Reality Rules: Picturing the World in Mathematics

An account of the syntax and semantics of the language in which these reality rules are written–the language of mathematics. Coverage includes a discussion of computation and complexity running the gamut from Godel’s Incompleteness Theorem and its connection to work in artificial intelligence to the problem of NP-completeness and the complexity of numerical algorithms to the relation between chaos and stock-price fluctuations. Each chapter contains a significant amount of research problems and ends with discussion questions. Features an extended, annotated bibliography.