Research Independent Study

The Director of Undergraduate Studies can set up an independent study course after a proposal has been received that follows the guidelines below.  The deadline for your proposal is the end of the first week of classes however an earlier submission is better in case you you are required to revise your proposal. The DUS can be reached at

  • If approved, mathematics department staff will e-mail you a section number and a permission number that will enable you to sign up for the course on DukeHub.
  • If your proposal needs further work before it can be accepted, you will be informed by e-mail.

Research Independent Study can be used as the basis for Graduation with Distinction.


  1. The first step is to download the Math Independent Study form. Please complete this form noting the following modifications which are specific to the math department:
    • The Description of Proposed Study (Item 1 on the bottom of the permission form) should be typed out on a separate sheet (or sheets) of paper according to the guide below.
    • The Nature of Final Product statement (Item 2) and the Grade to be based on statement (Item 4), should include a verbatim copy of the corresponding portions of this webpage below.
  2. Work together with your mentor to write the proposal. The length of your Description of Proposed Study will depend on the particulars, but should be ideally between 1-3 pages.
  3. In preparing your independent study proposal a good model to follow is a complete course syllabus. While your study proposal doesn’t need to be as full as an actual syllabus, it should be more substantial than a bulletin-style course description.
  4. Be sure to communicate clearly. You want your proposal to be well organized and carefully written so that your reader will be able to understand what you are writing. While your intended reader will be a mathematician with at least a basic working knowledge of mathematical concepts, they may not be as familiar with specialized terms in a given subfield. These specialized terms – or terms from science, economics, and engineering that may not be familiar to a broad range of well-educated lay people – should be defined in your proposal.
  5. Turn in your typewritten sheet (or sheets) together with the completed independent study permission form (signed by you, the supervising faculty member, and the instructor if different) to the Director of Undergraduate Studies for Mathematics. This should be done as early as possible during the first week of classes. It is acceptable to submit your forms as an e-mail attachment to (however scanned documents must be "clean" — the background cannot be gray).  If the application is not acceptable you will be notified of the problems and you may revise and re-submit.  If it is acceptable you will be notified in the second week of classes and given a course/section number and a permission number in order to register.
  6. At the end of the semester, on or before the last day of final exams, you must e-mail an electronic copy of your final paper to the Director of Undergraduate Studies of mathematics at

Guidelines for your Description of Proposed Study

  1. Clearly state the problem you will be working on in as precise a manner as possible.
    • The statement should be understandable to a mathematician whose specialty is far removed from the field in which you propose to work.
    • It may be necessary to include background information to provide context before coming to the statement of the actual problem.
    • In case the source of the problem is outside mathematics, it may be necessary to first discuss the scientific, engineering, or economic context and then explain how mathematics enters in before describing the specific problem itself.
  2. What previous work has been done related to the problem?
    • Did you work on this problem, or a related problem, during the summer or during a previous research independent study course? If yes, it is important to communicate any previous work that you completed. Please summarize what you did and include an electronic copy of your final paper from a previous semester.
    • If others have worked on this problem, you need only summarize what is necessary to set the context for how you propose to approach the subject.
  3. Describe how you propose to make progress towards solving the problem.
    • What methods will you try?
    • Will there be techniques that you need to learn? If so, from what sources will you learn them? List chapters in books or articles in journals.
    • What courses have you taken previously which will provide you with some of the background necessary to approach your problem?
  4. Proofread carefully what you have typed to be sure that the issues above have been addressed.

Nature of Final Product 

The final product for your research independent study will be a formal paper (as opposed to an informal report) that meets the criteria listed below.

  1. The paper describes important aspects of the work done during the course.
  2. The paper is thoughtful, well organized, and well written. It should be carefully proofread.
  3. The paper communicates well to as broad an audience as would reasonably be assumed to have interest in your research topic.
  4. The first part of the paper (two pages minimum) describes the broader context in which the project took place. This section should be written in a way that is understandable to an individual who has no specialized knowledge beyond the standard course content regularly offered by the Duke math department.
    • Specialized technical terms should be defined or avoided.
    • If your project involved a particular problem in a field of pure mathematics, it should be related to broader questions within that field.
    • If your project involved an application of mathematics, appropriate background material should be explained to motivate the problem and set it in a suitable context.
    • If non-standard mathematical techniques are used, they should be compared to standard techniques.

The final paper may, at the discretion of the instructor, include relevant excerpts from any paper or report that you had written for a previous related independent study course or in connection with a previous related research project. However, such excerpts may only constitute a small portion of your final paper.

Work on the final paper, especially on that part that explains the broader context of the research, may be begun early in the semester.

Student will e-mail an electronic copy of their final paper to the Director of Undergraduate Studies of mathematics on or before the last day of final exams.

Grade to be based on 

The final paper will contribute substantially to the course grade – that is to say, a student will not receive an “A” grade if their final paper clearly fails to meet the criteria listed above under "Nature of Final Product".