Stochastics, Algebra and Analysis in Classical and Quantum Dynamics

''Et moi, "''f si j''avait su comment en revenir, One service mathematics has rendered the je n''y serais point aile'':'' human race. It has put common sense back Jules Verne where it belongs, 011 the topmost shelf next to the dusty canister labelled ''discarded non- The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ Iinearities 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.