<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% everything after a `%' is a comment and is ignored by TeX

%  1. create a file like this one using your favorite editior, e.g., 
%     vi, emacs,...  The filename should end in `.tex', e.g., 
%      filenamee.tex

%  2.  run the command `latex filename'. If there are errors, fix them.
%     If not, the latex program produces the file `filename.dvi'

%  3. You can view the file by typing `xdvi filename'

%  4. Alternatively, you can create a postscript version of the output 
%     with the command `dvips filename'.  This creates a file called 
%     `filename.ps' which can be viewed with `gv filename.ps' or printed
%    with the command `lpr filename.ps'.

%  5. For sharing with other users (espcially non-TeX-users or non-Unix-users)
%    it is convenient to send them a pdf version. You can converte a .ps
%    file to a .pdf file with the command `ps2pdf filename.ps filename.pdf'.
%    One can also do a coversion straight from dvi to pdf, but I forget the 
%    exact command.



%----------------  BEGIN LATEX FILE ------------------------

%----------------  BEGIN PREAMBLE ----------------------------

%  these create some special symbols I find useful 

\def\Bbb{\mathbb}
\def\Haus{{\cal H}}
\def\dist{{\rm{dist}}}
\def\area{{\rm{area}}}
\def\dist{{\rm{dist}}}
\def\diam{{\rm{diam}}}
\def\dim{{\rm{dim}}}
\def\supp{{\rm{supp}}}
\def\Bbb{\mathbb}
\def\reals{\Bbb R}
\def\cal{\mathcal}
\newenvironment{pf}   {\begin{proof}}{\end{proof}}

% This  tells latex the basic format to use. This is a 
%  article. Other options are for books, letters, lecture
% slides,...
 
\documentclass[12pt]{amsart}  % use this with LaTeX2e 

% 'amsart' includes special symbols from the AMS. There are 
% other helpful packages to include here if you want to 
% include graphics, use special language fonts,...
% The second option 'psfig'  is used for induding postscript 
% files (e.g., figures) into the paper.

\usepackage{amssymb,psfig}    %use with LaTeX2e

% this set up the labeling and numbering of Theorems, 
% Lemma's, Corollaries,.... 

\theoremstyle{plain}                    %------- 'regular' theorem types
\newtheorem{thm}{Theorem}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{example}[thm]{Example}
%\newtheorem{remark}[rem]{Remark}   
\newcounter{ques}
\newtheorem{ques}[thm]{Question}   
\numberwithin{equation}{section}


% These control the placement of text onto the page, 
% e.g., setting the margins

%\addtolength{\textwidth}{1in}         % increases text width
%\addtolength{\textheight}{.80in}
\addtolength{\textwidth}{1.0in}
%\addtolength{\topmargin}{-.5in}
\addtolength{\leftmargin}{-.5in} 
\hoffset -.5in


% ------ END OF PREAMBLE, BEGINNING OF DOCUMENT ------------------

\begin{document}
%\renewcommand{\baselinestretch}{2}
\baselineskip=18pt



%%%%%%%%%%%%%%%%%%   title  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  You don't need a title for homework

%\title []
%          {}

%\footnote{}
%\subjclass{Primary: Secondary: }
%\keywords{}
%\author {}
%\address{\\
%         Mathematics Department\\
%         SUNY at Stony Brook \\
%         Stony Brook, NY 11794-3651}
%\email {bishop@math.sunysb.edu}
%\thanks{}
%\date
%\date{August 20, 2007}
%\maketitle

%%%%%%%%%%%%%%%%%%%%%%%% abstract %%%%%%%%%%%%%%%%%%%%%%%%

%\begin{abstract}
%\end{abstract}

%\clearpage

%%%%%%%%%%%%%%%%%%%%%%%% Introduction %%%%%%%%%%%%%%%%%%%%

\setcounter{page}{1}
\renewcommand{\thepage}{\arabic{page}}


%\section{Introduction}
%\subsection{}

%\begin{enumerate}
%\item 
%\end{enumerate}

\begin{center}
{\bf A LaTeX Template} \\
SUNY Stony Brook 
\end{center}


\section{ The first example}

{\bf Problem 0, Chapter 1, page 26:} Prove the circle is round.

\begin{proof}
This is  clear from the formula 
$ x^2+ y^2 =1,$
and even more so from the complex form 
\begin{eqnarray*}
  |z|^2  &amp;=&amp;  (x+iy) \overline{(x+iy)} \\
         &amp;=&amp;  1 \\
         &amp;=&amp;  \frac {1+i}{2+i-1},
\end{eqnarray*}
or it can be observed in Figure \ref{fig1}:

\begin{figure}[htb]
  \centerline{ 
     \psfig{figure=sample.eps,height=2.0in}
  }
  \caption{
     \label{fig1} 
     This picture was created using 
     xfig and then exporting to postscript. It clearly 
     demonstrates the roundness of a circle.
  }
\end{figure}

\end{proof}

\section{Some consequences}

The following result is left to the reader:

\begin{lemma} \label{rect-lemma}
Rectangles  are not circles.
\end{lemma}

Using Lemma \ref{rect-lemma}, the reader can also verify

\begin{cor}
Squares  are not circles.
\end{cor}


% ----------- REFERENCES, see bibtex  ----------------------------

%\bibliography{weight}
%\bibliographystyle{plain}


\end{document}


\begin{comment}
    A comment is a way of preventing text from being 
included into the TeX form.  You can read this when 
you edit the file but it is invisible to TeX (and easier 
that putting the percent sign in front of every line.

\end{comment}
%=======================================================

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