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THE TITLE HERE IN CAPS
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by \bigskip \\
My Name Here
\bigskip \bigskip \\
A thesis submitted in partial fulfillment of the requirements\\
for graduation with Honors in Mathematics.
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Whitman College \\ 2008
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%***********BEGIN CERTIFICATE OF APPROVAL PAGE HERE ********************
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\emph{Certificate of Approval}
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\begin{center}
This is to certify that the accompanying thesis by (your name as it is to appear on the commencement program)
has been accepted in partial fulfillment of the requirements for graduation with Honors in Mathematics.
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}
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My Thesis Advisor's Name, Ph.D.
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Whitman College \\ May 06, 2008
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ABSTRACT OF THESIS
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PUT TITLE OF THESIS HERE (IN CAPS)
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My Name Here \\
Whitman College\\
May 2008
}
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\tableofcontents
%*****************LIST OF FIGURES HERE
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%****************** TEXT STARTS HERE
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\section{Introduction}
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We see a sample figure in Figure \ref{SineWave}. This is sample text to explain the figure. The figure was
generated in Maple as:
\begin{verbatim}
plot(sin(x),x=-4..6,color=black)
\end{verbatim}
then the files {\tt Sine.eps} and {\tt Sine.jpg}
were both {\it exported} (right-click the figure in Maple). As of this writing (Sep 2009), all figures must
be in black and white (for archival purposes).
\begin{figure}
\centering
\includegraphics[width=3.0in]{Sine}
\caption{This is a sample caption. The sine figure was generated in Maple. See the
text if you want to incorporate it.}
\label{SineWave}
\end{figure}
\section{Preprocessing Data}
First we find the Singular Value Decomposition (SVD) of the matrix
$\mathbf{X}$ whose dimensions are $m \times n$. sample sample sample sample sample sample sample sample
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\subsection{Finding the Best Basis}
The Basis Theorem allows us to take a multivariate data set and find a
more compact representation. This means that if we have an $m \times n$ data set $\mathbf{X}$
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\newtheorem*{bestbasis}{The Best Basis Theorem}
\begin{bestbasis} Suppose that:
\begin{itemize}
\item $\mathbf{X}$ is an $m \times n$ mean-subtracted data matrix of $m$ points in $\mathbb{R}^n.$
\item $\mathbf{C}$ is the covariance matrix of $\mathbf{X}$
\end{itemize}
Then the best $k$-element basis $\Phi$ of $\mathbf{X}$ is found by taking the first $k$ eigenvectors of $\mathbf{C}$,
when arranged by eigenvalues from largest to smallest.
\end{bestbasis}
In his textbook, David Lay \cite{lay} gives an example of
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\singlespacing
\begin{thebibliography}{99}
\bibitem{matlab} The Mathworks Inc. (n.d.). Image types in the toolbox. In Image processing toolbox. Retrieved at \url{http://www.mathworks.com/access/helpdesk/help/toolbox/images/f14-13543.html}.
\bibitem{lay} D. C. Lay, \textit{Linear algebra and its applications}. Addison Wesley,
New York, NY 2003.
\end{thebibliography}
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