Math 455 Projects

Overview

In the project portion of Math 455 you and your team will prepare and deliver a short presentation about some supplementary material for the course. There are many topics in graph theory and combinatorics that we can't cover in class: interesting counting problems, applications of graphy theory or combinatorics to other sciences, various structures on graphs, graph algorithms, etc. The projects give a way for you to research and learn about such things and then present them to the class. I get to sit and learn something for a change!

How will it work?

• I will assign you to groups of four based on your responses to the questionnaire. I will try to build useful teams. You'll find that not everyone on the team will have the same experience, interests, or skillsets. That's the way it is in real life! Part of the process is seeing how to work together. (Students who didn't respond to the questionnaire were randomly assigned to teams.)
• You can meet with your team and decide on a topic that interests you. A list of topics can be found here. To learn more about these, go check out Wikipedia (that's how I would begin), and then use your Google skills (which are undoubtedly better than mine). This open-ended aspect to gathering knowledge is also a feature of the real world.
• Then you and your team should develop a short presentation about the material. The goal is to try to give your classmates an understanding of what the topic is about. We won't have team meetings during class; that will be up to you guys to figure out. But I and/or the T.A. can meet with your team to discuss things. For instance, if you picked the Traveling Salesman Problem (a very famous problem in graph theory), you could explain what it is, show examples, explain why it's a difficult problem, and explain why it's relevant to applications. If you have computer skills or someone on your team does, your team could implement an algorithm that computes solutions to the problem, and report on how that goes. There are many possibilities. Basically, I am trying to give you as much flexibility as possible with what you do. My only serious requirements are (1) you really work as a team, in both preparation and presentation, (2) your team expends honest effort on the project, and (3) your team really tries to teach something during your presentation. A lot of you are interested in teaching mathematics; now's your chance to try it out! (Beware ... I ask questions ...)

The presentation

Presentations will be done in class. I think we will have eight teams and will do two presentations per lecture. There is a projector in the classroom, so if you have a laptop you can use PowerPoint or something similar. Other options are transparencies or the blackboard. (We can discuss your requirements before you present.) Presentations are scheduled to begin April 16th; we may be able to push back to the next lecture.

How is the grade computed?

The grade for the project will be built of three equal components.

First, I'm going to do be radical and require attendance for the project presentations. I don't require attendance at all during the term, but there will be an exception for presentation days. This will contribute to 1/3 of the grade.

Second, as a team you will submit some kind of written record of your project. This can be as simple as giving me pdf of PowerPoint slides, if you present that way. Or it can be a short description of the topic and what you learned about it. This will be something that your entire team does together, and will be submitted jointly. Again this is 1/3 of the project grade.

Finally, the last 1/3 comes from an essay. To satisfy the requirements for an IE course, students should complete a self-reflective essay appropriate to the course. This essay should combine your knowledge of mathematics from across various courses with your knowledge about the real world to show how mathematics is used to solve a problem with origins outside the world of mathematics. Write a brief essay of 1500-2000 words (or longer if you like) that describes the learning experiences you have had and how they relate to the course and the project. In particular, pay close attention to experiences in prior General Education courses in college. For instance, if your project has a component which relates to exchange of money, to what extent do you think a course you may have taken in economics would be relevant to your work here? Discuss what you have observed about yourself as a learner: both within the mathematics major and outside of it. Wherever possible, include specific instances to support your claims.

Note that when one uses a standard 12-point Times New Roman font, a single-spaced page may have between 800 and 850 words. Thus I'm really talking about an essay of between 2-3 pages. This is not an English course, so I'm not going to be a martinet about grammar, style, and so forth. However, a large part of working in the real world is about effective communication. In particular, once you get a job in the real world you will end up doing far more writing than you ever thought possible, and your colleagues will judge you based on it (this is even true for my job in the not-so-real world ... believe it or not I have to write actual words all the time). Thus you should try hard to write something reasonable.

Deadlines

• The team writeup should be submitted soon after your in-class presentation.
• The individually-written essays can be submitted at any time; they must be submitted by the last day of our course.