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\begin{document}
\begin{center}
{\bf\large Coded Comments for Math Papers\\
18.310 Spring 2012}
\end{center}
\bigskip
\noindent
For examples that illustrate these guidelines, see the writing resources
on stellar.
\begin{enumerate}G
\item {\bf Guide the audience through the content. (This comment applies at
all scales from the paper scale to the paragraph scale and below.)}
\item
Say what you're going to do before you do it. {\it What is your
goal?} (E.g., ``We now determine a generating function for the $a_i$.")
\item Say \textit{why} you're going to do it. (E.g., ``To find explicit
expressions for the $a_i$, we determine their generating function.")
\item {\it Summarize your approach}. (E.g., ``To determine the generating
function for each $k$, we use relationships among the generating
functions to write a system of equations. Solving this system yields the
desired generating functions.")
\item Be sure the purpose of each section and paragraph is clear at the start.
\end{enumerate}
\begin{enumerate}S
\item {\bf If a paper has many parts, structure it carefully and
communicate that structure to readers.}
\item Break a long multi-part paper logically into sections.
\item Ideally, the paper's introduction should remain relatively nontechnical
while giving readers a good intuitive grasp of what the problem is.
\item In the introduction, clearly state the purpose(s) of the paper in
a position of emphasis, like the start or end of a paragraph. (E.g.,
``In this paper, we find the steady-state distribution of the
particles.")
\item In the introduction, let readers know what to expect
in the paper. (E.g., ``In Section 2 we briefly introduce Markov
processes, which we use in Section 3 to model our problem.)
\item
In a math paper, it's common to state the paper's results and
conclusions in the introduction.
\item Mathematics papers rarely end with a section titled ``Conclusion"
(see the previous note). The paper may just end with the completion of
the proof or problem.
\item Within the body of the paper, make clear to readers which results
are your main results.
\end{enumerate}
\begin{enumerate}A
\item {\bf It's professional to acknowledge the contributions of
others. Examples are on stellar.}
\item \label{Awriting}
Your writing, both the wording and the structure, must be your
own (even the problem statement). One reason for this requirement is to
ensure that you fully understand what you're writing. If your writing is
based on a source, set the source aside while you write. After you're
done, you may check for math errors but, once you understand the errors,
set the source aside again as you correct them.
\item Collaboration is encouraged. Be sure to acknowledge your
collaborators (otherwise you may appear to have plagiarized).
\item You may use information introduced in class, in the class notes,
or in the problem statement, but include enough information in your
writing so readers can follow your logical argument without referring to
these. In other words, you may assume that your readers have
mathematical background comparable to your typical classmate, but don't
assume that your readers have attended class or read the class notes or
the problem statement. (E.g., do not write ``We obtain the generating
function by using the strategy introduced in class" without summarizing
that strategy.)
\item If you take a figure from elsewhere, cite the source in the
figure caption. (E.g., ``Figure 1. A cycle within a complete
graph. Figure from [1, p.\,3].")
\item If your writing is based on a source, acknowledge the source and
the extent to which you have used it. For examples, see the materials
about acknowledging sources on stellar. (See also note \ref{Awriting}.)
\end{enumerate}
\begin{enumerate}E
\item {\bf Equations and other mathematical expressions should
integrate well with the text.}
\item\label{Eeqn}
Treat each equation (or other expression) as a grammatical part
of the text within which it appears. Notice the punctuation at the end
of each displayed equation in this example:
\qquad To simplify
$$ xy + y = 2x^2 + 3x + 1,$$
\qquad we can divide both sides by $x + 1$ (because $x > 0$). So
$$ y = 2x + 1.$$
\item When deciding whether to use words or notation, ask which would
be easier for readers.
(E.g., ``There are more than 3 edges" is easier to read than ``If $n$ is
the number of edges, then $n > 3$." In contrast, ``$7 - n > 3$" is easier to
read than ``$n$ less than seven is more than three.")
