Projects

As part of this course, I would like you to have the chance to explore some mathematics on your own. With this in mind, you will be required to complete a group project. You should work in groups of 3 or 4 to put together a 15-20 minute presentation, which will be given at the end of the term. In addition, each member of the group will need to turn in a paper addressing what they learned during the completion of the project. You are welcome to choose your own groups, and I can try to help in matching people up if necessary. In your presentation, you should tell the class about some interesting mathematical topic related to abstract algebra. Some vague suggestions are:

Learn about a more advanced topic in algebra which we have not covered in the class, and give the class a synopsis of it.

Tell us about an application of algebra that you find interesting.

Research some of the history behind abstract algebra and the mathematicians who developed it.

I will have a list of specific topics that I can suggest to you, or you can come up with a topic on your own and ask me if it is appropriate. I can also direct you toward sources that you can use to research your topic. To make sure that everyone is on top of things and that the topics are acceptable, I will set some deadlines for the project:

July 9: Give me your choice of partners, or tell me that you would like to be matched with someone.

August 1: Choose the topic for your presentation. Give me a written proposal (as a group) containing a tentative outline of what you plan to talk about.

August 13: Turn in a written outline (as a group) with a summary of your presentation and a description of the main points that you intend to cover. Also include a list of references.

Last week of classes: Give your presentation in front of the class, and turn in your individual papers.

Below are details regarding the different components of the project.

First (rough) outline: This should, first and foremost, tell me what you topic is and how you plan to approach it. You should give a brief description of what you plan to address in your presentation. It's fine if the details are somewhat tentative at this point. This need not be long (one page should suffice).

Second (detailed) outline: At this point you should have a pretty good idea of what you plan to accomplish in your presentation. This outline should give a detailed summary of your topic, including the major points that you intend to address. (For example, if you are investigating an advanced topic in abstract algebra, state some of the definitions and theorems that you plan to discuss.) Include a list of references that you have been using in your research.

Presentation: This is your chance to tell the class (and me) about your topic. Your talk should be roughly 15-20 minutes long, and all the group members should contribute in some way. You are free to give the presentation via whatever medium you find most comfortable (chalkboard or slides). There may also be time for you to field questions from me and your classmates at the end.

Individual report: Each group member needs to turn in a written report to accompany their project. In it, you should discuss some of the mathematics that you specifically contributed to the project. (For example, if your group chooses to divide the responsibilities, you could discuss the specific topic(s) that you were tasked with researching.) It is possible that there may be some overlap between the topics addressed by the different group members, but your paper should ultimately be written by you on your contributions. You may also want to address some of the following questions:
- How did you become interested in your group's topic?
- What did you feel that you learned or gained from the project?
- What aspects of the topic did you find particularly interesting?
The paper should be approximately two (2) pages, and it needs to be typed. It is due by the last day of class.

The following is a breakdown of how the project grade will be computed.

Component	Percent of Project Grade
First outline	10
Second outline	10
Presentation	50
Individual report	30

Updates regarding the project will appear here as they become available.

The deadline for the first (tentative) outline has been moved to Monday, July 30th to accomodate the midterm exam.
The deadline for the second, more detailed outline is no longer Monday, August 13th. This outline is simply due before the start of the presentations (preferably Wednesday, August 15th).
The tentative schedule of presentations is as follows:
- Thursday: Musical Set Theory, Tina Meng, Andrew Li, Andrew Hoh, and Henry Xu
- Thursday: Cryptography and the Diffie-Hellman Key Exchange, James Carlson, Jonathan Pedde, Dan Miao, and Julian Bangert
- Friday: The Fundamental Theorem of Algebra, Harry Gates and Dravid Joseph
- Monday: Wallpaper Groups, Rachael Bornstein, Arenne Clark, and Kellie MacPhee
- Monday: Group Theory and the Rubik's Cube, Sam Stern, Emily Schechter, and Raj Thaker

Math 31: Topics in Algebra

Projects