The natural world is filled with a wonderful variety of forms and is shaped and transformed by complex interactions. Careful observation reveals that behind this complexity is an underlying order. The order manifests itself as spatial arrangements, such as spirals in shells, branching in rivers and hexagonal cells in beehives, and in temporal sequences, such as in patterns of growth, the interference of waves, and the motion of planets. In this program we will investigate the physical constraints and simple mathematical rules that make sense of this order. We will also explore the conditions under which this order is lost in the transition to chaos and randomness.
The program will be structured around two main approaches to investigating order. First we will use nature as a guide to learn the mathematical methods for describing the patterns we see. Then we will learn the physical laws that give rise to order, from the clockwork universe of Newtonian dynamics to the strange world of quantum mechanics. In support of this study we will also learn how to model these natural phenomena by programming computer simulations.
This program is introductory in nature and is well suited to students who want to investigate the mathematical and physical underpinnings of natural phenomena. Students of all background are welcome, but everyone should be prepared to spend a full quarter working with quantitative material in a spirit of curiosity and engaged inquiry. This program would serve as a good introduction and preparation for some of our foundation programs in mathematics and the sciences and for students interested in becoming teachers.