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\fbox{\fbox{\parbox{7.4in}{\sc Math 2110 \hfill Final Project Guidelines \hfill By Bill Cook}}}

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Your last task this semester is a {\tiny small} project. 
You will pick a topic related to, but yet, a little beyond what was covered in class. Then 
you will write up your findings and record a short presentation.

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\noindent
\underline{\Large\bf Due Date:} Your handout, slides, and recorded presentation are due no later than\dots\\ \force \hfill \underline{\bf Wednesday, December $9^\mathrm{th}$ at noon}. \hfill \force

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\noindent
Here is what I expect from you (and what you will be graded on):

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\begin{description}
   \item[Project Selection:] Pick out a topic and outline what you plan to study. If you pick something off my list of suggestions, you should be good to go. If you want to do something different that's fine -- actually -- that's awesome! But you should talk to me about your selection to make sure it's appropriate for this project.

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   \item[Handout:] You are to create a 1 page (front and back) handout to go with your topic. If you want to make it longer, that's ok. But all I'm looking for is one double sided page. This ``handout'' is what you'd pass out to go with your presentation (if you were giving it to the class in person). Here are some features I will be looking for\dots
   
   \begin{itemize}
      \item It should be typed up nicely in \LaTeX.
      \item Your classmates are your audience. Make sure your handout is understandable from their current level of mathematical education [build on what we covered in class].
      \item You should have a title including your name. For example, something like what I have on this page of directions.
      \item You should have a list of references ({\it that you reference somewhere in the handout!}) at the end of your handout. You should have {\it at a minimum} 3 references. Make sure {\it at least} 1 reference is a {\sc solid} reference (i.e., something published and peer reviewed like a research article or textbook). This source (see \cite{wiki}) is not so solid, but this source (see \cite{bill}) is.
      \item Begin your paper with some background about your topic. you might want to include a little bit of history. If you are discussing Hilbert spaces, you probably should mention who this ``Hilbert'' guy is. If you are looking at the Intermediate Value Theorem, you should probably mention who is credited with proving it first and when (or if this unknown).       
      \item Your handout should include at least 1 ``big theorem'' and either its proof or a ``sketch'' of its proof (mentioning what is involved in proving it). 
      \item You should give at least 2 ``concrete'' examples illustrating your topic/theorem/subject.
      \item Your handout should include a discussion of some application or impact of your topic. This can be a scientific, ``real-world'', or mathematical application or consequence. 
               This includes a kind of ``where do we go from here'' discussion about what comes next.
   \end{itemize}

   \item[Presentation/Slides:] You should record a 5 minute presentation (approximately 5 minutes anyway) and create some slides in \LaTeX to show during your presentation. You should have a title slide, several content slides, and a final slide with references. Don't just read your handout, but do reference parts of it in your talk.
\end{description}

\noindent {\bf Point breakdown:} Handout 60\%, Slides 20\%, Presentation 20\%.

Handout: Required content (theorem, examples, consequences/application) included/quality/accuracy? 0--30pts, Length/background material? 0--10pts, Sources cited/quality? 0--10pts,  Professional/neatness? 0--10pts. Slides: Required content (title, guts, references)? 0--10pts, Professional/neatness? 0--10pts. Presentation: Appropriate length? 0--5pts, Clearly presented/accurate? 0--15pts.

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\begin{center}
\Large \sc Random Topic Suggestions!!!
\end{center}

Here are some suggested topics. Your don't have to pick from this list, these are just random suggestions.

\begin{itemize}
   \item From Calculus: You could pick a big theorem like: The Intermediate Value Theorem, The Extreme Value Theorem, or Rolle's/Mean Value Theorem.
   \item Something more algebraic like: The Fundamental Theorem of Algebra or Factorizations/The Fundamental Theorem of Arithmetic.
   \item What is a metric space? Or what is a normed space? Or what is a Hilbert space?
   \item What is uniform continuity? Or what are Cauchy sequences?
   \item Mersenne primes and perfect numbers.
   \item Error correcting codes, cryptography, and modular arithmetic.
   \item What is an Integral Domain? Or what is a Field? Or what is a (linear) algebra?  
   \item Difference equations.
   \item What is topology? Or what is path connectedness? Or what is compactness?
   \item What are permutations and symmetric groups?
   \item Symmetry groups like symmetries of platonic solids. 
   \item What is a quotient object? Quotient groups or quotient vector spaces or quotient topological spaces. 
   \item What is a dual space? What is a tensor?
   \item Ordinal arithmetic and/or transfinite induction.
   \item Permutations and determinants
\end{itemize}

\dots Don't see anything that strikes your fancy? Come talk to me, maybe I help find a topic for you.

\begin{thebibliography}{myshortbib}

\bibitem[WIKI]{wiki} ``Vertex Operator Algebra'', \href{https://en.wikipedia.org/wiki/Vertex_operator_algebra}{https://en.wikipedia.org/wiki/Vertex\underline{\ }operator\underline{\ }algebra}, Wikipedia, retrieved Nov. 2020. 

\bibitem[C]{bill} Cook, William J. and Noah Hughes, ``On the minuscule representations of type $B_n$'', {\it Involve} {\bf Vol. 11} (2018), No. 5, 721--733.

\bibitem[X]{xxx} Some guy, {\it This source is in my bibliography but wasn't cited in the handout}, I guess I didn't follow directions.

\end{thebibliography}



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