Combinatorics Project - Applications of Combinatorics in Math and Computer Science
As most of you have been aware since before this class began, the counting techniques we've been working on are useful in lots of different contexts. Combinatorics has deep connections in lots of areas of math, computer science, and other fields. The intent of this project is to explore some of those connections, and to get a taste of modern combinatorics.

To begin, browse some current research in combinatorics. If you have a topic in mind that you'd like to learn about, feel free to just dig into research papers. If you need ideas, you can start by looking at some of the combinatorics talks that will take place at the AMS-MAA Joint Math Meetings in January. Here are five sessions specifically on combinatorics topics at the conference:
• Special Session on Algebraic and Topological Methods in Combinatorics
• Special Session on Combinatorial Design Theory
• Special Session on Research from the 2014 and 2015 Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics
• Special Session on Graph Products
• Special Session on Topological Graph Theory: Structure and Symmetry

Now you've got some ideas about topics that look interesting...what next?

Start searching for papers! You can find math papers in a lot of places, but a particularly good resource is the arxiv. You can also find really great summaries of papers on MathSciNet. Your mission is to find a recent math paper (one that was published after you were born) that includes some combinatorics that we've talked about in class. Try to read it! Chances are you won't understand all of it and that's ok. Do a little extended research (try looking in your text book or the library) and try to at least understand what the paper is about.

Finally, you have a general sense of what this crazy paper is trying to tell you. Maybe it's an application of combinatorics to another area of mathematics, maybe it's an application of combinatorics to computer science, maybe it's just some really fancy combinatorics (an application of combinatorics to combinatorics?). Now, try to communicate that with us! Write a review of your paper (in the style of the reviews on MathSciNet). That is, give a summary (to the best of your understanding) of what the paper is talking about. Make sure you highlight any important developments. Make sure also that you consider your audience! (which in this case is another student in this class)

Your write up will be due Monday, Nov 16. It doesn't need to be long (a page is plenty), but it should be well-written and polished! It should be typed in LaTeX (resources below if you need them). It should include proper references (and should not include plagiarism). Please submit both your .tex file and the compiled .pdf.

When I've received everyone's write-ups, I'll compile them together as a short journal of reviews. I'll give them back to everyone to read and comment on eachother's work. Your grade will be based on three components: How well you understood the mathematics in your paper (graded by me), how well you wrote mathematics (graded by me), and how well you communicated mathematics (graded by your classmates).

Questions?

LaTeX resources
•This wikibook is a great intro and reference.
• Cloud-based LaTeX computing is available at www.writelatex.com and www.sharelatex.com.
• DeTeXify can help you find a symbol you need to use.
• TeX Stack Exchange is a Q&A site with descriptions of some of the more complicated TeXing techniques.
• The Comprehensive LaTeX symbols list.
• Symbol Search
• A general introduction
• Another brief introduction