\documentclass[12pt]{article}
\usepackage{amssymb}
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A Sample Note for \textsc{ Mathematics Magazine}
\end{center}

\begin{flushright}
Jack Q.~Firstauthor\footnote{Supported by the National Science
Foundation.}  \\
XXXX University \\
City, State 98765-4321\\
\verb+email@optional.edu+

\vskip 2 mm

Jill P.~Secondauthor \\
Department of Physics \footnote{Note that authors are in
alphabetical order unless there is an extraordinary reason to do
otherwise.  Also, the author address includes a department
\textit{ only} if the department is \textit{ not} mathematics. We
use as few footnotes as possible in the {\it Magazine}.  This one,
for instance, contains information that really belongs in the body
of the paper.
The previous footnote probably belongs among the Acknowledgments at the end.}\\
ZZZZ College \\
City, State 12345-6789
\end{flushright}



This document is meant to help you prepare a Note for submission
to \textsc{ Mathematics Magazine}.  Of course, editorial decisions
depend entirely on what you say and how you say it. Nonetheless,
we will all save time if you exercise some care in how you first
present the paper to us.

Now that I have caught your attention with an interesting
introductory paragraph, here is what you will find: specific
information about the style of Notes in the \textsc{ Magazine} and
a description of the \LaTeX\ code we prefer that you use to
prepare your manuscript.

Since this section is very clearly
an introduction, I thought that labeling it ``Introduction" would add
nothing.  Note that I am willing to use the first person in an Article
and you might be as well.  Another equally respectable choice is ``we,''
even when there is only one author; this can
create an author-reader partnership to
work through the mathematics together.
Whatever voice you choose, consistency is important.

You may be looking at this document in a variety of ways:  the .pdf or .ps files
are meant to be viewed on a screen or printed, while
the .tex file contains the codes used to create those
viewable versions via the program \LaTeX.  Even if you are a novice with \TeX,
there may be enough here to teach you what
you need to know.  And if you are an ace with \TeX,
we have a warning: please do not overload your
document with special kludges and tricks that will
only be removed later by our compositor.

This document is prepared with extremely simple \LaTeX\
formatting, using the unadorned \verb+article+ template. It is
designed for simplicity and ease of handling---not to imitate the
\textsc{ Magazine}'s final, typeset style in every detail.    For
authors less familiar with \LaTeX, we offer a brief lesson,
showing how certain common elements of mathematical style are
typeset using this program.  For hardcore technical
specifications, please see the Electronic Publication Guidelines
[\textbf{7}].

\paragraph*{Notes on writing a Note}
Notes in the \textsc{ Magazine} tend to be shorter than Articles,
usually because they focus on one particular mathematical gem that
can be explained clearly in a few pages.  For this reason, they do
not need much sectioning, and we use the \verb+\paragraph*+
command to create run-in titles for these sections.  Sections are
not usually numbered; this is what the \verb+*+ in
\verb+\paragraph*+ accomplishes.

To judge the length of your piece, you might consider that this
document prints to six pages with the current code, but would run
about four pages in the \textsc{ Magazine}.  The current settings
produce a document that is generously spaced in consideration of
referees' eyesight.

Few pieces of mathematical writing are entirely self-contained,
although we try to make Notes reasonably so.  Define
enough terms to enable an eager undergraduate student
to read your piece without having to consult
too many references.  Experts may know that a
{\it cyclic quadrilateral} is a quadrilateral that can
be inscribed in a circle, but many readers
need to be told.  Besides, it only takes a few words.
Note that we use italics for terms being defined.

For readers intrigued by your exposition,
you should provide friendly references.
Bibliographies may contain suggested reading along with sources actually referenced.  In all cases,
cite sources that are currently and readily available.

\LaTeX\ has a way to keep track of references automatically, but
for a Note, a simple list might be easiest, as illustrated in the
code that ends this file.  To refer to Halmos  [\textbf{3}], you
have to know Halmos is the third reference in the list, because
\LaTeX\ is not keeping track. (The template for Articles shows how
to use the more sophisticated format.) The simple code given
causes a minor error that you can see at the end of the document
after \LaTeX\ has run: each reference is indented.  However, this
is irrelevant for the purpose of submission, and the things you
might do to fix it would probably have to be undone later.


Please follow our bibliographic format carefully, based on the
examples below.  Entries may appear either in alphabetical order
or in order of citation (but choose one order and stick to it).
Journal titles are abbreviated as in \textit{ Mathematical
Reviews}, for instance, {\it Amer. Math. Monthly}; volume numbers
of journals are set in \textbf{bold}.  Authors names are not
inverted: Frank A. Farris, not Farris, Frank A. [\textbf{2}]. The
abbreviation pp. is used for books, but not journal articles. Note
the slightly different style for citing articles in the \textsc{
Magazine}.


\paragraph*{How to do things in \LaTeX}

Roman letters used as variables will be correctly
italicized if enclosed with \$s in your code, as in ``functions $f$, $g$, and $h$.''
This makes for typing lots of \$s when writing in \TeX.
Other popular fonts are $\mathcal A$, for sets and the like, and
${\mathbb Z}$ for the integers, etc.

This last symbol, the ``blackboard'' ${\mathbb Z}$, actually
is not part of basic \LaTeX.  If you look in the {\it preamble}
of this document, the part before the \verb+\begin{document}+
command, you will see the instruction \verb+\usepackage{amssymb}+ .
This enables you to use the blackboard font, as well as certain special symbols:
$$\lceil \  , \rceil \  , \lfloor \  , \rfloor  \ , {\rm \ and  \ so \  on.}$$
\noindent
If you do not have this package, you are welcome to mark these
symbols in by hand. While we are talking about packages,
please do not use any package that redefines major environments,
such as the theorem environment.

