Table Of ContentKarl Menger
Selecta Mathematica
Volume 2
Bert Schweizer, Abe Sklar,
Karl Sigmund, Peter Gruber,
Edmund Hlawka, Ludwig Reich,
Leopold Schmetterer (eds.)
Springer-Verlag Wien GmbH
Prof. Dr. Bert Schweizer
Department of Mathematics and Statistics
University of Massachusetts, Lederle Graduate Research Center
Amherst, MA, USA
Prof. Dr. Abe Sklar
Department of Mathematics, Illinois Institute of Technology
Chicago, IL, USA
O. Univ.-Prof. Dr. Karl Sigmund
em. O. Univ.-Prof. Dr. Leopold Schmetterer
Institute of Mathematics, University of Vienna, Austria
O. Univ.-Prof. Dr. DDr. h.c. Peter Gruber
em. O. Univ.-Prof. Dr. DDr. h.c. Edmund Hlawka
Institute of Analysis and Technical Mathematics
Technical University, Vienna, Austria
O. Univ.-Prof. Dr. Ludwig Reich
Institute of Mathematics, University of Graz, Austria
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ISBN 978-3-7091-7294-0 ISBN 978-3-7091-6045-9 (eBook)
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Table of Contents
Menger's Work on Logic and Foundations ................. 1
Van Dalen, D.: Commentary on Menger and Intuitionism 3
Bemerkungen zu Grundlagenfragen I: Über
Verzweigungsmengen, Jahresbericht der Deutschen
Mathematiker-Vereinigung 37 (1928), 2l3-226 .............. 9
Selected Papers on Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
Reich, L.: Commentary on Karl Menger's
Contributions to Analysis ............................. 25
On Cauchy's Integral Theorem in the Real Plane,
Proc. Nat. Acad. Sei. 25 (1939), 621-625 ................. 35
On Green's Formula, Proc. Nat. Acad. Sei.
26 (1940), 660-664 ................................. 41
The Behavior of a Complex Function at Infinity,
Proc. Nat. Acad. Sei. 41 (1955), 512-5l3 ................. 47
A Characterization of Weierstrass Analytic Functions,
Proc. Nat. Acad. Sei. 54 (1965), 1025-1026 ................ 49
Analytische Funktionen, Wissenschaftliche
Abhandlungen der Arbeitsgemeinschaft für
Forschung des Landes Nordrhein-Westfalen,
Vol. 33, Köln (1965), 609-612 ......................... 51
Une caracterisation des fonetions analytiques,
Comptes Rendus Acad. Paris 261 (1965),4968-4969 55
Weierstrass Analytic Functions, Mathematische
Annalen 167 (1966),177-194 .. . . . . . . . . . . . . . . . . . . . . . . .. 57
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Selected Papers on Length ............................. 75
Senechal, L.: Commentary on Menger's
Path Length Papers ................................. 77
On Shortest Polygonal Approximations to a Curve,
Reports of Math. Colloq. Notre Dame, Indiana
2 (1940), 33-38 ................................... 81
Definition intrinseque de la notion de chemin,
Comptes Rendus Acad. Paris 221 (1945), 739-741 87
Stieltjes Integrals Considered as Lengths, Annales
Societe Polonaise Math. 21 (1948), 173-175 ............... 91
What Paths Have Length?, Fundamenta Mathematicae
36 (1949), 109-118 ................................. 95
A Topological Characterization of the Length of Paths,
Proc. Nat. Acad. Sei. 38 (1952), 66-69 ................... 105
Selected Papers on Algebra of Analysis 109
Sklar, A.: Commentary on the Algebra of Analysis
and Algebra of Functions ............................. 111
Kaiser, H.: The Inftuence of Menger's Ideas
on the Work of Nöbauer and His School .................. 127
Algebra of Analysis, Report Notre Dame Mathematical
Lectures, Vol. 3, 1944 (pp. I-lI, 1-44) .................... 135
Tri-Operational Algebra, Reports of Math. Colloq.
Notre Dame, Indiana 5/6 (1944),3-10 .. . . . . . . . . . . . . . . . . .. 181
General Algebra of Analysis, Reports of Math. Colloq.
