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
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.
- 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:
- 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.
- 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).
- 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).)
- 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.
- 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.
- 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.
- 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.
- 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.
- 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?
- Proofread what you have typed to be sure that the issues
above have been addressed.
- 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 firstname.lastname@example.org. 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.
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:
- The paper describes some important aspects of the work done during the course.
- The paper is thoughtful, well organized, well written and carefully proofread.
- 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
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.