Math 327 – Final Paper Presentations

Overview.  During the final block of the semester (Lessons 22-28), we will read and present research papers to one another.  Each student is responsible for ½ of a lesson.  Preferably, this means that students pair up to present one paper per lesson.  The reading list will be determined by both the students (to ensure that there is ample student interest in the topics covered) and the instructor (to ensure that the papers chosen are accessible to the students).


Three Components. The paper presentations will consist of three components:


1. Paper Proposal and Outline

- Due Tuesday, November 1

2. Written Paper

- Due Thursday, November 17

3. Paper Presentation

- Between Nov. 15 and Dec. 13

  (see sign-up sheet and choose your 

   date before Tuesday, Nov. 15)


1. Paper Proposal and Outline:


Choosing a paper: Each student is responsible for finding an accessible number theoretic research paper to present to the class.  By “accessible,” I mean that the paper should be understandable not only to you, but also to your classmates in Math 327.  Do not assume that others have had the same mathematical coursework that you have had.   To ensure accessibility, you should get feedback from your professor regarding the appropriateness of your paper at least one week prior to the proposal deadline.  In fact, it is advised that you find several papers to share with your professor.  With proper feedback, you will be in good shape to read and present an interesting paper.

For help on searching and retrieving mathematical papers, see the “Research Resources” webpage on the Math 327 course website:


Paper Proposal and Outline: After the initial approval of your choice of research paper, you will write a proposal that describes the purpose and direction of the paper you will write (which, in turn, will provide the basis of your paper presentation to follow.) Your proposal should be 2-3 pages long, including an introductory discussion, an outline of the relevant background information to be included, theorems and proofs to be covered (in the appropriate order,) and an indication of the importance/relevance of the theory involved. If you plan to use other sources (besides the research paper itself,) include a bibliography of such sources.  Finally, you should include a copy of the actual research paper, so that your professor can read the paper and xerox copies for the class.  Your proposals are due

Tuesday, November 1.


2. Written Paper:

The paper component of this assignment will serve as a written version of the presentation that you will ultimately give to the class. However, your written paper will be more detailed than your actual presentation, as you will not have enough time during your presentation to cover everything in full. For example, in your paper you will want to include all details of any proof you will discuss, and you will want to include a significant level of discussion to support and motivate the theorems and proofs along the way.  On the other hand, in your presentation, you might decide to include only a sketch of a proof of one theorem to allow more in-depth coverage of another.  The length of the papers will vary from one student to the next, depending on the nature of the material to be covered and the amount of detail or graphics included. However, I'm guessing that they will be approximately 5 pages long for students working alone and 10 pages long for students working in pairs.  Your written paper is due Thursday, November 17.


3. Paper Presentation:

Each student will have 1/2 of a lesson between Nov. 15 and Dec. 13 to present his or her paper. This could be accomplished in one of two ways. In the first way, a student works alone and has 35-40 minutes to cover an entire paper (or a cohesive portion of a paper). In such a situation the student would probably be working with a shorter paper. In the second case, two students work together to cover a single paper. In this case, the two students work together on all three components of the paper presentation and would have an entire lesson between the two of them to present their paper. This latter option is preferable because it allows the class to focus on one main idea or set of ideas per lesson, and it allows the presenters more freedom to cover the material at an adequate level.  Please try to make your presentations both accessible and interesting for your audience!  You will be graded not only on content, but also on your delivery.  In fact, I will be seeking feedback from the class on each presentation, and this feedback will be considered when determining your final presentation grade.  Sometime between now and Tuesday, November 15, you need to pick a presentation date.  Dates will be given on a first-come first-serve basis.  Look at your schedule now and pick a date that works well with your other courses and deadlines.  Do not wait until the last minute!


Grading.  You will be graded on all three components of your final presentation.  Hence you should view the proposal as a significant graded event (and not just a hoop that you need to jump through.) 


A Final Remark.  Please feel free to get advice from your professor on this assignment at every step along the way. Most of you will be reading and presenting mathematical research papers for the first time. You will likely have a lot of questions. Be assured that you will learn a great deal during this experience, and what you learn here will likely prove helpful to your future work (e.g., students from my last offering of this class tell me they found this assignment to be very helpful to them when it came time to complete their senior exercise in mathematics.)


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