Edmund Hlawka - Böcker

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 a personal selection by himself out 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.

Based on lectures given by Professor Hlawka in Vienna and in Pasadena, the book covers diophantine approximation, uniform distribution of numbers modulo 1 and geometry of numbers, as well as analytic number theory. It also proves the irrationality of zeta (3) and presents the important method of A. and H. Lenstra for the decomposition of polynomials, neither available in any other textbook. Various proofs of the prime number theorem are described. This monograph on number theory, real analysis, algebra/algebraic number theory is intended for students and lecturers in the above fields.

This volume contains original research papers presented at a seminar given at the Technical University of Vienna. Contributors discussed methods drawn originally from number theory but applied now to numerical analysis, discrete mathematics and theoretical computer science.

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, is among the most original mathematicians and thinkers of the twentieth century.