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Karl Menger, one of the founders of dimension theory, is among the
most original mathematicians and thinkers of the twentieth century.
He was a member of the Vienna Circle and the founder of its
mathematical equivalent, the Viennese Mathematical Colloquium. Both
during his early years in Vienna and, after his emigration, in the
United States, Karl Menger made significant contributions to a wide
variety of mathematical fields, and greatly influenced many of his
colleagues. These two volumes contain Menger's major mathematical
papers, based on his own selection from his extensive writings.
They deal with topics as diverse as topology, geometry, analysis
and algebra, and also include material on economics, sociology,
logic and philosophy. The Selecta Mathematica is a monument to the
diversity and originality of Menger's ideas.
Edmund Hlawka is a leading number theorist whose work has had a
lasting influence on modern number theory and other branches of
mathematics. He has contributed to diophantine approximation, the
geometry of numbers, uniform distributions, analytic number theory,
discrete geometry, convexity, numerical integration, inequalities,
differential equations and gas dynamics. Of particular importance
are his findings in the geometry of numbers (especially the
Minkowski-Hlawka theorem) and uniform distribution. This Selecta
volume collects his most important articles, many of which were
previously hard to find. It will provide a useful tool for
researchers and graduate students working in the areas covered, and
includes a general introduction by E. Hlawka.
Karl Menger, one of the founders of dimension theory, belongs to the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna, and after his emigration to the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced some of his colleagues. The Selecta Mathematica contain Menger's major mathematical papers, based on his own selection of his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas.
In the English edition, the chapter on the Geometry of Numbers has
been enlarged to include the important findings of H. Lenstraj
furthermore, tried and tested examples and exercises have been
included. The translator, Prof. Charles Thomas, has solved the
difficult problem of the German text into English in an admirable
way. He deserves transferring our 'Unreserved praise and special
thailks. Finally, we would like to express our gratitude to
Springer-Verlag, for their commitment to the publication of this
English edition, and for the special care taken in its production.
Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface
to the German Edition We have set ourselves two aims with the
present book on number theory. On the one hand for a reader who has
studied elementary number theory, and who has knowledge of analytic
geometry, differential and integral calculus, together with the
elements of complex variable theory, we wish to introduce basic
results from the areas of the geometry of numbers, diophantine ap
proximation, prime number theory, and the asymptotic calculation of
number theoretic functions. However on the other hand for the
student who has al ready studied analytic number theory, we also
present results and principles of proof, which until now have
barely if at all appeared in text books.
Karl Menger, one of the founders of dimension theory, is among the
most original mathematicians and thinkers of the twentieth century.
He was a member of the Vienna Circle and the founder of its
mathematical equivalent, the Viennese Mathematical Colloquium. Both
during his early years in Vienna and, after his emigration, in the
United States, Karl Menger made significant contributions to a wide
variety of mathematical fields, and greatly influenced many of his
colleagues. These two volumes contain Menger's major mathematical
papers, based on his own selection from his extensive writings.
They deal with topics as diverse as topology, geometry, analysis
and algebra, and also include material on economics, sociology,
logic and philosophy. The Selecta Mathematica is a monument to the
diversity and originality of Menger's ideas.
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