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{\bf Homework \#6:  Typing mathematics with \LaTeX}\\
Craig L. Zirbel\\
February 3, 2003
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{\bf 1.} The first thing that you might notice about properly typed
mathematical text is that variables such as $x$, $y$, and $z$ are typeset
in a different font from the rest of the text.
Usually an italic font is used, although $\mathbf{A}, \mathbf{B},$ and
$\mathbf{C}$ can be typed in a bold math font as well.

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{\bf 2.} Next, you might want to know that the names of functions are
typeset in an upright font, so that we have $\sin(2x) = 2\sin(x)\cos(x)$
instead of $sin(2x)=2sin(x)cos(x)$, which looks lousy.  
{\em Note that this is true even when the surrounding text is italic; one
  still types standard functions such as $\ln$ and $\log$ in a roman font.}

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{\bf 3.} Eventually, you will become brave enough to try to typeset a
really big and exciting equation that is so important that it needs to be
set apart from the text.
$$
    \sum_{n=0}^{\infty} \frac{\lambda^{n}}{n!} = e^{\lambda}
$$
There is nothing so satisfying as seeing a nicely displayed equation,
except, perhaps, seeing it displayed with an automatically generated
equation number!
\begin{equation}
    \int_{0}^{x} (1+u)^{25} \,\mathrm{d}u = \frac{1}{26}(1+x)^{26}-1
\end{equation}
You will notice that the differential d is set in a roman font, whereas the
variable $u$ is set in an italic font.
I have read in the textbook that this is a high point of mathematical style.

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