Group Project


You and your teammate will be asked to prepare a project on a number theoretic topic of your choosing. The topic should be something which your team finds interesting and which you can adequately report on in the 40 to 45 minute duration of your project presentation. Afterwards you will write-up your presentation for the Wiki. In addition to the presentation and write-up, there are several other components to the project as a whole.


There are several reasons you will be working on a final project for this class, though the primary motivation is to give you a chance to explore some of the many interesting number-theoretic topics we won't have the chance to discuss in class. This is one of your major opportunities for creative engagement in the course, and you are encouraged to treat it as such.

Aside from the conspicuous mathematical content, however, this project is designed to sharpen your skills as an analytical thinker — to challenge your ability to both understand and transmit information. Along those lines, your team will present your findings to the class, both in an in-class setting as well as on the course Wiki.

Project Components

There are 5 major components to your project: the project contract, summary, proposal, presentation, and write-up.

Project Contract (Due Oct 13)

After teams are assigned, team members are expected to meet and draft a short (half-page) contract which details the team’s and individual members’ commitment to making their project succeed. The contract can include anything necessary to meet this goal, but it should indicate that you’ve discussed how your group will operate, that you’ve thought about how to make working together as pleasant as possible, and that everyone is ‘on the same page,’ as they say. You’ll probably want to begin with discussing questions like the following:

  1. What does each of us hope to take away from this project? What, then, will our group objectives be?
  2. When, where, and how often will we meet?
  3. How will we contact each other and keep each other informed?
  4. How will we delegate duties?
  5. How will we make decisions?
  6. How will we ensure that every document we write is perfect?
  7. How will we deal with tardiness or missed meetings?
  8. How will we deal with members who are not pulling their own weight?
  9. How will we encourage and support each other?

It is to your benefit to determine an appropriate method for dealing with any potential problems before the group begins working, so take this part of the project seriously.

If at this phase your team is also prepared to select the topic for your project, you can also include this in the contract.

Project Summary (Due Oct 31)

Once your team has decided on the project it would like to pursue, you should write up a short (2 or 3 paragraph) summary of the topic you'd like to cover as well as some of the ideas you're likely to pursue in your presentation. Giving a detailed outline at this point is unnecessary; instead, the summary is your chance to show the instructor that you have a rough idea of what you'd like to study and what kinds of results you might be able to present to the class. Some good questions to ask yourself include

  1. Is this topic "big enough" to merit basing my project around it?
  2. Is this topic "small enough" that I can reasonably cover it (or an interesting part of it) in 45 minutes?
  3. Is this topic "interesting enough" to keep me motivated while preparing my project?

If the instructor feels that your project summary will leave you working on a project that you cannot reasonably complete, he reserves the right to ask you to select another topic.

Project Proposal (Due 1 Week Before Presentation)

After you've submitted your project summary you'll have several weeks to research your topic and decide on a plan for the 40-45 minute project presentation and the subsequent your write-up. Your proposal is an outline of the content of your presentation, including a timetable, and, when necessary, a full account of supplemental tools and materials you plan on using. Your project proposal should conclude with 3 to 4 "homework style" problems which naturally come out of your topic; these problems should be tractable for students enrolled in this class.

Your team needs to schedule a time to submit and discuss this proposal with the instructor in person. It is your responsibility to make sure this happens at least 1 week before your in-class presentation. You are also encouraged to schedule a "practice run" of the presentation with the instructor at this time; this will help to ensure that you have chosen a reasonable amount of material to cover, and will also help you gauge the pace at which you need to present your project.

Project Presentation

The presentation is your chance to share your chosen topic with your classmates. It should take the majority of the class period, between 40 and 45 minutes. Presentations which fall significantly short of this time requirement will be penalized, as will presentations which don't conclude by the end of 50 minutes. Your presentation should discuss an interesting topic in a clear and understandable way. You should be prepared to respond to questions which classmates might have about your topic. You should also work to ensure that your classmates stay engaged during the class: ask them questions, have them solve simple problems, etc. Your project should strike an appropriate balance of mathematical theory, examples, proof and/or application.

Project Write-Up

Much as the instructor posts course notes at the end of each class, you will be expected to write up a Wiki page for your project. This should include all the relevant topics you discussed in your presentation as well as any supplemental information that might be interesting. Your write-up should be posted on the Wiki by 5pm on the day after your presentation.

Beware of plagiarism! Plagiarized write-ups will automatically be given an "F".


This project is worth 7.5% of your final grade. Scores for the projects will be determined for the group as a whole, though I reserve the right to give individual grades if

  • team members do not attend any of the group meetings or final project presentations (5 points per absence); or
  • team members are not actively and thoroughly engaged in all aspects of the project (point deductions as appropriate).

The total grade for the project is calculated as follows: Project Contract (5%), Project Summary (5%), Project Proposal (15%), Project Presentation (40%), Project Write-Up (35%).

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