the reciprocals that make up the LHS,
thus we have our desired
\[ \Big(1 + \frac{a}{b}\Big)^m + \Big(1 + \frac{b}{a}\Big)^m \ge
\Big(2\sqrt{\frac{a}{b}}\Big)^m + \Big(2\sqrt{\frac{b}{a}}\Big)^m \ge 2^{m+1}. \]

In the latter, there are indents after each display math, which we clearly don't want. These are caused by the blank lines (and could be suppressed with \noindent).

Sections

For longer documents that you want to split into parts, you can use LaTeX sectioning commands. Here's an example illustrating them. If you use the book document class, you can also use \chapter, but for most documents short of books, these should be sufficient.

\section{In This First Section}

This is the first section.

\subsection{We Have This First Subsection}

This is the first subsection.

\subsubsection{And This Subsubsection}

A subsubsection.

\paragraph{And This Paragraph}

A notable paragraph.

\subparagraph{And This Subparagraph}

A notable subparagraph.

\subsubsection{And Then This Subsubsection}
\section{The This Second Section}
\subsection{We Have This Subsection}

Font Sizes and Styles

To change the font size, use any one of the following commands. To change it for just a portion of the page, enclose that potion in { } and have the relevant font size command occur right at the beginning of the text inside the curly braces. In order from smallest to largest, the font sizes you can use are:

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

Try this out; the effects should be pretty clear:

When I was born, I was {\small small}. Actually, {\scriptsize I was
very small}. When I got older, I thought some day {\Large I would be
large}, {\Huge maybe even gigantic}. But instead, I'm not even
normalsize. {\small I'm still small.}

Here is a simple example that will probably show you all you need to know about bold, italics, and underlining.

When something is \emph{really}, \textbf{really} important, you can
\underline{underline it}, \emph{italicize it}, \textbf{bold it}. If
you \underline{\textbf{\emph{must do all three}}}, then you can nest
them.

Here is another example that demonstrates font families:

You may want to write things \textsf{in a sans-serif font}, or
\texttt{in a typewriter font}, or \textsl{in a slanted font} (which
is \emph{slightly different} than italics). Sometimes it pays
\textsc{to write things in small capitals}. You can next go to
\textbf{bold and then \textsl{bold and slanted} and then back to just
bold} again.

Spacing

There are a few spacing items you'll find useful in LaTeX. First, you can force a normal-size space (as between words) by using a single backslash followed by a space. This is particularly useful after periods: LaTeX interprets periods as ends of sentences, so it puts extra space after them, but if a period doesn't in fact end a sentence, you don't want that extra space. Try this to see an example.

When Mr. Rogers read this, he was confused because the first sentence
was only two words long. Mrs.\ Rogers wasn't confused at all.

In math mode, it's a little different. LaTeX ignores normal spaces in math mode, so all three of the following will come out the same:

Spacing in math mode:

$x + y$

$x     +       y$

$x+y$

Notice that the three math expressions come out all exactly the same. In general, you can trust math mode to space things out right rather than forcing any special spacing. This means that you should write formulas in your source document to be easily readable (by you), and trust LaTeX to do the right spacing.

However, if you do need to tweak the spacing in math mode, there are some special commands:

\, a small space
\: a medium space
\; a large space
\quad a really large space
\qquad a huge space
\! a negative space (moves things back to the left)

Here are examples of these in action:

$x+y$

$x+\,y$

$x+\:y$

$x+\;y$

$x+\quad y$

$x+\qquad y$

$x+\!y$

Two spacing tools that can can be bluntly used to move things are \hspace and \vspace.

I \hspace{2in} like \hspace{1in} space.

\vspace{5in}

In every direction.

Sometimes, \hspace and \vspace will not produce the space you want; this happens most frequently at the beginning or the end of a line or of a page. If you want to force space there, use \hspace* or \vspace* instead.

Two more that can be used even more bluntly are \hfill and \vfill, which cause LaTeX to create as much horizontal or vertical space as possible (within the boundaries of a page as defined in the preamble):

I\hfill like \hfill space.
\vfill
In every direction.

Finally, you can force line breaks and prevent them in LaTeX. To force a linebreak somewhere in a block of text, simply use \\. To prevent a linebreak, you can use ~. The ~ in the text below prevents LaTeX from breaking a line between Professor and Reiter:

This website is largely a result of Professor Harold Reiter getting
me involved in math education again.\\ Professor~Reiter's dedication
to educating eager math students is an inspiration. Students,
parents, and educators who like this site should thank
Professor~Reiter. If you don't already know Professor~Reiter, don't
worry, you'll eventually meet him. Professor~Reiter meets everybody.

