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I.M.Gelfand, one of the leading contemporary mathematicians,
largely determined the modern view of functional analysis with its
numerous relations to other branches of mathematics, including
mathematical physics, algebra, topology, differential geometry and
analysis. With the publication of these Collected Papers in three
volumes Gelfand gives a representative choice of his papers written
in the last fifty years. Gelfand's research led to the development
of remarkable mathematical theories - most now classics - in the
field of Banach algebras, infinite-dimensional representations of
Lie groups, the inverse Sturm-Liouville problem, cohomology of
infinite-dimensional Lie algebras, integral geometry, generalized
functions and general hypergeometric functions. The corresponding
papers form the major part of the Collected Papers. Some articles
on numerical methods and cybernetics as well as a few on biology
are included. A substantial part of the papers have been translated
into English especially for this edition. This edition is rounded
off by a preface by S.G.Gindikin, a contribution by V.I.Arnold and
an extensive bibliography with almost 500 references. Gelfand's
Collected Papers will provide stimulating and serendipitous reading
for researchers in a multitude of mathematical disciplines.
The popular literature on mathematical logic is rather extensive
and written for the most varied categories of readers. College
students or adults who read it in their free time may find here a
vast number of thought-provoking logical problems. The reader who
wishes to enrich his mathematical background in the hope that this
will help him in his everyday life can discover detailed
descriptions of practical (and quite often -- not so practical )
applications of logic. The large number of popular books on logic
has given rise to the hope that by applying mathematical logic,
students will finally learn how to distinguish between necessary
and sufficient conditions and other points of logic in the college
course in mathematics. But the habit of teachers of mathematical
analysis, for example, to stick to problems dealing with sequences
without limit, uniformly continuous functions, etc. has,
unfortunately, led to the writing of textbooks that present
prescriptions for the mechanical construction of definitions of
negative concepts which seem to obviate the need for any thinking
on the reader's part. We are most certainly not able to enumerate
everything the reader may draw out of existing books on
mathematical logic, however.
This volume of the EMS contains four survey articles on analytic
spaces. They are excellent introductions to each respective area.
Starting from basic principles in several complex variables each
article stretches out to current trends in research. Graduate
students and researchers will find a useful addition in the
extensive bibliography at the end of each article.
One service mathematics has rendered the 'Et moi, .. ., si j'avait
su comment cn rcvenir, human race. It has put common sense back. je
n'y serais point aile.' where it bdongs, on the topmost shelf neAt
Jules Verne to the dusty canister labelled 'discarded non. sense'.
The series is divergent; therefore we may be Eric T. Bdl able to do
something with it. O. Heaviside 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 a, rguably true. And all statements obtainable this way form
part of the raison d'etre of this series."
The popular literature on mathematical logic is rather extensive
and written for the most varied categories of readers. College
students or adults who read it in their free time may find here a
vast number of thought-provoking logical problems. The reader who
wishes to enrich his mathematical background in the hope that this
will help him in his everyday life can discover detailed
descriptions of practical (and quite often -- not so practical )
applications of logic. The large number of popular books on logic
has given rise to the hope that by applying mathematical logic,
students will finally learn how to distinguish between necessary
and sufficient conditions and other points of logic in the college
course in mathematics. But the habit of teachers of mathematical
analysis, for example, to stick to problems dealing with sequences
without limit, uniformly continuous functions, etc. has,
unfortunately, led to the writing of textbooks that present
prescriptions for the mechanical construction of definitions of
negative concepts which seem to obviate the need for any thinking
on the reader's part. We are most certainly not able to enumerate
everything the reader may draw out of existing books on
mathematical logic, however.
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