\documentclass{amsart}
\usepackage{amsmath, amssymb, amsthm}

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\newtheorem{problem}{Problem}
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\setcounter{problem}{9}
% Change 9 to n-1 where n is the first exercise of your p-set.

\title{Effective Peer Review}
\date{October 14, 2011}

\begin{document}
\maketitle

\begin{center}
Below are several examples of dialogue between a reviewer (Alice) and author (Bob).  Consider what might be effective or ineffective about how they interact.
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\bigskip

\begin{center}
\textbf{Example \#1}
\end{center}

\noindent \textsc{Alice}: Well everything looked pretty good.  It seems like you did all the math right and I can read it and stuff.

\smallskip

\noindent \textsc{Bob}: Oh, thanks.  So, were there any parts that needed some work?

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\noindent \textsc{Alice}: I don't know.  There were a few parts where maybe you could have used some different words, but I understood all of it.  There was guiding text and everything.

\smallskip

\noindent \textsc{Bob}: Cool --- so I shouldn't change anything?

\smallskip

\noindent \textsc{Alice}: Yeah.  I think it's fine.

\bigskip

\begin{center}
\textbf{Example \#2}
\end{center}

\noindent \textsc{Alice}: Gosh, where to start?  I guess there are some proofs, but just look at this!  Your introduction: hardly makes sense.  You state Theorem 1 without defining some of its terms.  There's no indication of why you're introducing the sets $A$ and $B$ at the start of the proof.  And you say you're proving by contrapositive but this is contradiction!

\smallskip

\noindent \textsc{Bob}: Oh, um\ldots  yeah, I guess I see what you're saying.  So what about\ldots

\smallskip

\noindent \textsc{Alice}: No, that paragraph is horrible.

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\noindent \textsc{Bob}: Hm.  So, where do you think I should go from here?

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\noindent \textsc{Alice}: Well, starting over from scratch would be one idea\ldots

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\begin{center}
\textbf{Example \#3}
\end{center}

\noindent \textsc{Alice}: This was pretty nice.  There's strong motivation at the start and you state your claim in Theorem 1 very clearly.  Now I did want to look at the start of your proof:  you leap into a number of technical details without indicating why they're important.  I thought you could ease into that with a short guiding paragraph.

\smallskip

\noindent \textsc{Bob}: What do you mean?  I mean, it's clear what I'm doing, you have to introduce all those concepts, and I put the pieces together in the fourth paragraph.  It's perfectly clear!

\smallskip

\noindent \textsc{Alice}: Right --- I figured it out eventually.  I just think you'd place less of a burden on the reader by providing a roadmap of where things are headed.

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\noindent \textsc{Bob}: But then won't I say everything twice?  I want this to be concise and clean, not boring.

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\noindent \textsc{Alice}:  OK\ldots well, let's look at Theorem 2.  In the proof, you argue for sequential compactness, but you never mention that Heine-Borel reduces the problem to that matter.

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\noindent \textsc{Bob}: Oh come on!  Everyone knows Heine-Borel!

\bigskip

\begin{center}
\textbf{Example \#4}
\end{center}

\noindent \textsc{Alice}:  So I enjoyed this paper --- I think you have a nice perspective on the problem.  Things are well-motivated in the first paragraph, the proofs seem complete, and you make some nice use of guiding text.

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\noindent \textsc{Bob}:  OK, thanks.

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\noindent \textsc{Alice}:  I did feel that some of the information could have been organized better.  For instance, your proof of Theorem 1 is only two paragraphs, but there are at least four distinct steps to your argument.

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\noindent \textsc{Bob}: Uh-huh.  So maybe it would be better if I split the ideas by paragraph?

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\noindent \textsc{Alice}:  Exactly.  I think that would help a lot.  And then I also wanted to draw your attention to the third-to-last paragraph.  It's a little hard to tell how you use $\Xi_{15}$ in the rest of the proof.

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\noindent \textsc{Bob}: Well, I guess I thought it was important because of the r\^{o}le it plays in a related problem\ldots

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\noindent \textsc{Alice}: Right --- I can sort of see that, but I wonder if you should cut that part since it's not really mentioned elsewhere in this paper.

\smallskip

\noindent \textsc{Bob}: Hmm.  OK, well, I'll consider that when I make my revisions.

\end{document}