Try taking out the ~ symbols, and you'll probably see Professor and Reiter get split up at least once. Notice also that the \\ forces LaTeX to start a new line, but not a new paragraph.

Justification (Centering, etc).

We can center text using

\begin{center} text \end{center}

and can justify it left or right with

\begin{flushleft} text \end{flushleft} \begin{flushright} text \end{flushright}

\begin{center}
Fourscore and seven years ago our fathers brought forth on this
continent a new nation, conceived in liberty and dedicated to the
proposition that all men are created equal.
\end{center}

\begin{flushleft}
Now we are engaged in a great civil war, testing whether that nation
or any nation so conceived and so dedicated can long endure. We are
met on a great battlefield of that war. We have come to dedicate a
portion of it as a final resting place for those who died here that
the nation might live. This we may, in all propriety do. But in a
larger sense, we cannot dedicate, we cannot consecrate, we cannot
hallow this ground. The brave men, living and dead who struggled here
have hallowed it far above our poor power to add or detract. The
world will little note nor long remember what we say here, but it can
never forget what they did here.
\end{flushleft}

\begin{flushright}
It is rather for us the living, we here be dedicated to the great
task remaining before us--that from these honored dead we take
increased devotion to that cause for which they here gave the last
full measure of devotion--that we here highly resolve that these dead
shall not have died in vain, that this nation shall have a new birth
of freedom, and that government of the people, by the people, for the
people shall not perish from the earth.
\end{flushright}

You can also use \raggedleft to replace \begin{flushright} (and omit the \end{flushright}) and use \raggedright to replace \begin{flushleft} (and omit the \end{flushleft}).

Tables

The primary way to build a table is to use the tabular environment. Here's an example:

\begin{tabular}[t]{|l|ccccc|c|}
\multicolumn{7}{c}{USAMTS Scores Round 1}\\\hline
Name&\#1&\#2&\#3&\#4&\#5&Total\\\hline
John Doe&5&5&3&2&1&16\\
Jane Doe&5&5&5&4&5&24\\
Richard Feynman&5&5&5&5&5&25\\\hline
\end{tabular}

When you typeset that code, you should see a simple table like this one. Read through the following general description of the tabular environment to understand how the code above produced the table.

General form of the tabular environment:

\begin{tabular}[alignment]{columns}
rows
\end{tabular}

The italics show where you have to put code to create your table.

alignment - put either b or t, or omit this completely. This determines how your table is vertically positioned with the text around it. This entry is not too important - experiment using different values (or omitting it) when you have a table in the midst of a document to get a better feel for it.

columns - this describes the number of columns and the alignment of each column. Put r for a right-justified column, c for a centered column, and l for a left-justified column. Put a | if you want a vertical line between columns. For example, the column declaration {||rr|cc|l} will produce a table that has 2 vertical lines on the left, then two columns that are right-justified, then a vertical line, then 2 columns that are centered, then another vertical line, then a left-justified column. There are more complicating things that you can do, and even more complicated things if you include the array packing in your document (check a good LaTeX book for more details), but for most tables, the options we've described here are sufficient.

rows - You can have as many rows as you like. For each row, you need an entry for each column. Each of these entries is separated by an &. Use \\ to indicate that your input for that row is finished. Hence, if your column declaration was {cccc}, a possible row entry could be

5&5&5&5\\

If you wish for one row to have fewer columns (i.e. one column takes up several of the usual table columns), use the command \multicolumn. In the example above, we had as our first row

\multicolumn{7}{c}{USAMTS Scores Round 1}\\

The first { } indicates how many regular columns this entry will take up. The second { } indicates whether the text in this entry is right (r), left (l) or center (c) justified. The final { } contains our entry. As with the regular column declaration, use | if you want a vertical line before or after the entry of \multicolumn.

In general, you can use \vline to introduce a vertical line anywhere in a table (try putting one between John and Nash in the example below and see what happens).

Finally, at the end of some of the rows in our example, we have the command \hline. This produces a horizontal line after the row it follows. If you want a horizontal line atop a table, use \hline right before the first row. If you only want a horizontal line under a portion of the row, use \cline{start column-end column} as indicated in the example below:

\begin{tabular}[t]{|l|l|cccc|c|}\hline
\multicolumn{7}{|c|}{USAMTS Final Scores by Round}\\\hline
Medal&Name&\#1&\#2&\#3&\#4&Total\\\hline\hline
&Richard Feynman&25&25&25&25&100\\\cline{3-7}
Gold&Albert Einstein&25&25&25&25&100\\\cline{3-7}
&Marie Curie&25&24&24&25&98\\\hline
Silver&John Nash&20&20&25&24&89\\\hline
&Jane Doe&23&\multicolumn{2}{c}{None}&25&48\\\cline{3-7}
None&John Doe&\multicolumn{2}{c}{None}&25&20&45\\\cline{3-7}
&Lazy Person&5&\multicolumn{3}{c|}{None}&5\\\hline
\end{tabular}

When you typeset this, you should get output like this. Note how we made a double horizontal line after the table headings.

