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 Oberlin College, who has developed a method for recreating an image, such as a painting or photograph, using full sets of double nine dominoes.  The image is created from the solution of a huge linear system of equations that must be constructed and solved using very powerful software that is designed and used by industry (dashoptimization.com).  One of the outcomes of the project will be the creation of the image of John Marshall. In addition, the researcher will consider other medium for image replication using other items such as polyominoes (pentominoes or tentominoes).

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.