LaTeX Lesson 5
Typesetting Math in LaTeX

Typing Mathematics

Fractions

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.

Integrals

Expanding Delimiters

\[
   \left| \frac{A+B}{3} \right|
\]

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.

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

\[
\int_0^1 \cdots dx = x \tan^{-1} x \right]
\]

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

Spacing.

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

$a  b$

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}

You can also get horizontal space in a more flexible way by using LaTeX's text boxes.

Boxes

• 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. }

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

Exercise.

Tutorial at Cornell.

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.

Matrices in LaTeX

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 ]