**Mathematics Scholarship Proposal - Example**

**Project Goal:** The goal of this research project is a study
of recently developed uses of

optimization theory to create
images and the expansion of the theory to other medium. The project idea was ignited by the recent
work of Dr. Robert Bosch, of

**Uniqueness:** The researcher will consider alternative
medium for image replication using medium such as polyominoes
of various shapes such as pentominoes or tentominoes. This
will require that he create the system that describes
the image and determine if a unique integer solution can be found. This will be covering new frontiers not
previously considered.

**Significance: **Linear Programming problems with
restraints are common in a variety of fields.
This project incorporates image recreation with optimization ideas. Perhaps the results of the work could offer
in some sense a better way to present a desired image.

**Approach: **The researcher will construct a grid over
the photograph to be re-imaged and determine the intensity of the color in each
grid square. He will then create a system of linear equations that describes the
image, solve it, and construct the image using double nine dominoes. He will also attempt to recreate the image
from another medium.

**Outcomes:** The researcher will develop a visual feel for
a mathematical concept, linear programming.
In addition, he will have an opportunity to experience the trials,
tribulations, and joys of the research world.
The material outcome will be the likeness of John Marshall recreated
first using full sets of dominoes and then, ideally, with a new alternative
medium.