Selecta Mathematica II

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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Menger's Work on Logic and Foundations.- 1 Overview of Neural and Symbolic Systems.- Bemerkungen zu Grundlagenfragen I: Über Verzweigungsmengen, Jahresbericht der Deutschen Mathematiker-Vereinigung 37 (1928), 213-226.- Selected Papers on Analysis.- Commentary on Karl Menger's Contributions to Analysis.- On Cauchy's Integral Theorem in the Real Plane, Proc. Nat. Acad. Sci. 25 (1939), 621-625.- On Green's Formula, Proc. Nat. Acad. Sci. 26 (1940), 660-664.- The Behavior of a Complex Function at Infinity, Proc. Nat. Acad. Sci. 41 (1955), 512-513.- A Characterization of Weierstrass Analytic Functions, Proc. Nat. Acad. Sci. 54 (1965), 1025-1026.- Analytische Funktionen, Wissenschaftliche Abhandlungen der Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Vol. 33, Köln (1965), 609-612.- Une caractérisation des fonctions analytiques, Comptes Rendus Acad. Paris 261 (1965), 4968-4969.- Weierstrass Analytic Functions, Mathematische Annalen 167 (1966), 177-194.- Selected Papers on Length.- Commentary on Menger's Path Length Papers.- On Shortest Polygonal Approximations to a Curve, Reports of Math. Colloq. Notre Dame, Indiana 2 (1940), 33-38.- Définition intrinsèque de la notion de chemin, Comptes Rendus Acad. Paris 221 (1945), 739-741.- Stieltjes Integrals Considered as Lengths, Annales Société Polonaise Math. 21 (1948), 173-175.- What Paths Have Length?, Fundamenta Mathematicae 36 (1949), 109-118.- A Topological Characterization of the Length of Paths, Proc. Nat. Acad. Sci. 38 (1952), 66-69.- Selected Papers on Algebra of Analysis.- Commentary on the Algebra of Analysis and Algebra of Functions.- The Influence of Menger's Ideas on the Work of Nöbauer and His School.- Algebra of Analysis, Report Notre Dame Mathematical Lectures, Vol. 3, 1944 (pp. I-II, 1-44).- Tri-Operational Algebra, Reports of Math. Colloq. Notre Dame, Indiana 5/6 (1944), 3-10.- General Algebra of Analysis, Reports of Math. Colloq. Notre Dame, Indiana 7 (1946), 46-60.- An Axiomatic Theory of Functions and Fluents, in:The Axiomatic Method (eds. L. Henkin, P. Suppes and A. Tarski) North Holland, 1959, 454-473.- The Algebra of Functions: Past, Present, Future, Rendiconti di Matematica 20 (1961), 409-430.- On Substitutive Algebra and Its Syntax, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 10 (1964), 81-104.- Superassociative Systems and Logical Functors, Mathematische Annalen 157 (1964), 278-295.- Two Theorems on the Generation of Systems of Functions (with H. I. Whitlock), Fundamenta Mathematicae 58 (1966), 229-240.- Selected Papers on Didactics, Variables, and Fluents.- Commentary on Didactics, Variables, Fluents.- A Mengerian Tour Along Caratheodory's Royal Road.- Calculus - A Modern Approach, Introduction and Chapter 1, Ginn and Co., Boston, 1955, xi-xvii and 1-18.- The Mathematics of Elementary Thermodynamics, American Journal of Physics 18 (1950), 89-103.- Random Variables from the Point of View of a General Theory of Variables, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (1954-1955), eds. L. M. Le Cam and O. Neyman, University of California Press, Berkeley, 1956, Vol. 2, 215-229.- What are x and y? The Mathematical Gazette 40 (1956), 246-255.- Rates of Change and Derivatives, Fundamenta Mathematicae 46 (1958), 89-102.- Selected Papers on Probabilistic Geometry.- Commentary on Probabilistic Geometry.- Statistical Metrics, Proc. Nat. Acad. Sci. 28 (1942), 535-537.- Probabilistic Theories of Relations, Proc. Nat. Acad. Sci. 37 (1951), 178-180.- Probabilistic Geometry, Proc. Nat. Acad. Sci. 37 (1951), 226-229.- Ensembles flous et fonctions aléatoires, Comptes Rendus Acad. Paris 232 (1951), 2001-2003.- Selected Papers on Group Theory and Algebra.- Commentary on Menger's Work on Algebra.- Beiträge zur Gruppentheorie I. Über eine Gruppenmetrik, Mathematische Zeitschrift 33 (1931), 396-418.- Une théorie axiomatique générale des déterminants, Comptes Rendus Acad. Paris 234 (1952), 1941-1943.- Selected Papers on Sociology.- Commentary on Menger's Work on Sociology.- An Exact Theory of Social Groups and Relations, American Journal of Sociology 43 (1938), 790-798.- On Social Groups and Relations, Mathematical Social Sciences 6 (1983), 13-25.- Menger's Work on Economics.- Commentary on Menger's `Austrian Marginalism and Mathematical Economics'.- Austrian Marginalism and Mathematical Economics, in: Carl Menger and the Austrian School of Economics, eds. R. O. Hicks and W. Weber, Oxford, 1973, 38-60.- Miscellaneous.- Editors Comments.- Otto Schreier, Nachruf, Monatshefte für Mathematik 37 (1930), 1-6.- Hans Hahn t, Fundamenta Mathematicae 24 (1935), 317-320.- Memories of Moritz Schlick, in: Rationality and Science, ed. by E. T. Gadol, Springer, Wien-New York, 1982,83-103.- to: Ernst Mach: The Science of Mechanics, 6th American Edition, Open Court, La Salle, Illinois 1960, v-xxi.- to: Hans Hahn: Empiricism, Logic and Mathematics, Vienna Circle Collection Vol. 13, Reidel, Dordrecht, 1980, ix-xviii.- You Will Like Geometry, A Guide Book for the Illinois Institute of Technology Geometry Exhibition at the Museum of Science and Industry, Chicago, 1952, 1-36.- Table of Contents ?Vol. I.- Table of Contents of Karl Menger: "Selected Papers in Logic and Foundations, Didactics, Economics".- List of Publications ?Karl Menger.