\LaTeX\ is able to number theorems automatically, using what is
called a theorem {\it environment}.  This is usually overkill for
pieces in the \textsc{ Magazine}; the following example shows a
simple method for displaying theorems; the theorem need not even
be numbered unless you refer to it by number later.

\textsc{ Theorem 1.} {\it Let $a$ be any real number.   Then $a^2
> -1$. }

{\it Proof}.  The result follows from well-known properties of
flabby sheaf cohomology over algebraically closed fields. This
parody of a proof, the likes of which you would not see in the
\textsc{ Magazine}, ends here, but you don't need to insert an
end-of-proof marker.  You could put a comment in the file to mark
the end of the proof.
%%End of Proof


A remarkable result that has been the target of many proofs in the
\textsc{ Magazine} is the Pythagorean theorem.    If $a$, $b$, and
$c$ are the sides of a right triangle, then
\begin{equation}
a^2+b^2=c^2 . \end{equation} The equation above is called a
\textit{displayed equation}.  The reference number was added using
the equation environment (enclosing the code for the equation
between \verb+\begin{equation}+ and \verb+{\end{equation}+). You
should give numbers only to those equations that you cite by
number later; to refer to his equation without having to remember
which number it had, we gave it a descriptive label, Pythagoras,
whose use is shown in the code below.  The sentence ended with the
equation, so we used a period.

It can be shown from equation \ref{Pythagoras}, by means of a
routine calculation, that $b^2+a^2=c^2$.   Indeed, many related
equations can be derived, such as these:
\begin{eqnarray*}
a^2-c^2 &=& -b^2   \\
b^2-c^2 &=& -a^2 .
\end{eqnarray*}
This is an example of a \LaTeX\ environment that you may find
useful; it aligns the equations on the equals sign. The asterisk
in the code \verb+\begin{eqnarray*}+ suppresses numbering.To
display a single equation without numbering it, enclose the code
in a pair of double \$s, as shown below.

Another useful environment is \verb+tabular+.  Note that
environments must have \verb+begin+ and \verb+end+ markers.  The
code that makes the brace shows how \LaTeX\ uses the commands
\verb+\left+ and \verb+\right+ to
resize delimiters automatically. This also demonstrates the \verb+\center+
environment.
\vskip 2mm
\begin{center}
$\left (
\begin{tabular}{lcr}
This text & is arranged& in a table\\
with an ampersand \& & to delimit& columns\\
and double & backslashes& to end rows.
\end{tabular}
\right )$
\vskip 3mm
\end{center}
The main point of your interesting Note might be illustrated by
something like \textsc{ Figure 1}, which I did not include in this
template, partly because it's fictional, but also because I would
have had to provide an additional electronic file for you to
download (presumably in {\it encapsulated PostScript} format,
eps). Figures should have brief explanatory captions,  like
\verb+Figure 1 Worth 1000 words+, without a period at the end.
Figures may be included in the printed output, using a package
such as \verb+epsfig+. The simplest alternative is to put the
figures at the end, and note:   \textbf{FIGURE 1 GOES NEAR HERE}.

In the previous paragraph, a portion of the text hangs out into
the right margin.  \TeX\ did not know how to hyphenate the verbose
text string.  In preparing your manuscript, you do not need to
worry about things like this.  The line breaks will all change
later anyway. There is much to say about producing figures that
will look good in print.  Before you invest a great deal of time
creating figures, please read the detailed Electronic Production
Guidelines [\textbf{7}].  Here, suffice it to say that we strongly
prefer PostScript formats for figures. Programs such as {\it
Maple} and {\it Mathematica} give you the option of saving
pictures this way.  {\it Geometer's Sketchpad} does not, but our
compositor knows how to handle this type of file.

\paragraph*{Conclusion}
Now replace all the text in this file with a crackling exposition of
some interesting mathematics, \TeX\ it up, and send three hard copies to:
\vskip 3mm

\noindent Frank A. Farris, Editor, \textsc{ Mathematics Magazine}, Santa Clara University,\\
\noindent 500 El Camino Real, Santa Clara, CA 95053-0373
\vskip 3mm

Electronic submission is possible in limited circumstances; ultimately, we need two hard copies to send to referees and one to retain. To request that we do this printing for you, please inquire at \verb+mathmag@scu.edu+ or 408-554-4122.

\paragraph*{Acknowledgment}
We thank our spouses, the anonymous referees, granting agencies, and our moms
for everything they've done for us.    If the editor
helped, that's fine, but we don't thank him here
since he's only doing his job.


\subsection*{References}

1.  R.P. Boas, Can we make mathematics intelligible? {\it Amer.
Math. Monthly} \textbf{88} (1981), 727--731.

2.  Frank Farris, {\it A \textsc{ Mathematics Magazine}
Retrospective}, this \textsc{ Magazine}, \textbf{79} (2006), 1-88.

3. Paul Halmos, How to write mathematics, {\it Enseign. Math.}
\textbf{16} (1970), 123--152. Reprinted in Halmos, {\it Selecta,
expository writings}, Vol. 2, Springer, New York, 1983, 157--186.

4.  Andrew Hwang, Writing in the age of Latex, {\it AMS Notices}
\textbf{42} (1995), 878--882.

5.  D.E. Knuth, T. Larrabee, and P.M. Roberts,
{\it Mathematical Writing}, MAA Notes \#14, 1989.

6.  Steven G. Krantz, {\it A Primer of Mathematical Writing},
American Mathematical Society, 1997.

7. Mathematical Association of America, {\it Electronic Production Guidelines}, http://www.maa.org/pubs/bev.html .

8.  N. David Mermin, {\it Boojums All the Way Through}, Cambridge Univ. Pr., Cambridge, UK, 1990.





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