\documentclass[12pt]{article}

%can add or comment out packages as desired
\usepackage{graphicx}
%If you want to include images, then pdf jpg png formats of images are recognized, for example with the command \includegraphics[height=2in]{filename}

\author{Name}
\title{Paper Template}

\begin{document}
\date{}
\maketitle





\begin{abstract}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus ut quam vel ipsum porta congue ac sit amet urna. Fusce non purus sit amet sem placerat ultrices. Nulla facilisi. Morbi quis orci erat, a tincidunt sapien. Phasellus gravida tristique bibendum. Maecenas ac felis at felis lobortis cursus. Proin lobortis tristique est, rutrum scelerisque lacus aliquet quis. Fusce risus urna, rhoncus at placerat nec, laoreet ac est. Duis molestie congue erat id pretium. Nulla facilisi. 

Do not make the abstract  too long.  
\end{abstract}



%Note, the table of contents only appears after TWO typesettings, like the reference citations.  The first is to find everything and the second put in the TOC.
\tableofcontents

\section{Introduction}


Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urna eu gravida tincidunt, dolor sem tempor leo, sed rutrum lorem magna ut quam. Mauris malesuada ipsum in nulla accumsan mollis ullamcorper tellus facilisis. 



\subsection{Prior Experience}

%Note: This project will build upon previous research experiences, independent studies on advanced mathematics, foreign exchange program experiences, or advanced topics from 3000 or 4000 level classes in which the student has developed an interest. 


\subsubsection{MAT 2240: Introduction to Linear Algebra}

Information about your prior experience with the topic before the capstone, including how and in what context you covered the topic in classes and other experiences as above, including definitions and a summary of examples, important results, proofs, etc.  This also serves an an introduction to the topic aimed at others in this class who may not have had the coursework you did.


\[
A=
\left(\begin{array}{ccc}
\cos{\theta} & -\sin{\theta}& 0\\
\sin{\theta}& \cos{\theta}& 0\\
0& 0& 1\\
\end{array}\right)
\]  represents a counterclockwise rotation by $\theta$ in the $x-y$ plane with the $z$ coordinate fixed.




\subsubsection{MAT 3110: Modern Algebra}




\subsubsection{MAT 3610: Introduction to Geometry}

\section{Developments}

%The course project will investigate some aspect of mathematics in significant depth including an exploration of recent research. 


\subsection{Prior Progress}

%Investigate and include prior progress in the area [into at least the 20th century] via a literature review in your own words that includes at least five sources.

\subsubsection{Earliest Work}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urna eu gravida tincidunt, dolor sem tempor leo, sed rutrum lorem magna ut quam. Mauris malesuada ipsum in nulla accumsan mollis ullamcorper tellus facilisis. 

\subsubsection{18th-20th Century}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urna eu gravida tincidunt, dolor sem tempor leo, sed rutrum lorem magna ut quam. Mauris malesuada ipsum in nulla accumsan mollis ullamcorper tellus facilisis. 


\subsection{Recent Scholarly Research}


Find at least two scholarly research articles from the last ten years that relates to the topic, to show that related work continues, and include them in your bibliography.

Here are in text citations for the bibliography \cite{Cullen72, Kastrup08, Kleiner07, Mactutor, Rosenfeld88} which should be placed where appropriate, like \cite{Cullen72}.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urna eu gravida tincidunt, dolor sem tempor leo, sed rutrum lorem magna ut quam. Mauris malesuada ipsum in nulla accumsan mollis ullamcorper tellus facilisis. 


Here are some sample mathematics commands

\[
\overline{Z}_{n}=\left\{
\begin{array}
[c]{cl}%
e^{-\delta T} & ,0\leq T\leq n\\
0 & ,T>n
\end{array}
\right.
\]
The expected cost over the initial term period is given by
\begin{equation}
\overline{C}_{0:n}=E[b_{T}\overline{Z}_{n}]=\int_{0}^{n}b_{t}e^{-\delta
t}P(t)dt
\end{equation}

The cost over the next $n$-years can be found,

\[
\overline{C}_{x:n}=\int_{0}^{n}b_{x,t}e^{-\delta_{x}t}f_{T}(t)dt \label{term}%
\]
\[
\overline{C} =
{\displaystyle\sum\limits_{k=0}^{\infty}}
e^{-\delta k}\int_{k}^{\infty}P(t)dt\,\overline{C}_{k:1} %
\]


$e^{-\delta k}$ is the discount factor discounting back to time $t=0$, $\ \int_{k}^{\infty}P(t)dt\,\ $is the expected percentage of stock left undecayed at time $t=k$, and $\overline{C}_{k:1}$ is the one year term cost per ton of CO$_{2}$ emitted during the time interval $t=k$ to $t=k+1$ (year $k+1$) from the stock that has been exposed to the decay hazard for $k-$years and survived. 


