The Ross Program
"Think deeply of simple things."

June 22 - August 14, 2009

The first year course in the Ross Program is organized around a series of daily problem sets in number theory. These sets invite the participants to contemplate a variety of seemingly simple questions about numbers and their relationships. As the summer progresses the students are encouraged to investigate these questions in increasing depth, and to return to them periodically as their skill at abstract reasoning and their collection of available tools become more powerful.

This spiraling of concepts is summarized in the Ross Program's motto:

"Think deeply of simple things."

With this in mind, participants concentrate on one central topic:  integers and their properties. We resist the temptation to touch lightly on many different topics, even though those ideas may be interesting and accessible. Instead, Ross students learn one subject deeply, focusing attention on the many aspects of numbers.

The term begins with investigations of topics involving prime numbers and modular arithmetic. Starting with everyday knowledge of familiar numbers, students observe curious numerical properties and search for satisfactory explanations of them. Those early numerical questions allow students to become familiar with basic ideas. After making some computations, they are asked to formulate more general statements that include their numerical examples as special cases. Later they try to explain their new observations, thus returning to the original questions at a different level.

After mastering these more complex issues, they encounter versions of those questions in other contexts and begin to appreciate them from a deeper perspective. Some of these investigations eventually lead to significant insights about the structure of number systems, the underpinnings of algebraic formalism, and the relationship between numbers and geometry. By considering simply stated questions from several directions and depths, participants attain some understanding of how professional mathematicians and scientists work: gathering data, looking for patterns and analogies, making conjectures, and finally testing and proving those conjectures.

The range of topics discussed in the Ross Number Theory course indicates the depth and scope of this fast-paced but rigorous course.

In order for this intensely problem-based approach to succeed, students must be given careful and personal feedback on their work. This job is done by the counselors, who live in the dormitories along with the younger participants.

The counselors are graduates of the Ross Program who are studying mathematics and science as undergraduates in some of the best colleges and universities of the United States. Each counselor works directly with several first year students, and the counselors contribute a tremendous amount of time and energy to their students. In addition to their jobs as student advisors, the counselors add to the overall atmosphere of excitement at the Ross Program by working on challenging advanced courses or on other topics they find of interest. Their enthusiasm is contagious and their dedication is inspiring for the younger students. The counselors work to bring the program participants together to form a true community, but ultimately much of this task falls to the students. It is the students themselves who devote their energy to meet the challenges set for them.

Beginning students who do well are invited back for a second summer, and may return as junior counselors or counselors in subsequent summers. Returning students, junior counselors, and counselors take advanced courses which vary from year to year.

Many alumni of the Ross Program have kept in contact with us. Some of their enthusiasm for the Program is evident in their comments posted on the alumni home page.

Introduction | Students | Course Topics | Application
Past Summers | Alumni | Reunions

For further information about this mathematics program
contact ross@math.ohio-state.edu.