Free download скачать Singularities of Caustics and Wave Fronts by V. I. Arnold
English | PDF | 1990 | 271 Pages | ISBN : 0792310381 | 23.8 MB
Mathematics is a tool for thought. A highly necessary tool  in  a world where both feedback and non-

linearities abound. Similarly, all kinds  of  parts of mathematics serve as tools for other parts  and  for
other sciences.
Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics  ..  .'; 'One service logic  has  rendered com- puter science  ..  .'; 'One service category theory has rendered mathematics  ..  .'. All arguably true.  And all statements obtainable this way form  part  of the raison d'etre of this series.
This series,  Mathematics and Its Applications,  started  in  1977. Now that over one hundred volumes have appeared  it  seems opportune  to  reexamine its scope.  At  the time I wrote
"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."
By  and large, all this still applies today.  It  is still true that  at  first sight mathematics seems rather fragmented  and  that  to find,  see,  and exploit the deeper underlying interrelations more effort is needed  and  so are books that can help mathematicians and scientists do so. Accordingly MIA  will continue to try to make such books available.
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