Finally, sometimes you'll want to create a table that consists solely of items in math mode. For such a table, use the array environment. The array environment works exactly like tabular, except that all its entries are rendered in math mode:

\[\begin{array}[b]{ccc}
x&y&z\\
y&x&z\\
1&2&3
\end{array}\]

Change both array declarations to tabular and delete the \[ and \] and see what happens. You can do a number of other things with the array and tabular environments, but the above should cover most of what you'll want to do with them.

If you build a table in which some entries are text that will take up multiple lines, you'll probably want to learn about boxes (below).

Boxes

To create boxes of text that behave differently from the rest of the text, we can use

\makebox[width][pos]{text}

The width sets the width the of the box. The pos sets the positioning of the text - either r (right justified text), l (left justified), or s (stretched to fill the box). If the pos parameter is left out, as in \makebox[1in]{centerme}, the text is centered. The text is placed in the box. If you want to draw a box around the text, use \framebox just as you would use \makebox.

\mbox{text} and \fbox{text} are quick versions of \makebox and \framebox, which create a box to fit the size of the text.

Try the following example to see some of these features:

I can create basic boxes for text \makebox[2in]{like this}. Notice
that there's a 2in wide space with `like this' in the middle of it.

If I want to put a box around the text, I can use a frame box. The
result looks \framebox[2in]{like this}.

I can also justify the text to the right within a box
\makebox[1.5in][r]{like so} or \framebox[2.5in][l]{like so}.

We can also use quick versions of these. We can just \mbox{do this}
or \fbox{this} to create a quick box that's exactly the size of what we put in it.

In some of the boxes above, you'll see the limitations of these boxes. In particular, LaTeX won't do a line break in the middle of a box, so your box might run off the right side of the page. For boxes that span many lines, we can use

\parbox[pos]{width}{text}

The pos is used to align the box with the text outside the box - set it to either b or t to align the bottom or top edge of box with the current baseline (try both and see what happens). You can also just omit this parameter and the box is centered vertically on the current line of text. Look at the following example to see how pos affects the box.

The parameter width sets the width of the box and the text is what is in the box.

Here's an example:

\parbox[b]{2in}{I like using parbox to create funny little boxes of
text all over my page. This one has its bottom edge aligned with the
current line}
CURRENT LINE.
\parbox[t]{2in}{The top of my text is aligned with that current
line.}

\parbox{1.5in}{I'm just centered on the current line.} CURRENT LINE
\parbox{2.5in}{You probably got a few Overfull or Underfull warnings
when you typeset this. Sometimes narrow boxes will do that; if you're
happy with the output, don't sweat it.}

\parbox is very useful with tables, as it can be used to include multirow input on a single row. Without it, long input in a cell will sometimes cause a table to stretch out into the margins. Note how boxes are used to create the tables below, and notice the effect of not using the \parbox in the second table.

\begin{tabular}[t]{ccccc}
\makebox[2.0in]{}&&\makebox[1.5in]{}&&
\makebox[1.5in]{}\\\cline{1-1}\cline{3-3}\cline{5-5}
Student Name&&\parbox[t][0.2in]{1.5in}{Art of Problem Solving
Community Username}&&Student Email\\
\end{tabular}

\begin{tabular}[t]{ccccc}
\makebox[2.0in]{}&&\makebox[1.5in]{}&&
\makebox[1.5in]{}\\\cline{1-1}\cline{3-3}\cline{5-5}
Student Name&&Art of Problem Solving Community Username&&Student
Email\\
\end{tabular}

Lists

There are three simple versions of lists you can make with LaTeX.

To separate list items with bullet points, use itemize:

\noindent Here's my list:

\begin{itemize}
\item Item 1.
\item Item 2.
\item Item 3.
\end{itemize}

The \noindent is there to exhibit how the list is indented.

