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How to prepare a research independent study proposal

This website provides a guide to preparing a proposal for a research independent study course in mathematics. (If instead you are preparing a proposal for a non-research independent study course in mathematics, consult this webpage instead.)

The necessary material should be submitted to the Director of Undergraduate Studies in Mathematics no later than the end of the first week of classes in which the course is to take place. As applications may be returned with a request for further information, you are encouraged to submit the proposal as early as possible during the first week of classes.

General instructions

  1. The first step is to get a copy of the independent study permisssion form. This is available towards the bottom of the webpage
    under the heading, "Online Form".

    Please complete this form noting the following two modifications which are specific to the math department:

    1. The Description of Proposed Study mentioned in item 1 on the bottom of page two of the permission form should be completed on a separate sheet (or sheets) of paper according to the guide below. It should be typed.
    2. The Nature of Final Product statement mentioned in item 2 on the bottom of page two of the permission form should include a copy of the part of this webpage titled Nature of Final Product (see below).
    3. The "Supervising Faculty Member" must be a regular rank faculty member with their primary appointment in mathematics. (Regular rank means a lecturer, a research professor (of any level), a professor of the practice (any level), or a tenure-track professor (any level).)

  2. Work together with your mentor to write the proposal. The length of the Description of Proposed Study part of the proposal will depend on the particulars. It will probably not be much less than one page and might be as long as three pages.

  3. Bulletin course descriptions are not good models for independent study proposals. A complete course syllabus is an ideal model, something to keep in mind as a goal to strive towards. However most course proposals will fall short of the precision of a course syllabus.

  4. Be sure to communicate clearly. The proposal should be well organized and carefully written. Ask yourself if the reader will be able to understand what you are writing. The reader will be a mathematician who is generally familiar with the most basic concepts which appear in standard undergraduate courses, but who may not familiar with specialized notions in a given subfield of mathematics. Thus specialized mathematical terms should be defined. Terms from science, economics, and engineering should also be defined if they are not familiar to a broad range of well educated lay people.

Specific Instructions

  1. State the problem you will be working on clearly.

    The problem should be stated as precisely 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 provide some background information to explain the context prior to coming to the statement of the actual problem. In case the source of the problem is outside mathematics, it may be necessary to first explain the scientific, engineering, or economic context and then describe how mathematics enters before the specific problem can be explained.

  2. What previous work has been done related to the problem?

    It is especially important to communicate previous work which you have done. Did you work on this problem or a related problem during the summer or during a previous research independent study course? If so, please summarize what you did and include an electronic copy of your final paper from the previous semester. As for the work of others on the problem, you need only quickly note 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 what you have typed to be sure that the issues above have been addressed.

  5. Turn in your type written sheet (or sheets) together with the completed independent study permission form to the Director of Undergraduate Studies in the math department. This should be done as early as possible during the first week of classes. Submission may be done electronically by e-mailing an attachment to Scanned signatures are acceptable. Hard-copies may be brought to the office of the Director of Undergraduate Studies or may be left in his or her mailbox located in room 117 Physics Building.

  6. The Director of Undergraduate Studies will set up the independent study course after a satisfactory proposal been received. He or she will e-mail you a section number and a permission number to enable you to sign up for the course on ACES. In the event that the proposal needs further work before it can be accepted, you will be informed by e-mail.

Nature of Final Product

A formal final paper (as opposed to an informal report) meeting the following criteria will be written in this course:

  1. The paper describes some important aspects of the work done during the course.

  2. The paper is thoughtful, well organized, well written and carefully proofread.

  3. The paper communicates well to as broad an audience as would reasonably be assumed to be interested in the topic of the research.

The final paper will contribute substantially to the course grade. In particular an A grade will not be given if the final paper clearly fails to meet the criteria above.

The final paper may at the discretion of the instructor include relevant excerpts from any paper or report that the student has 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 the final paper.

The student will e-mail an electronic copy of the final paper to the Director of Undergraduate Studies in the math department on or before the last day of final exams.

Although this is the "final" paper, work on it, especially on that part which explains the broader context of the research, may be begun early in the semester. 
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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320