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This text embodies at advanced and postgraduate level the professional and technical experience of two experienced mathematicians. It covers a wide range of applications relevant in many areas, including actuarial science, communications, engineering, finance, gambling, house purchase, lotteries, management, operational research, pursuit and search. In mathematical studies drawn from algebra, geometry, analysis, statistics and computational methodology, applications are discussed in separate chapters, each prefaced by a summary of content and relevance. Some branches of the mathematics covered might be regarded as old-fashioned but they are still vigorous and relevant today. The material is original, either in content, presentations or both, and includes topics not usually found in other texts. It treats serious mathematics respectfully and, if sometimes light in its touch, maintains the instructive tenor.