Selecta Mathematica I
Published on 12. March 2013
X, 611 pages
978-3-7091-6110-4 (ISBN)
Description
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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10/2012
Springer
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04/2002
1st Edition
Springer
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Content
Karl Menger and Vienna's Golden Autumn.- Commentary on Menger's Work on Dimension Theory.- Zur Dimensions- und Kurventheorie. Unveröffentlichte Aufsätze aus den Jahren 1921-1923, Monatshefte für Mathematik und Physik 36 (1929), 411-432.- Das Hauptproblem über die dimensionelle Struktur der Räume, Proceedings Amsterdam 30 (1927), 138-144.- Dimension und Zusammenhangsstufe, Mathematische Annalen 100 (1928), 618-633.- Allgemeine Räume und Cartesische Räume. I., Proceedings Amsterdam 29 (1926), 476-482.- Allgemeine Räume und Cartesische Räume. II.: Über umfassendste n-dimensionale Mengen, Proceedings Amsterdam 29 (1926), 1125-1128.- Über die Dimension von Punktmengen III. Zur Begründung einer axiomatischen Theorie der Dimension, Monatshefte für Mathematik und Physik 36 (1929), 193-218.- Axiomatische Einführung des Dimensionsbegriffes, Comptes Rendus du Premier Congrès des Mathématiciens des Pays Slaves. Warszawa. 1929, 57-65.- Remarques sur la théorie axiomatique de la dimension, Monatshefte für Mathematik und Physik 37 (1930), 169-174.- Über die Hinweise auf Brouwer in Urysohns Mémoire, Selbstverlag, Wien 1932.- Commentary on Menger's Work on Curve Theory and Topology.- Einige Überdeckungssätze der Punktmengenlehre, Akademie der Wissenschaften zu Wien, Sitzungsberichte 133 (1924), 421-444.- Grundzüge einer Theorie der Kurven, Mathematische Annalen 95 (1925), 277-306.- Grundzüge einer Theorie der Kurven, Proceedings Amsterdam 28 (1925), 67-71.- Une forme abstraite du théorème de Borel-Lebesgue généralisé, Comptes Rendus Acad. Paris 206 (1938), 563-565.- On the Origin of the n-Arc Theorem, Journal of Graph Theory 5 (1981), 341-350.- Commentary on Menger's "Untersuchungen über allgemeine Metrik".- Untersuchungen über allgemeine Metrik (Erste Untersuchung: Theorie der Konvexität; Zweite Untersuchung: Die euklidische Metrik; Dritte Untersuchung: Entwurf einer Theorie der n-dimensionalen Metrik), Mathematische Annalen 100 (1928), 75-163.- Bemerkungen zur zweiten Untersuchungüber allgemeine Metrik, Proceedings Amsterdam 30 (1927), 710-714.- Untersuchungen über allgemeine Metrik. Teil IV: Zur Metrik der Kurven, Mathematische Annalen 103 (1930), 466-501.- Commentary on Menger's Work on the Calculus of Variation and Metric Geometry.- Sur un théoréme général du calcul des variations, Comptes Rendus Acad. Paris 201 (1935), 705-707.- Calcul des variations dans les espaces distanciés généraux, Comptes Rendus Acad. Paris 202 (1936), 1007-1009.- Courbes minimisantes non rectifiables et champs généraux de courbes admissibles dans le calcul des variations, Comptes Rendus Acad. Paris 202 (1936), 1648-1650.- Metric Methods in Calculus of Variations, Proc. Nat. Acad. Sci. 23 (1937), 244-250.- A Theory of Length and its Applications to the Calculus of Variations, Proc. Nat. Acad. Sci. 25 (1939), 474-478.- Commentary on Menger's Work on the Algebra of Geometry.- Bemerkungen zu Grundlagenfragen. IV: Axiomatik der endlichen Mengen und der elementargeometrischen Verknüpfungsbeziehungen, Jahresbericht der Deutschen Mathematikervereinigung 37 (1928), 309-325.- New Foundations of Projective and Affine Geometry. Algebra of Geometry, Annals of Mathematics, II. Ser. 37 (1936), 456-482.- A Note on a Previous Paper "New Foundations of Projective and Affine Geometry", Annals of Mathematics, II. Ser. 38 (1937), 450.- A New Foundation of Non-Euclidean, Affine, Real Projective and Euclidean Geometry, Proc. Nat. Acad. Sci. 24 (1938), 486-490.- Self-Dual Fragments of the Ordinary Plane, The American Mathematical Monthly 56 (1949), 545-546.- The Projective Space, Duke Math. Journal 17 (1950), 1-14.- Frammenti piani autoduali e relative sostituzioni, Rendiconti Accad. Nazionale di Lincei 30 (1961), 713-717.- The New Foundation of Hyperbolic Geometry, in: A Spectrum of Mathematics (Essays Presented to H. G. Forder), ed. by J. C. Butcher, Auckland University Press 1971, 86-97.- Commentary on Menger's Expository Papers on Geometry.- Some Applications of Point-Set Methods,Annals of Mathematics, II. Ser. 32 (1931), 739-760.- Generalized Vector Spaces. I. The Structure of Finite-Dimensional Spaces, Canadian Journal of Mathematics 1 (1949), 94-104.- The Theory of Relativity and Geometry, in: Albert Einstein, Philosopher-Scientist, The Library of Living Philosophers, vol. VII, ed. by P. A. Schilpp, Evanston, Illinois 1949, 459-474.- The Formative Years of Abraham Wald and His Work in Geometry, The Annals of Mathematical Statistics 23 (1952), 14-20.- Mathematical Implications of Mach's Ideas: Positivistic Geometry, The Clarification of Functional Connections, in: Ernst Mach, Physicist and Philosopher, Boston Studies in the Philosophy of Science VI, eds. R. S. Cohen and R. J. Seeger, D. Reidel, Dordrecht 1970, 107-125.- List of Publications - Karl Menger.
