The authors explain the "bit-model" of computability and complexity of real functions and subsets of real n-space and argue that this is a good way to formalize problems of scientific computation. (pp. 318)
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Hash functions are easy-to-compute compression functions that are used as compact repesentations, or digital fingerprints, of data and to provide message integrity. Some hash functions in current use have been shown to be vulnerable. The author argues that their replacements should be based on a mathematical theory, which has yet to be created. (pp. 330)
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Mushroom billiards are examples of systems with mixed regular-chaotic dynamics whose relatively simple geometry makes their precise analysis possible. The authors analyze and illustrate a number of these problems. (pp. 334)
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