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\title{Writing Math}

\author{Matt~Ollis \\
\small Group Tutorial: 1--2 credits   \\[-0.8ex]
\small \texttt{matt@marlboro.edu}}

\begin{document}
\maketitle





\section{Introduction}

This is a course about writing mathematics (you may have guessed this from the title).  We will start by looking at the typesetting package \LaTeX \ and move on from there to think about

\begin{itemize}
\item mathematical grammar (for example, don't start sentences with formul\ae)
\item how to write proofs
\item what makes for a good example?
\end{itemize} 

\section{\LaTeX}

When writing \LaTeX, imagine that you are back in the olden days.  The 1970s, say.  To produce a mathematical document you would write it by hand, explaining the logical structure of the text as you went.  You would send this to a typesetter who would turn it into a well-formatted printed document.
You will write \LaTeX \ files as plaintext files, with the logical structure explained.  \LaTeX will then do the typesetter's job for you.

For example, if you want the greek letter $\alpha$ to appear in a mathematical formula, you type ``$\backslash$\texttt{alpha}".  \LaTeX \ will do the rest.  You can also produce almost any mathematical symbols:
\[  \setof{n \in \Z: n \geq 2}\]
\[lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\]
\[ \lfloor \eta \rfloor \subseteq {\mathbb R}^n \doteq \clubsuit \ldots \bot \Rightarrow \widehat{A}, \omega \in \Omega, a^{(b^c)} \neq {(a^b)}^c, \frown, \odot \vee \pm \infty \]



There is a useful online guide to using \LaTeX:
\begin{center}
\texttt{www.tex.ac.uk/tex-archive/info/lshort/english/lshort.pdf}
\end{center} 


I will email you all the plaintext file for this document.  The easy way to get started is to play with the details and worry about the necessary global structure of the file later.

\section{Writing}

\LaTeX will make your output look impressive.  However, you must bear the following result in mind:

\begin{thm}\label{th:writing}
Beautifully typeset nonsense is still nonsense.
\end{thm}

Proof: See the last line of displayed math in the previous section 
\qed


Theorem~\ref{th:writing} must be borne in mind at all times---typesetting an incorrect solution will not make it any more correct.    

Through the semester I'll give you several articles to read about the stylistic aspects to writing math, in particular we'll use \cite{Knuth}.  We'll also read and discuss as a group what we write.


\begin{thebibliography}{99}

\bibitem{Knuth}
D.~E.~Knuth, T.~Larrabee, P.~ M.~Roberts, {\em Mathematical Writing}, MAA Notes (1996).

\end{thebibliography}







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