Projects


Towards the end of the class we will be doing projects in groups of 2 to 3. These projects will give you a chance to explore a topic of algebra that you find interesting. The projects should either be an application of abstract algebra, or an extension of abstract algebra that we did not talk about in class. Either way, there should be a relationship between what you are exploring and what we have done in class. Each group will give a 20-25 minute presentation during the last week of class, and each student will turn in an individual paper, which I will talk more about below.

Project Ideas

  • Crystallographic Groups
  • Geometric Constructions (Ruler/Compass)
  • Cayley Graphs
  • Rubik's Cube (2x2 or 3x3 depending on how ambitious you are feeling)
  • Burnside's Lemma (also called Burnside's counting theorem)
  • Algebraic Coding Theory
  • Quotient Spaces
  • Group Actions (Class Equation)
  • Relationship between cycle type and conjugacy classes in symmetric groups
  • Sylow Groups
  • Anything else that seems interesting to you!

Due Dates

  • August 1: Project Proposal
  • August 13: Paper Outline
  • August 20-22: Presentations
  • August 22: Paper

Project Proposal

The project proposal should tell me what you are planning to work on and who you are planning to work on it with. By this point in the class, you will hopefully know your fellow class-mates, so I am anticipating that you will form your own groups. However, if you are having trouble and would like me to assign groups, I can also do that. I will check back in with you all on this as the term progresses. If you would like to do a project that is not on the list of project ideas please check in with me before the project proposal is due so that we can make sure it works with what we are doing in class.

Each of you should turn in an individual project proposal. The proposal should have a brief description of what topic you plan to do, how it relates to what we've done in class, and why you are interested in looking at it. You will expand on the first two of these in your final paper - this is meant to be a preliminary look at the topic information. The whole proposal should be about two paragraphs.

Project Outline and Paper

Your final paper should be an overview of your topic that another student in the class can understand. You can take content that we learned in class as a given, but please explain all other information so that someone in our class working on another project would be able to follow your paper. Your paper should cover a brief introduction to the historical motivation of the topic (how did it come to be, who were the mathematicians who contributed to it, etc), a description of the math involved, at least one proof and one example (where appropriate - if you think this does not apply to your topic, please come talk to me), and how it relates to what we've been doing in class. The entire paper should be 3-5 typed pages (please come see me if you are trying to type math equations and haven't seen LaTeX before). Every student should turn in an individual paper.

The project outline should be a detailed outline of what will be in your paper. Though you do not need to include complete paragraphs, I expect more than a couple of bullet-points for this (i.e. your outline should not be so general that I can't tell what project it is for). Your outline should also include what you are planning to cover in your presentation. Each student should turn in an individual outline.

Presentation

Your presentation should be 20-25 minutes long, and each group member should contribute equally. You may use the blackboard, slides, or any other medium you desire, as long as you can effectively use it to communicate your topic. You do not need to cover everything that your paper covers - focus on an understandable presentation that your classmates can follow over a presentation that covers a ton of material.

Project Grade Breakdown

Project Proposal 5%
Project Outline 15%
Presentation 30%
Paper 50%