# Senior projects

#### Current projects

I don't currently have any students working on a senior project.#### Past projects

- Mara Holloway, ``Generalizations and Relationships of the Descartes Circle Theorem'' June 2015.
- Cory Simpson, ``What is a Matroid?'' June 2015.
- Seth Arnold, ``Inflating the Platonic Solids while Preserving Distance'' May 2014.
- Courtney Thomas, ``Groebner bases and Sudoku puzzles'' May 2014.
- Briana Lawson, ``R-trivial simple voting games'' May 2013.
- Alexa Creech, ``A congruence problem for polyhedra'' May 2013.
- Brian Heger, ``Using Generating Functions to Compute Power Indicies'' April 2013.
- Nick Dewaele, ``An Explanation of Period Three Implies Chaos.'' December 2011.
- Stephanie Kuban, ``Power Indices, Explaining Paradoxes Dealing With Power and Including Abstention.'' May 2011.
- Emily Sowers, ``Fair Division of Pie.'' April 2011
- Chelsey Poettker. ``Topology and the Four Color Theorem.'' May 2010
- Holly Crider. ``Finite and Infinite Hat Problems.'' May 2010
- Paul Michael Antonacci. ``Vanishing mean curvature and related properties.''January 2009.
- Elizabeth Schaab.``Finding bounds for the number of Sudoku squares.''July 2008.
- Anthony Scoles. ``An investigation of closed geodesics on regular polyhedra.'' May 2008.
- Glenn Harris. ``Billiards in polygons using unfoldings.'' April 2007.
- Meagan Heckert. ``Understanding special Sudoku solutions through geometry and error correcting codes.'' April 2007.

#### Guidelines for writing senior projects with me

Please note that these are not necessarily departmental rules, but are simply some of the things that I like to see. I encourage others (especially students) to suggest additions to this list!- A sample file that you may use is here You should compile this file in LaTeX; see my LaTeX page or ask me for more information.
- Your project must be typed with a program capable of typesetting professional looking mathematics. I strongly prefer simply learning and writing in LaTeX. You may also use LyX or Scientific Workplace, which is available on campus. Be aware of the following caveats: (1) you must use the alphabib bibliography style, see, e.g. Emily Sowers' project, (2) Your presentation must have professionally typeset mathematics as well, as can be easily accomplished with the Beamer class of LaTeX, (3) I can not and will not help
you with Scientific Workplace AT ALL, (4) I have no sympathy for you when you complain about how hard it is to get Scientific Workplace to do what I want, and (5) you must follow all of the
quidlines below. However, I won't prohibit you from using Scientific Workplace, as long as you can get it to
meet these criteria. If you use LaTeX, I will provide unlimited help and troubleshooting. Some specific typesetting information:
- Equations should be numbered only if you are going to refer to them later.
- All pages, except for the first page, should get a page number.
- All figures must be centered and have a caption.
- All tables must be centered and have a caption.
- Definitions, theorems, propositions, etc. must use the \begin{theorem} ... \end{theorem} style provided by the amsmath package.
- Citations should use the format seen in Emily Sowers' project. In LaTeX, this is accomplished with the alpha bib style.
- Sentences should not begin with a variable unless absolutely necessary.
- It is difficult to decide what to call oneself in a mathematical paper. Although perhaps not acceptable in an English class, it is common to refer to yourself as ``we'' in a math paper. (We sometimes call this usage the ``royal we''.)
- Theorems should be numbered as ``Theorem 2.5'' where the theorem appears in Section 2 and is the 5th numbered thing in that section.
- On the first page, you should have a title, your name, the name of your advisor, the **current date**, and the name of your University (which has neither a dash nor the word ``at'' in the name).
- Only include in your references those items which you actually refer to in the paper.
- Your proposal should follow the same style and should be from 2-4 pages. You must define everything in your proposal and clearly indicate WHAT you will DO. You must also indicate what sort of tools you will use (i.e., what sort of material from what classes you will use).

- Write for your peers (or only slighly above the level of your peers). The professors reading your paper will not all be experts in your field, so you should strive to explain yourself very clearly.
- Taking a graphic off the web without citing it is stealing and plagiarism. I much prefer that you create your own graphics, but this is sometimes not feasible. Cite, cite cite!
- Web sources are OK only as a very last resort. I will happily teach you how to find mathematics resources that are books or journals (and thus have been at least somewhat vetted by the mathematical community). The web is a wonderful place to start, but you need to verify and cite all information using more durable media.
- The Chicago Manual of Style will answer any questions about commas, grammar, etc.