The term costs below illustrate 1-year term costs for three different wood products

\bigskip
{\small
\begin{table}[h]
%\centering
\begin{tabular}[c]{cccc}%
\\ Year & Waste, bark, fuel & Pulpwood & Fencing\\ \hline
$1$ & $\$4.69$ & $\$19.08$ & $\$4.0x10^{-8}$\\
$2$ & $\$5.81$ & $\$14.95$ & $\$3.6x10^{-6}$\\
$3$ & $\$5.68$ & $\$8.28$ & $\$4.6x10^{-5}$\\
$4$ & $\$5.25$ & $\$4.23$ & $\$2.5x10^{-4}$\\
$5$ & $\$4.72$ & $\$2.08$ & $\$9.0x10^{-4}$\\
PV Total Cost & $\$23.74$ & $\$46.15$ & $\$1.0x10^{-3}$\\
&  &  & \\
5-year Term & $\$23.74$ & $\$46.15$ & $\$1.0x10^{-3}$%
\end{tabular}
\end{table} }
Assume $1$ ton of production (tons CO$_2$ potential), initial cost $b=\$50$ per ton CO$_2$, inflation rate in the cost of CO$_{2}$, $r=2\%$ and a long term continuous discount rate, $\ \delta=5\%$.

\vspace*{1cm}

If you want to include {\bf images}, then pdf jpg png formats of images are recognized, for example with the command \texttt{\textbackslash includegraphics[height=2in]\{filename\}} 
% \includegraphics[height=2in]{filename}
and the image must be in the same directory as the tex file.

\vspace*{1cm}
{\bf Caution}: There are special codes for symbols like 

$\sim$ \hspace*{1.3cm} \_  \hspace*{.6cm} \$
 \hspace*{.3cm}  \# 
 \hspace*{.3cm}  \% 
  \hspace*{.2cm}  \& 
    \hspace*{.3cm}  \{ 
    \hspace*{.2cm} ``

\vspace*{-.5cm}
\begin{verbatim}$\sim$ \_  \$ \#  \% \& \{ ``\end{verbatim} 

{\bf Caution}: ``2 single left quotes" versus "double quotes on left"
  \begin{verbatim}``  \end{verbatim} \vspace*{-.5cm}gives ``
while    \hspace*{.1cm} `` \hspace*{.3cm} gives "


\section{Acknowledgements and References}





%-------------------------------------------
%        Begin References
%-------------------------------------------

\begin{thebibliography}{99}


\bibitem{Cullen72} Cullen, Charles.  \emph{Matrices and Linear Transformations, 2nd edition}. Reading, MA: Addison-Wesley Publishing Company, 1972

\bibitem{Kastrup08} Kastrup, Hans A. \emph{On the Advancements of Conformal Transformations and their Associated Symmetries in Geometry and Theoretical Physics.} Annalen der Physik (v. 17/9-10, 2008)

\bibitem{Kleiner07} Kleiner, Israel.  \emph{A History of Abstract Algebra.}  Boston:  Birkhauser, 2007

\bibitem{Mactutor} O'Connor, John and Edmund Robertson. \emph{MacTutor History of Mathematics Archive: Search Results for Transformations.} Available online: 
\texttt{http://www-history.mcs.st-andrews.ac.uk/Search/\newline historysearch.cgi?SUGGESTION=transformations\&CONTEXT=1} (accessed February 2011)

\bibitem{Rosenfeld88} Rosenfeld, Boris Abramovich. \emph{A History of Non-Euclidean Geometry:  Evolution of the Concept of a Geometric Space.}  New York:  Springer, 1988

\bibitem{More} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urn

\bibitem{More2} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut lobortis, urn

\end{thebibliography}



\vspace*{.5cm}
{\sl Author's e-mail address:}  emailaddress@appstate.edu
\end{document}               % End of document.


