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%This LaTeX document is a template to be used by Bates mathematics rising seniors to create a thesis proposal. 

%As a guide, the document is already filled out to represent a fictitious proposal, and all you need to do is modify the entries below to represent your own proposal.

%A PDF version of the fictitious proposal is available on the department's FAQ and Policies pages, at
%                   http://abacus.bates.edu/acad/depts/math/faq.html
%      and
%                   http://abacus.bates.edu/acad/depts/math/policies.html
%      respectively.

%Once you have finished your proposal, export it to a PDF file. Give the file a USEFUL name, for example, RiemannThesisProposal.PDF. Email the PDF file to Laura Wardwell, the 
%Academic Administrative Assistant for Hathorn Hall, at lwardwel\@bates.edu

%                This LaTex document was created Feb/Mar 2010, updated Feb 2015 by Adriana Salerno, and updated Feb 2017 by Meredith Greer 



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\centerline{\textbf{\Large{Senior Thesis Proposal}}}

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\noindent \textbf{Name:} %Your name goes here.
Bernhard Riemann

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\noindent \textbf{Major + 2:} %Write your majors, minors or GECs.
Mathematics Major, German Minor, Latin GEC.

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\noindent \textbf{Proposed Topic:} %Write a brief description of the topic you wish to work on. This should be done in 25 words or less. 
I want to work in number theory. In particular, I want to study functions which might help in understanding the distribution of prime numbers. I have a hypothesis, which I will expand in the narrative portion of this proposal. 

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\noindent\textbf{My thesis proposal is} %Remove the comment (percentage) symbol in front of the appropriate category:
mathematics only.
%double with another major.

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\noindent\textbf{I am considering the following thesis option(s):}%Remove the comment (percentage) symbol in front of the appropriate category, and tell us your preference (if you have any) and the rationale for the preference:
\begin{itemize}
\item fall one-semester 
%\item winter one-semester 
%\item two-semester non-honors
\item two-semester honors (I would prefer this option, but if I do one semester only I would rather it be the Fall semester because I will busy in the Winter with a German theater course)
\end{itemize}



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\noindent \textbf{Potential Advisor(s) (all relevant fields):} %Write the name of any professor(s) you think you might want to work with on this topic. You may leave this section blank if you don't know. 
Carl Friedrich Gauss (Mathematics Department)

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\noindent \textbf{Courses I have had which support my thesis proposal:} 
%List the courses which are relevant, you don't need to list every mathematics course you have ever taken. 

\begin{enumerate}
\item Real Analysis (Math 309)
\item Complex Analysis (Math 308)
\item Abstract Algebra (Math 301)
\item Topology (Math 313)
\item Number Theory (Math 225)
\end{enumerate} 

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\section*{Proposal}

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%This is where you would explain, in detail, what you plan to work on. This should be 2 to 3 pages in length. Here is an example of how you would cite your references in the body of your proposal.

{\em [Explain here, in detail, what you plan to work on. The very brief example below shows how to cite references.]}\\

{\Large \bf [THIS SECTION SHOULD BE 2-3 PAGES LONG.] } \\

This project came from discussing with Dr. Gauss about the distribution of prime numbers. Does the distribution follow some pattern, or is it completely random? Dr. Gauss suggested I look at functions of complex variables. My main resource for complex analysis is the book by Churchill and Brown \cite{cb}.

Interesting results have been found by Jacques Hadamard in \cite{hadamard}. 



\begin{thebibliography}{9}

\bibitem{cb} James Ward Brown, Ruel V. Churchill. \textit{Complex Variables and Applications.} Seventh Edition, McGraw Hill, 2004.   

\bibitem{hadamard} Jacques Hadamard. \textit{Sur la distribution des z\'{e}ros de la fonction $\zeta(s)$ et ses cons\'{e}quences arithm\'{e}tiques}, Bulletin de la Societ\'{e} Math\'{e}matique de France \textbf{14} (1896) pp 199--220.


\end{thebibliography}






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