Numbers, Models, and Chaos

Catalog description

The hallmark of a successful scientific theory is its ability to predict the outcome of experiments. Yet the last century's most shocking scientific development is the mathematical theory of chaos, with the subsequent realization that predictability has intrinsic limits. Such limits may have no practical importance (as in many engineering problems). Sometimes they shape an entire branch of science (as in meteorology). This course provides a challenging, but accessible, way to understand predictability's limits, while still appreciating the bedazzling richness of phenomena that only theories which face these limits can possibly describe. The course brings together, in a cohesive whole, ideas about numbers and infinities; the inner working of computing machines; nuances and concessions occurring in model-building; the meaning of randomness and of determinism. Students will participate in the construction of mathematical models (mostly inspired by population biology) under the form of iterated maps, and interact with simple computer simulations of those models to illustrate key concepts of nonlinear dynamics: stability, limit cycles, attractors, and predictability.