P.M. Alberti, A. Uhlmann, "Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing"
1982 | pages: 126 | ISBN: 9027713502 | PDF | 13,6 mb
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 Minkowski 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.
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