The goal of the course project is to give you a chance to understand a topic in the cutting edge of Graph Theory research and share your knowledge with the class.

This can take the form of:

• Read and digest main ideas and results of an article in a graph theory journal such as:
• Journal of Graph Theory
• Journal of Combinatorial Theory, Series B
• Discrete Mathematics
• SIAM Journal on Discrete Mathematics
• Electronic Journal of Graph Theory and Applications
• Explore one of the following topics and its connections with graph theory:
• Random Graph Theory
• Graph Matrices and the Spectrum of Graphs
• Hypergraphs
• Graph Enumeration
• Group Theory of Graphs
• Very Large Graph Visualization
• Social Network Analysis
• Graph Algorithm Analysis
• Wolfram Physics Project
• New graph functionality in Wolfram Mathematica Version 13.
• (Feel free to suggest another area of personal interest)
• Learn an algorithm about graphs we are not discussing in class and how to implement it in a programming language of your choice.
• Propose another idea that you'd like to explore.

If you are enrolled in Math 334, the following options are also available:

• Read and understand a comprehensive blog post about a topic from graph theory.
• Learn about the history of a graph theory discovery or mathematician.
• Dive further into one of the topics from our class.

Specifications:

You will be writing a two-page summary of the ideas and giving an 8–10-minute presentation about what you learn. The presentation will focus more on conveying the information to the audience in a digested way so that learn about your subject, as well as the human aspect of your research into the topic. The presentation will be 8–10 minutes, which sounds like a lot of time, but it is not. It will take a lot of time to organize your information and practice to convey everything that you want to. The two-page summary will take similar information and put it into a written narrative format, with more of a focus on the mathematics you encountered in doing research into the topic.

For the presentation:

• Introduce the topic you chose and what inspired you to choose it.
• Give key definitions that the audience will need to understand your key results. There is no need to repeat definitions that we discussed as a class.
• Explain a few key results that you were able to digest from your topic. The number of results will depend on the type of topic you chose. If it is a research paper, there may be only two or three main results. If it is a sub-area of graph theory, there will probably be more.
• Share some aspect of the topic that you thought was interesting using precise language from graph theory. Help the audience to understand why your topic is interesting.
• What open directions or questions have you learned are of interest? What is known and what is unknown? If you chose a research paper, what are future directions of work? If you chose a sub-area of graph theory, what do researchers want to learn next?
• Share your project experience. What was the biggest hurdle? What was your biggest accomplishment? What did you get out of this opportunity? What does it make you want to learn next?
• Prepare your presentation using Powerpoint/Keynote/Beamer or a similar digital slide format.

For the written narrative:

• Start by describing the topic you chose. (But don't discuss why you chose it.) This should be no more than one paragraph.
• Share key definitions from the paper you read or the sub-area you researched that are necessary to understand the rest of your narrative. These definitions should be written carefully and in paragraph form. Do not repeat definitions that we discussed in class. This should be no more than 1/2 page.
• Explain the key results that you found in your research and put them into context. Why would someone care about your topic? (For a research paper, this has to do with situating the paper in terms of it being an answer to a research question; for a sub-area, this will relate to applications or other areas of mathematics where this topic arises.)
• What open directions or questions have you learned are of interest? What is known and what is unknown? If you chose a research paper, what are future directions of work? If you chose a sub-area of graph theory, what do researchers want to learn next?
• Your report should be two full typed pages. If you use LaTeX, use \documentclass[12pt]{article} and text height 9in, textwidth 6.5in. If you use Word, use Times New Roman 11pt font and one-inch margins and 1.5x spacing.

Timeline:

In order to help your time management, I have broken up the project into pieces.

Just as with the other homework assignments, if you are running into trouble or you would like my input on your project, I suggest coming to see me earlier rather than later.

• Project Topic Proposal due Wednesday, October 19. Fill out the online form with the topic you want to investigate.
• Initial organization due Monday, October 31. Email Prof. Hanusa the resources that you have found related to your project, and what you think are the main results of the topic.
• Further Study due Monday, November 21. Email Prof. Hanusa an outline of what you want to put in your presentation—key definitions and key results. If you are having difficulty understanding key ideas, make sure to schedule time during office hours to discuss.
• Initial draft due Monday, December 5. Your project should be complete. You will bring in a draft of your presentation and written narrative to share with classmates for peer review day.
• Project presentations on Monday December 12 and Monday, December 19.Class members will be doing their presentations during the last day of class and during the scheduled final exam period.

More details about grading will be coming at a later date.