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\noindent
{\Large {\bf Writing Math}} \\

\noindent
{\bf Credits:} 1 \\
{\bf Level:} Intermediate \\
{\bf Prerequisite:} Several math classes or permission of instructor \\ 
{\bf Location:} My office (Sci218) \\
{\bf Times:} Friday 3.30--4.50pm  \\
{\bf Instructor:} Matt Ollis, \texttt{matt@marlboro.edu} \\
{\bf Website:} \texttt{http://cs.marlboro.edu/courses/fall2008/writing\_math/home}





\section{Introduction}\label{sec:intro}

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{enumerate}
\item math-specific rules of grammar (for example, don't start a sentence with a formula);
\item how to write proofs;
\item how to select a good example.
\end{enumerate} 

\section{\LaTeX}\label{sec: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 in the margins 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:
\[  \setof{n \in \Z: n \geq 2}\]
\[ \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\]
\[ \lfloor \eta \rfloor \subseteq {\mathbb R}^n \doteq \clubsuit \ldots \bot \Rightarrow \widehat{A}, \omega \in \Omega, a^{(b^c)} \neq {(a^b)}^c, \frown, \odot \vee \pm \infty \]

I will email you all the plaintext file for this document.   I've included many of the common \LaTeX \ tricks and structures that you'll need to master.  The easy way to get started is to play with the details and worry about the necessary global structure of the file later.    There is also a useful online guide to using \LaTeX:
\begin{center}
\texttt{www.tex.ac.uk/tex-archive/info/lshort/english/lshort.pdf}
\end{center} 


\section{Writing}\label{sec:writing}

\LaTeX \ will make your output look impressive.  However:

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

\noindent
Proof: See the last line of displayed math in Section~\ref{sec:latex}. 
\qed


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

Open a math book or paper at random and you'll see that the words massively outweigh the formul\ae \ or calculations.  Now look at a sheet of your math homework.  I bet the opposite is true.  Most of our time will be spent working on the words: how to structure a math paper (or plan), what makes for a valid proof (and what makes for a {\em good} proof), the importance of a well-chosen example, how to cite the work of others, why mathematical writers so often use the first-person plural, and much more. 

Through the semester I'll give you several articles to read about the stylistic aspects to writing math and in particular we'll read most of  \cite{Knuth}.  We'll also read and discuss some of our own mathematical writing as a group.

\section{Academic Integrity}\label{sec:ai}

You are expected to be aware of the college's policy on academic integrity and to abide by it.  It can be found on the college website, and is linked from the course website.  
In particular, be careful not to ``double-dip".  While close links to your work outside this class are strongly encouraged, any work you do cannot count for credit twice.
Please come and talk to me if anything is unclear.


\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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