Typesetting Math in LaTeX

`\frac{a}{b}`

, which will give a small fraction with
numerator ` a `

and denominator ` b `

for
in-line formulas. Using the "displayed fraction" command
`\dfrac{a}{b}`

gives an upright fraction, and makes the line
a little larger vertically to provide sufficient vertical space for the
displayed fraction. In a `displaymath`

environment or
` equation`

environment it is not necessary to use the `\dfrac`

command;
the command `\frac{a}{b}`

will give an
upright fraction, and the resulting line will also take extra vertical
space.
**Warning:** note that the fraction command has two
arguments, each enclosed in curly braces.
Avoid non-LaTeX-style argument lists, like
`\frac{a,b}`

, an error that many beginners make when they
first start typing LaTeX documents.

`\int`

, and
one can attach the limits of integration by giving them as subscript
and superscript to the command `\int`

.
\[ \left| \frac{A+B}{3} \right| \]It produces a displayed version of the formula |

NOTE: The symbol | is located above the backslash on most keyboards. It works
properly only in math environments. You can also use
`\vert`

to get the same result.

Now please look at the page of integral calculus provided by one
of the two links below.

As an exercise, you are going to use LaTeX to typeset your own version of this page. [WORK IN PROGRESS]

In it we encounter the problem of using a single right delimiter, ], (with subscript and superscript attached) to indicate the difference of values of a function. LaTeX produces typeset copy in which the symbol ] is too small.

It is natural to think of using the idea introduced above for matching
delimiters (such as []) to the text inside, and to try the code

\[ \int_0^1 \cdots dx = x \tan^{-1} x \right] \]but LaTeX complains if you try to use

`\right]`

without a corresponding `\left]`

command
earlier in the file. To get only a single right delimiter, say ],
sized correctly
you can use `\big]`

or, if that is still too small,
`\bigg]`

;
`\left.`

, that is
`\left`

followed immediately by a period. For example, can be typeset by

\documentclass[12pt]{article} \begin{document} \[ \left. F(x) \right]_{0}^{1} = F(1) - F(0) \] \end{document}

- a space is one of the characters that indicates the end of a command.
- you can insert a text box (see below) in which everything is in text mode.

$a b$is typeset as

Therefore, to achieve the appearance that you want, you may have to add or
remove space. For example, in an integral, between the integrand and
the differential it is usually better to add a "thinspace"
`\,`

.

Perhaps you will find this feature of LaTeX to be disagreeable, but eventually you should be able to appreciate the balance struck in LaTeX between convenience and the power to control the whitespace completely whenever it seems desirable. Here is a list of the most widely used commands for horizontal spacing.

\, (thinspace)

\; (thickspace)

\quad (quadspace)

\qquad (double quadspace)

\! (negative thinspace)

There are other ways of getting space. If you want 12 points of
horizontal whitespace between two characters, you can get it by using
the command `\hspace{12pt}`

between them. The argument to the `\hspace`

command can be
specified in inches, for example, .5in if you want a half inch of
horizontal whitespace. This command also works in both math and text
environments. You may want to keep in mind that there are 72 points
to the inch.

If you want whitespace at the beginning of a line, you need the
variant form of the
`\hspace`

command, namely `\hspace*`

because
LaTeX generally swallows all space at the beginning of a line.

While we are on the subject of creating space, we should mention that there
is a command `\vspace`

which works very much like
`\hspace`

but creates *vertical* space in a document. This is needed,
for instance, if you want to create vertical space for including a picture.

For simple vertical spacing one can use the predefined vertical spaces provided by the commands

\smallskip

\medskip

\bigskip

It is sometimes convenient to use *relative* size units rather
than absolute size units.
You can refer to the relative size units in the current font by
using the units *em* and *ex*. At one time,
*em* and *ex* corresponded, respectively, to the widths of
the letters M and X in whatever font was being used at that point.
In LaTeX that is no longer true, but it is true that the size of these
units will scale with the font, so that a change to a different font
size will not disturb the proportions of the typeset material.

Here is some LaTeX code that will create a small table showing the effects of the various horizontal spacing commands.

```
\documentclass[12pt]{article}
\begin{document}
\begin{table}[ht]
\begin{center}
\begin{tabular}{ l l }
\hline
\verb=||= gives & $||$ \\
\verb=|\,|= gives & $|\,|$ \\
\verb=|\;|= gives & $|\;|$ \\
\verb=|\quad|= gives & $|\quad |$ \\
\verb=|\qquad|= gives & $|\qquad|$ \\
\verb=|\hspace{.5in}|= gives & $|\hspace{.5in}|$ \\
\verb=|\hspace{6em}|= gives & $|\hspace{6em}|$ \\
\hline
\end{tabular}
\caption{Horizontal Spacing} %NOTE: this is within the
````center`

environment
\end{center}
\end{table}
\end{document}

It gives this table:
You can also get horizontal space in a more flexible way by using LaTeX's
text boxes.

`amsmath`

package, one could use the command `\makebox`

,
which has a short form `\mbox`

. These take
- an optional length argument, such as 3.5in (or cm or pt),
- an optional alignment argument
- l for flushed left (this is the default)
- r for flushed right,
- s for stretched,

- a text argument.

\makebox[3in][r]{This is in a line box. }This gives a 3 inch horizontal space in which the text "This is in a line box." is right justified. If you want to put a frame around your box, that is easy. Use

\framebox[3in][r]{This is in a line box. }

The part of the tutorial on errors in LaTeX is appropriate reading now since the most common error messages in LaTeX, besides misspelled commands, involve "overfull hbox" errors.

Go to their tutorial now.

Here is an example of some LaTeX code that will typeset a matrix.

\left[ \begin {array}{ccc} 9&13&17\\ \noalign{\medskip} 14&18&22 \end {array} \right]

If you put this code inside a LaTeX `displaymath`

environment, you will get the matrix typeset. (Since
matrices are large, they are almost always set as displays.)
Here are some points to observe about this code.

- The
`\left[`

and`\right]`

are delimiters of adjustable size that make the brackets around the matrix. If you want parentheses instead of square brackets, use`\left(`

and`\right)`

. To make vertical bars for determinants, use`\left\vert`

and`\right\vert`

. You can also make curly braces via`\left\{`

and`\right\}`

. (For curly braces, you need to put a backslash in front of the braces so that LaTeX realizes they are not LaTeX grouping symbols.) - The LaTeX
`array`

environment has an argument, in this case`ccc`

, that determines how the entries in each column are aligned. In this example, all entries are centered in their columns. If you change`ccc`

to`lrc`

, for example, then the entries in the first column will be left-aligned, the entries in the second column will be right-aligned, and the entries in the third column will be centered. - The ampersand
`&`

character is used to separate entries in different columns. - A double backslash
`\\`

is used to terminate each row of the matrix except the last one. - This example was produced by Maple. The source code
`\noalign{\medskip}`

in this example gives an extra space between the rows of the matrix. This extra space is not necessary and could be deleted.

(If you `\usepackage{amsmath}`

, and you are willing to
settle for centered entries in matrices, then you can replace
the `array`

environment with the `matrix`

environment, which does better spacing. The `amsmath`

package also has a `pmatrix`

environment that has
enclosing parentheses built in.)

**Exercise**: Typeset the following matrix.

[ 47 41 31 33 ] [ ] [ 1 12 27 12 ] [ ] [ 41 1 28 58 ] [ ] [ 35 24 23 34 ]

email: Martin Karel