% LESSON SIX
          
\documentclass{amsart}
\thispagestyle{empty}
\begin{document}
             
\begin{center}
	\textbf{Lesson Six: Sizing and Spacing}
\end{center}  

\textbf{Sizing Text}

We can use a variety of text sizes, as shown below.

\Tiny math,  \tiny math, \SMALL math, \Small math, \small math, \normalsize math,
 \large math, \Large math, \LARGE math, \huge math, \Huge math\\
\normalsize

\textbf{Sizing Delimiters}

The first equation below doesn't look quite right: the brackets aren't big enough. 
But we can have them sized automatically, as in the second version.

$$\sum_{k=1}^n k^3=1^3+2^3+3^3 + ... + n^3=[\frac{n(n+1)}{2}]^2$$
$$ \sum_{k=1}^n k^3=1^3+2^3+3^3 + ... + n^3=\left[\frac{n(n+1)}{2}\right]^2$$

Similarly, compare the following.

$$\int_e^\pi\frac{dx}{x(\ln x)^2}=-\frac{1}{\ln x}|_e^\pi$$

$$\int_e^\pi\frac{dx}{x(\ln x)^2}=-\left.\frac{1}{\ln x}\right|_e^\pi$$
% Here, we've used a 'blank delimiter' \left. because LaTeX requires 
%   that delimiters be paired.
% An alternative would be to omit \left. and replace \right with one of:
%   \bigr, \Bigr, \biggr, or \Biggr.

\textbf{Spacing}

We can use fixed spacing commands: $x x\, x\: x\; x\quad x\qquad x$.
% The vertical spacing equivalents are \smallskip, \medskip, and \bigskip.

Items \hfill can \hfill be \hfill spaced \hfill uniformly.
% For uniform vertical spacing, use \vfill.

Or, we can set our own spacing:

Dude, you \hspace{12pt} are \hspace{2.3cm} so \hspace{1.5in} spaced.

% The command \vspace{ } works in a similar way.

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