Participants

# Math at Ross

Participants in this six-week summer course attend class for a rough minimum of three hours per day, some of which are spent in small "family groups" led by a counselor. Apart from classes, students structure their own time, with the understanding that they will spend many hours concentrating on the challenging mathematical ideas presented in class and on the problem sets.

The first-year course in the Ross Program is organized around a series of problem sets in number theory. Along the way, participants build a vibrant mathematical community by engaging in exciting mathematical discussion and productive collaboration with peers.

## Motivation

The motivation for the Ross curriculum is summarized in the Ross Program's motto:

Think deeply about simple things.

We achieve this through several means: focused work, focused content, and focused community. Participants should expect to engage deeply with mathematics throughout the duration of the program. Some of the activities at the Ross Program which engage participants in these pursuits include,

- daily number theory lectures,
- daily family group discussions,
- working on problem sets,
- attending elective lectures, and
- discussing and sharing math with peers.

### Work

Participants are required to attend a daily number theory lecture and daily family group discussions, which total to about three hours daily. Although the required activities only make up a small portion of each day, students are expected to work hard during the unstructured time.

The Ross curriculum is designed around a series of problem sets which invite the participants to contemplate a variety of seemingly simple questions about numbers and their relationships. By investigating a sequence of related problems throughout the program, students observe patterns, make conjectures, explore further examples to test the conjectures, formulate theorems, write up proofs, polish the arguments, and investigate generalizations. Learn more about the Ross Program problem sets.

### Content

We concentrate on one central subject (number theory), rather than touching lightly on many disjoint mathematical topics. Ross students spend the entire summer focusing their attention on integers and their properties. Number Theory was chosen as the central topic for the Ross Program because many of its ideas are close to the surface and easily noticed, but deeper concepts and connections are available for exploration. Ross participants investigate this one subject deeply and at length. Although students might not encounter these topics in standard high school or college courses, there is tremendous value in the experience of delving deeply into one subject.

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

### Community

The Ross program is propelled by the strong mathematical community it fosters among participants, which brings together individuals of diverse mathematical backgrounds to collaborate and share in the joy of mathematics. Ross participants spend much of their time working on problem sets together, helping each other learn about mathematics. The Ross counselors strive to build a "community of scholars" in the dormitory, encouraging everyone to work on these challenging mathematical ideas, to share their ideas and insights, and to experience the joy of solving a difficult problem.

## Problem Sets

Learn more about the Ross Program problem sets.

## Math Topics

Learn more about the Ross Program course topics.