% LaTeX class specification.  Any changes will not appear in the final version
\documentclass[12pt,letterpaper, reqno]{aimpl}

% The problem list should be arranged like a research paper, with
% introductory material followed be one or more main sections.
% Do not divide the sections into subsections.
% Each section could have its own introductory material.
% The main part of each section is a "problem block" which has the format
% [[see elsewhere for more documentation]]

% New macros.
% If at all possible, please do not define any new macros.  Each
% macro you introduce has the potential to cause problems with the
% long-term maintenance of the problem list.

% removed \n from join and moved it to MACROS in app.js
\newcommand{\Cat}{{\rm Cat}}
\newcommand{\A}{\mathcal A}
\newcommand{\freestar}{ \framebox[7pt]{$\star$} }

\begin{document}
\title{Try out this list!}
\author{Edited by David Farmer and Jason Davies}

\urlstub{test}

\maketitle

This problem list is for testing purposes.

Problem lists have three types of users:  
\begin{enumerate}
\item editors, who can change anything and who approve all changes 

\item privileged users, who can suggest changes to almost everything in the problem list, but whose changes must be approved by an editor.

\item everyone else, which includes other registered users as well as
anonymous users.
\end{enumerate}

Privileges are assigned on each problem list separately.  An editor
of one list might not have any special status on another list.


On the list you are looking at right now, you can login a user "aaa" (password "aaa111") to become an editor.  Or you can login as
user "bbb" (password "bbb111") to be a privileged user.  Or you can
logout and be an anonymous user.

Problem lists have the following structure:

\begin{enumerate}
\item The list is divided into sections

\item the problems in each section have the following structure:

a) An optional title

b) Optional introductory statement

c) Optional attribution (the person who posed the problem)

d) Optional "status" of the problem, which can be anything,
but typically indicates any known progress on the problem.

\item Following the problem are any number of remarks.
\end{enumerate}

Following that structure makes it easier to maintain the list.

Feel free to make changes to this list.

Feedback is welcome: \emph{problemlists@aimath.org}




\section{Food from Italy}

Italy is the European country that is shaped like a boot.

Many popular dishes have their origin in Italy test



\begin{problemblock}
\name{This is the heading of the problem}
These are introductory words meant to be read before the problem statement.

\begin{problem}[.1] How many pieces of pizza are in a typical pizza pie?  \end{problem}




\begin{remark}
\by{David Faermer}Eight is the most common, in my experience.\end{remark}

\begin{remark}
\by{Kent}See \ref{piece-def} for its definition.\end{remark}

\begin{remark}
\by{Jason Davies}test\end{remark}

\begin{remark}
\by{Terry}Costco Pizza has 18 slices on average.\end{remark}

\end{problemblock}



\begin{problemblock}The following is actually a real mathematics problem.

\begin{Problem}[.2] Given a plate of spaghetti with $N$ noodles, suppose you randomly connect each end
of a noodle to another end, with all connections equally likely. What is the expected
number of loops? \end{Problem}




\begin{remark}When $N=1$ there is exactly one loop.

When $N=2$ there can be either 1 or 2 loops, with 2 loops occurring 1/3 of the time.
So the expected number of loops is $\frac13 2 + \frac23 1 = \frac43$.\end{remark}

\end{problemblock}



\begin{problemblock}
\name{Sample heading about dessert}


\begin{problem}[.3] Canneloni is a type of desert. \end{problem}




\begin{remark}
\by{Jason}Interesting problem.\end{remark}

\end{problemblock}



\begin{problemblock}

\begin{problem}[.4] This is a placeholder for the statement of a problem. \end{problem}




\begin{remark}\label{piece-def}
\textbf{Definition} A \textbf{piece} of pizza is a connected component.\end{remark}

\end{problemblock}



\section{Food from Greece}





\begin{problemblock}Some sample words of introduction, just filler.



\begin{problem}[.1] The statement \end{problem}




\begin{remark}
\by{some random person at JMM}frfefdffgfsddsvdv\end{remark}

\begin{remark}
\by{JMM person}sdfasdfasfsadfasdf\end{remark}

\begin{remark}Just a test remark\end{remark}

\end{problemblock}



\section{Another section}

testing $ x^x $ foo bar



\begin{problemblock}Let 
$c(h/k):=V(\overline{h},k).$

\begin{problem}[.05] Prove that $c$ satisfies a reciprocity formula
\begin{eqnarray}
xc(x)+c(1/x)-\frac{1}{\mbox{Den}(x)}=\psi(x)
\end{eqnarray}
where $\psi(x)$ can be analytically continued to $\mathbf{C}'$, the complex plane minus the negative real axis. \end{problem}




\begin{remark}What does "Den" mean?\end{remark}

\end{problemblock}



\begin{problemblock}This is a complicated equation

\begin{problem}[.15] \begin{eqnarray*}
\sum_{n=1}^\infty \frac{1}{n^2}&=& 1+\frac{1}{2^2}+\frac{1}{3^2}+\dots
\\ &=& \frac{\pi^2}{6}.
\end{eqnarray*}
 \end{problem}




\end{problemblock}



\begin{problemblock}
\name{The Four Color theorem}
This is a famous old problem.

\begin{conjecture}[.2] A planar map can be colored with four or fewer colors and there is a proof without a laborious number of cases. \end{conjecture}




\begin{remark}Test remark\end{remark}

\begin{remark}33\end{remark}

\begin{remark}Something new.\end{remark}

\begin{remark}testo\end{remark}

\end{problemblock}



\begin{problemblock}Recall that the Vasyunin sum is
$$V(h,k)=\sum_{a=1}^{k-1}\frac{a}{k} \cot \frac{\pi \overline{a} h}{k}.$$

\begin{problem}[.45] Prove that 
$$V(-h,k)=V(h,k).$$ \end{problem}




\end{problemblock}



\begin{problemblock}

\begin{problem}[.5] asddassad \end{problem}




\end{problemblock}



\section{Yet another section}

test



\begin{problemblock}

\begin{problem}[.1] Solve the quadratic equation. \end{problem}




\begin{remark}Remark, part 1\end{remark}

\begin{remark}Remark, part 2\end{remark}

\end{problemblock}



\begin{problemblock}
\name{blah}
stuff

\begin{problem}[.2]  \end{problem}




\end{problemblock}



\section{One more section}







\begin{thebibliography}{99}

\end{thebibliography}


\end{document}
