Undergraduate Research

Valparaiso University offers many research opportunities which may include grants for research materials and presentations. Students can participate in group or individual research and present their papers at academic conferences throughout the year or at the Valparaiso University annual undergraduate research fair with the guidance of V.U. professors. Research courses not only allow students to present their projects to the class but also attend preview and comment on research by other students and professors.

Each summer, a letter is sent to all of the incoming freshmen mathematics and computer science majors inviting them to write a letter of application to join the student research program. This letter briefly explains the program and asks the students interested in participating to explain why they want to do this and to describe why they feel they are prepared to work in a project involving independence and leadership skills.

Program Overview

The students, both incoming and current, participating in the research program are assigned to the teams based on their interests, talents, and to some degree on their personalities. Usually, the team will consist of one or two freshmen and a single upper-class student.

The letter inviting the incoming students to participate makes it clear that while they are expected to contribute to the research effort, their primary role is to learn about the research process. In particular, they are not being called on to lead a research effort, but they are "interning" in the process. The letter specifies that they will be asked, and expected, to take leadership roles if they continue to work on research projects after their first year.

Generally, research teams are organized around projects selected by the faculty mentors. (Examples will be offered in the following section.) Occasionally, teams are assembled to work on projects proposed by students who have approached faculty members for support and assistance.

The research teams stay together for a period of one year, although it is possible for some teams to continue working on a project for longer periods. In the latter case, new students are introduced to the project as older students leave the team. Students are expected to commit themselves for two semesters of work on a given project.

A very active student could earn a total of eight credits for their research efforts over four years, but few are able to maintain this active a program in mathematics alone. Probably the best way of describing appropriate problems is by illustrative examples.

Analysis of the Kerf-cut Algorithm:

This project, which resulted in a published paper, investigated the effectiveness and justification of an algorithm used by carpenters to create semi-circular arches out of strips of wood. The work involved using approximation techniques and geometry.

Analysis of the game of RISK:

This project used a Markov Chain approach to explore strategies and outcomes in the game RISK. About the time the students were completing their work, someone else published a paper which presented the same analysis.

Creation of Fractal Music:

A team of computer science students created fractal music and investigated its "musicality". This team has taken ownership of the work by staying together for four years, adding new members each year and establishing ongoing project goals.

Embedding of Knots into Planar Graphs:

One of the more esoteric problems worked on by a team of students resulted in a paper that was submitted for publication. The topic involved a technical area of mathematics beyond what is usually taught in most undergraduate math classes.

Adapting Ground Water Models:

This team investigated the suitability of using ground water flow equations to model subsurface airflow. The students collected airflow case studies, but did not complete the comparison to the mathematical models.

Textbook adoption of the NCTM Standards:

A team of students investigated how well high school mathematics books matched the NCTM Standards. This project was held during a text adoption year for the state.