This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz,...

Over the past three years I have grown accustomed to the puzzled look which appears on people's faces when they hear that I am a mathematician who studies sleep. They wonder, but are usually too polite to ask, what does mathematics have to do with sleep? Instead they ask the questions that fascinate us all: Why do we have to sleep? How much sleep do we really need? Why do we dream? These questions usually spark a lively discussion leading to the exchange of anecdotes, last night's dreams, and other personal information. But they are questions about the func- tion of sleep and, interesting as...