If you want a numbered list, use enumerate:

\noindent Here's my list:

\begin{enumerate}
\item Item 1.
\item Item 2.
\item Item 3.
\end{enumerate}

If you want to make your own headings for each item, use description:

\noindent Here's my list:

\begin{description}
\item[Heading 1.] Item 1.
\item[Heading 2.] Item 2.
\item[Heading 3.] Item 3.
\end{description}

Lists can be nested up to four levels. Here's one nested 2 levels deep:

\noindent Here's my list:

\begin{itemize}
\item Item 1.
\begin{itemize}
\item List 2, Item 1
\item List 2, Item 2
\end{itemize}
\item Item 2.
\item Item 3.
\end{itemize}

You can use the command \renewcommand to change the labels for items. The labels for itemize have the names \labelitemi, \labelitemii, \labelitemiii, \labelitemiv (one for each level of nesting, with \labelitemi being the first):

\renewcommand{\labelitemi}{$\heartsuit$}
\renewcommand{\labelitemii}{$\spadesuit$}

\noindent Here's my list:

\begin{itemize}
\item Item 1.
\begin{itemize}
\item List 2, Item 1
\item List 2, Item 2
\end{itemize}
\item Item 2.
\item Item 3.
\end{itemize}

As expected, you can also get pretty fancy with enumerate:

\renewcommand{\labelenumi}{\Roman{enumi}.}
\renewcommand{\labelenumii}{\Roman{enumi}. \alph{enumii}}

\noindent Here's my list:

\begin{enumerate}
\item Item 1.
\begin{enumerate}
\item List 2, Item 1
\item List 2, Item 2
\end{enumerate}
\item Item 2.
\item Item 3.
\end{enumerate}

The \labelenumi and \labelenumii are our labels for the two levels of nesting (as with itemize, there are four levels possible). The

\renewcommand{\labelenumi}{\Roman{enumi}.}

causes each item in the primary list to have a capitalized Roman numeral followed by a period. The enumi is the counter for the main items. The

\renewcommand{\labelenumii}{\Roman{enumi}. \alph{enumii}}

causes each item in the secondary list to have a capitalized Roman numeral of the primary list followed by a period, then a lowercase letter corresponding to the item of the secondary list. As you probably guessed, enumii is the counter that tells us which number of the secondary list we're on.

In addition to \Roman and \alph, you can use \arabic, \roman, and \Alph to format counter numbers such as enumii to numbers, lowercase Roman numerals, or uppercase letters. Try them in place of \Roman and \alph above.

Referencing

Sometimes you'll want to refer to past equations, or even to past pages. Rather than having to manually number equations then change your text if the equation labels change, or having to manually put in page numbers which might change later, you can use the referencing built into LaTeX. To tell LaTeX to note where something is so you can refer to it later, use

\label{label name}

To refer to it later, use

\ref{label name}

or

\pageref{label name}

The latter gives you the page number, and the former gives you the Theorem number or equation number or whatever other special number might be attached to the item labeled with label name.

When using \label, you'll have to compile your LaTeX code twice. The first compilation will produce a .aux file that contains all the label information based on your \label commands. The second compilation reads and uses that information to fill out your \ref and \pageref commands.

Here's an example with several uses of \label and \ref.

\section{Some Sums}

Here are a few sums I know.\label{sec:formulas}

\begin{eqnarray}
1+2+3+\cdots+n&=&\frac{n(n+1)}{2}\label{linear}\\
1^2+2^2+3^2+\cdots+n^2&=& \frac{n(n+1)(2n+1)}{6}\label{squares}\\
1^3+2^3+3^3+\cdots+n^3&=& \frac{n^2(n+1)^2}{4}\label{cubes}
\end{eqnarray}

I can find the sum of the first 10 squares easily with formula~(\ref{squares}) above.

\pagebreak

\section{A Cool Relationship}

Take a look at formulas~(\ref{linear}) and~(\ref{cubes}) on
page~\pageref{linear} of section~\ref{sec:formulas}. Notice that the
right side of~(\ref{cubes}) is the square of the right side
of~(\ref{linear}).

Remember, you have to compile the previous example twice in order the see the references. After the first compilation, LaTeX will warn you about "undefined references", and you'll see "??" in your document where the references should be. Compile it a second time, and the references will work.

The \label commands in the \begin{eqnarray} allow us to use \ref later to refer back to the equations. The \label{sec:formulas} allows us to use \ref to refer to the section. Note that we can use the same label for the \pageref as we use for the \ref. Also, note the ~ before each of the references; these aren't required, but are used for style concerns. They prevent a line break right before the reference. Generally, it's poor style to start off lines with numbers or references; these ~ symbols prevent that if possible.

See Also

ACS WASC
ACCREDITED
SCHOOL

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