Synopsis
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Fother 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GWs The Chinese More Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Review
'The authors bring together expertise from East and West to present an authoritative, thoroughly up-to-date and detailed treatment of work in this area.'
The International Statistical Review.
'As a survey, of what is available and which techniques show promise in further investigations, the book certainly provides what one could wish for.'
'What this reviewer enjoyed most is the technical virtuosity required, and generously present, in quite a few of the analyses. This is a book to have your Ph.D. student read, to show him what life is like.'
Mathematical Reviews, issue 88i
'In summary, this book competently fills a certain niche and will be interesting and provocative to probabilistically inclined statisticians who enjoy studying new and important phenomena.'
Journal of the American Statistical Association 86, March 1991.
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