Overview

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.

Full Product Details

Author:   Karl Menger ,  Berthold Schweizer ,  Abe Sklar ,  Karl Sigmund
Publisher:   Springer Verlag GmbH
Imprint:   Springer Verlag GmbH
Edition:   Softcover reprint of the original 1st ed. 2002
Dimensions:   Width: 17.80cm , Height: 3.20cm , Length: 25.40cm
Weight:   1.154kg
ISBN:  

9783709172827

ISBN 10:   3709172829
Pages:   614
Publication Date:   21 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Language:   ger, eng

Table of Contents

Karl Menger and Vienna's Golden Autumn.- Commentary on Menger's Work on Dimension Theory.- Zur Dimensions- und Kurventheorie. Unveroffentlichte Aufsatze aus den Jahren 1921-1923, Monatshefte fur Mathematik und Physik 36 (1929), 411-432.- Das Hauptproblem uber die dimensionelle Struktur der Raume, Proceedings Amsterdam 30 (1927), 138-144.- Dimension und Zusammenhangsstufe, Mathematische Annalen 100 (1928), 618-633.- Allgemeine Raume und Cartesische Raume. I., Proceedings Amsterdam 29 (1926), 476-482.- Allgemeine Raume und Cartesische Raume. II.: Uber umfassendste n-dimensionale Mengen, Proceedings Amsterdam 29 (1926), 1125-1128.- Uber die Dimension von Punktmengen III. Zur Begrundung einer axiomatischen Theorie der Dimension, Monatshefte fur Mathematik und Physik 36 (1929), 193-218.- Axiomatische Einfuhrung des Dimensionsbegriffes, Comptes Rendus du Premier Congres des Mathematiciens des Pays Slaves. Warszawa. 1929, 57-65.- Remarques sur la theorie axiomatique de la dimension, Monatshefte fur Mathematik und Physik 37 (1930), 169-174.- Uber die Hinweise auf Brouwer in Urysohns Memoire, Selbstverlag, Wien 1932.- Commentary on Menger's Work on Curve Theory and Topology.- Einige Uberdeckungssatze der Punktmengenlehre, Akademie der Wissenschaften zu Wien, Sitzungsberichte 133 (1924), 421-444.- Grundzuge einer Theorie der Kurven, Mathematische Annalen 95 (1925), 277-306.- Grundzuge einer Theorie der Kurven, Proceedings Amsterdam 28 (1925), 67-71.- Une forme abstraite du theoreme de Borel-Lebesgue generalise, 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 uber allgemeine Metrik .- Untersuchungen uber allgemeine Metrik (Erste Untersuchung: Theorie der Konvexitat; Zweite Untersuchung: Die euklidische Metrik; Dritte Untersuchung: Entwurf einer Theorie der n-dimensionalen Metrik), Mathematische Annalen 100 (1928), 75-163.- Bemerkungen zur zweiten Untersuchung uber allgemeine Metrik, Proceedings Amsterdam 30 (1927), 710-714.- Untersuchungen uber 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 theoreme general du calcul des variations, Comptes Rendus Acad. Paris 201 (1935), 705-707.- Calcul des variations dans les espaces distancies generaux, Comptes Rendus Acad. Paris 202 (1936), 1007-1009.- Courbes minimisantes non rectifiables et champs generaux 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 Verknupfungsbeziehungen, 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.

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