\item Be precise. Definitions and theorems should be clear and
correct. You may use looser language when motivating a definition or
result, but statements and proofs must be mathematically precise.
\item To make the paper easy to read, ``display" math by centering
each expression on a line by itself (as in the example in note
\textsf{E}1). Display math if it's long, if it's important, if you need
to refer back to it, if readers need to be able to compare lines, if, left within the text,
the equation would break across the end of a line or if it would
stick into the right margin, or if displaying it would simply make the paper easier to read.
(Often, simply rewording improves the situation.)
\item Displayed math should usually be interspersed with text
explaining how each line relates to the preceding lines, as in the
example in note \ref{Eeqn}. If you have many equations with nothing
between them, add explanations or ask yourself whether you're showing
too many details. (The example in note \ref{Eeqn} does not show the
division by $x + 1$, but is still sufficiently clear for an audience of
peers.)
\item Number displays so you can refer to them later in the paper,
but number only those to which you do refer. (If you're using
\LaTeX, search online for ``\LaTeX\ suppress equation number.")
\end{enumerate}
\begin{enumerate}P
\item {\bf Leave time to set the paper aside for a while, reread,
revise, and repeat (as many times as needed). After the content is
correct and clearly presented, polish the paper. }
\item Check your paper's structure by writing the main point of each
paragraph in the margin to create an outline. Revise to create a more
logical structure and/or to communicate the structure to readers.
\item Check that all variables are introduced and are used
consistently.
\item Don't start a sentence with a symbol: it's easier to read
sentences that start with a capitalized word. Similarly, don't run math
expressions together; separate them with words, not commas.
\item Don't use mathematical symbols as shorthand in text (e.g., do
not write ``The number of edges is $> x$"); however, it is acceptable to
include complete expressions in text (e.g., Because $x < 3,\dotsc$).
\item Make a personalized editing checklist for yourself. Include
those things you often forget to do.
\item Use a spell checker. Many LaTeX editors have a spell checker
that ignores TeX code; if yours doesn't, you can strip the TeX code by
copying from the pdf into a program that has a spell checker.
\item Have a classmate or someone else read over your draft, checking
for grammatical errors, convoluted sentences, confusing explanations,
etc. Return the favor, and acknowledge your collaborator.
\item Print the paper to do a final proofreading: you'll catch errors
on paper that you'd miss on screen.
\end{enumerate}
\begin{enumerate}L
\item {\bf To learn how to do something in LaTeX, search online and
skim to find a good response.}
\item To create curly quotes like the ones on the left side of ``this,
type two single left quotes. The single left quote ` may be
just left of the 1 on your keyboard.
\item Indent only when you intend to start a new paragraph. To remove
an indent after a displayed equation, remove the blank line from the tex
code.
\item If you're looking for a particular symbol, search online for
``latex symbols." The Detexify website allows looking up symbols by
drawing them, \url{http://detexify.kirelabs.org/classify.html}.
\item To start a new paragraph, add a blank line to the tex. To add
space between paragraphs, use \verb-\smallskip-, \verb-\medskip-,
\verb-\bigskip-, \verb-\vspace{\baselineskip}-, or a finer measure,
e.g., \verb-\vspace{4pt}-.
\end{enumerate}
\begin{enumerate}T
\item {\bf If you use concepts that are new to your readers, design
the paper to help the readers build understanding.}
\item Add examples or illustrations whenever you can. A paper littered
with examples is often easier to read. Make sure the examples illustrate
as many of the subtleties of the definition or theorem as
possible. Nonexamples are sometimes just as useful. (E.g., a planar
graph $K_4$ and the nonplanar graph $K_5$).
\item Plan and write from the theorems out. In other words, write down
the theorems you plan to prove, then list what examples you need to
help readers understand the theorem and what supporting lemmas you need to make the proof easier. Then list the definitions
you need. Then list the examples you need to help readers understand the
definitions.
\end{enumerate}
\end{document}