Notre Dame, Indiana 7 (1946),46-60 .................... 189
An Axiomatic Theory of Functions and Fluents, in:
The Axiomatic Method (eds. L. Henkin, P. Suppes
and A. Tarski) North Holland, 1959,454-473 ............... 205
The Algebra of Functions: Past, Present, Future,
Rendiconti di Matematica 20 (1961), 409-430 .............. 225
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On Substitutive Algebra and Its Syntax, Zeitschrift
für mathematische Logik und Grundlagen
der Mathematik 10 (1964), 81-104 ...................... 247
Superassociative Systems and Logical Functors,
Mathematische Annalen 157 (1964), 278-295 271
Two Theorems on the Generation of Systems of Functions
(with H. I. Whitlock), Fundamenta Mathematicae
58 (1966), 229-240 ................................. 289
Selected Papers on Didactics, Variables, and Fluents 301
Schweizer, B., Sklar, A.: Commentary on Didactics,
Variables, Fluents .................................. 303
Senechal, L., Schweizer, B.: A Mengerian Tour Along
Caratheodory's Royal Road ........................... 317
Ca1culus - A Modem Approach, Introduction and Chapter 1,
Ginn and Co., Boston, 1955, xi-xvii and 1-18 .............. 325
The Mathematics of Elementary Thermodynamics,
American Journal of Physics 18 (1950), 89-103 ............. 351
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 .......... 367
What are x and y? The Mathematical Gazette 40 (1956),
246-255 ......................................... 383
Rates of Change and Derivatives, Fundamenta Mathematicae
46 (1958), 89-102 .................................. 393
Selected Papers on Probabilistic Geometry ................. 407
Schweizer, B.: Commentary on Probabilistic Geometry .......... 409
Statistical Metrics, Proc. Nat. Acad. Sci. 28 (1942),535-537 ...... 433
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Table of Contents
Probabilistic Theories of Relations, Proc. Nat. Acad. Sci.
37 (1951), 178-180 ................................. 437
Probabilistic Geometry, Proc. Nat. Acad. Sci. 37 (1951),
226-229 ......................................... 441
Ensembles fious et fonctions aleatoires, Comptes Rendus
Acad. Paris 232 (1951), 2001-2003 ...................... 445
Selected Papers on Group Theory and Algebra . . . . . . . . . . . . .. 449
Lausch, H.: Commentary on Menger's Work on Algebra ......... 451
Beiträge zur Gruppentheorie I. Über eine Gruppenmetrik,
Mathematische Zeitschrift 33 (1931), 396-418 .............. 463
Une theorie axiomatique generale des determinants,
Comptes Rendus Acad. Paris 234 (1952), 1941-1943 487
Selected Papers on Sociology ........................... 491
Leonard, R.: Commentary on Menger's Work on Sociology ....... 493
An Exact Theory of Social Groups and Relations, American
Journal of Sociology 43 (1938), 790-798 .................. 501
On Social Groups and Relations, Mathematical Social
Sciences 6 (1983), 13-25 ............................. 511
Menger's Work on Economics .......................... 525
Sigmund, K.: Commentary on Menger's 'Austrian
Marginalism and Mathematical Economics' ................ 527
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 ............ 531
Miscellaneous ...................................... 555
Editors Comments ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 557
Otto Schreier, Nachruf, Monatshefte für Mathematik
37 (1930), 1-6 .................................... 559
Hans Hahn t, Fundamenta Mathematicae 24 (1935),
317-320 ......................................... 565
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Table of Contents
Memories of Moritz Schlick, in: Rationality and Science,
ed. by E. T. Gadol, Springer, Wien-New York,
1982, 83-103 ..................................... 569
Introduction to: Ernst Mach: The Science of Mechanics,
6th American Edition, Open Court, La SaUe, Illinois
1960, v-xxi ...................................... 591
Introduction to: Hans Hahn: Empiricism, Logic and
Mathematics, Vienna Circle CoUection Vol. 13, Reidel,
Dordrecht, 1980, ix-xviii ............................. 609
You Will Like Geometry, A Guide Book for the Illinois
Institute of Technology Geometry Exhibition at the
Museum of Science and Industry, Chicago, 1952, 1-36 619
Table of Contents - Vol. I .............................. 655
Table of Contents of Karl Menger: "Selected Papers
in Logic and Foundations, Didactics, Economics" 659
List of Publications - Karl Menger ........................ 663
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List of Authors
Prof. Dr. Dirk van Dalen, Department of Philosophy, Universiteit Utrecht,
Heidelberglaan 8, NL-3584 CS Utrecht, The Netherlands
Prof. Dr. Hans Kaiser, Institut für Algebra und Computermathematik,
Technische Universität Wien, Wiedner Hauptstraße 8-10/118,
A-1040 Wien, Austria ([email protected])
Prof. Dr. Hans Lausch, School of Mathematical Sciences, Monash University,
Victoria 3800, Australia ([email protected])
Prof. Dr. Robert Leonard, Departement des Sciences Economiques,
a
Universite du Quebec Montreal, Succursale Centre-Ville, Montreal,
Quebec H3C 3P8, Canada
Prof. Dr. Ludwig Reich, Institut für Mathematik, Universität Graz,
Heinrichstraße 36, A-80 10 Graz, Austria ([email protected])
Prof. Dr. Bert Schweizer, Department of Mathematics and Statistics,
University of Massachusetts, Amherst, MA 01003-9305, USA
([email protected])
Prof. Dr. Lester Senechal, Mount Holyoke, South Hadley, MA 01075, USA
([email protected])
Prof. Dr. Kar! Sigmund, Institut für Mathematik, Universität Wien,
Strudlhofgasse 4, A-1090 Wien, Austria ([email protected])
Prof. Dr. Abe Sklar, 5044 Marine Drive, Chicago, IL 60640, USA
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