This coincidence of an explosion of mathematical activity with greatly enlarged scope for its application is, unhappily, overshadowed by a communication barrier. Between those who have mathematical knowledge and those who wish to use it there lies a great gulf. One can try to bridge this by bringing to the notice of abstract mathematicians the intriguing and challenging problems waiting for them in other fields - but mathematicians are not easily tempted from their ivory towers. This book starts, instead, from the other side, putting into the hands of the users of mathematics an array of powerful tools, of whose existence they may be unaware, with precise directions for their use. To achieve this in a reasonable compass something has to be sacrificed and the authors took the bold step of omitting virtually all proofs - an unorthodox but highly sensible procedure, since otherwise the book might have been ten times its present size. As it is, these covers contain the equivalent of a small library of standard texts on the uses of mathematics.

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