Selecta Mathematica

by Menger, Karl; Schweizer, Bert; Sklar, Abe; Sigmund, Karl; Schmetterer, Leopold

• ISBN13: 9783211838341
• ISBN10: 3211838341
• Format: Hardcover
• Copyright: 2003-02-01
• Publisher: Springer Verlag

Summary

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 'œSelecta 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.

Table of Contents

Menger's Work on Logic and Foundations	1	(23)
Commentary on Menger and Intuitionism	3	(6)
Van Dalen, D.
Bemerkungen zu Grundlagenfragen I: Uber Verzweigungsmengen, Jahresbericht der Deutschen Mathematiker-Vereinigung 37 (1928), 213--226	9	(14)
Selected Papers on Analysis	23	(52)
Commentary on Karl Menger's Contributions to Analysis	25	(10)
Reich, L.
On Cauchy's Integral Theorem in the Real Plane, Proc. Nat. Acad. Sci. 25 (1939), 621--625	35	(6)
On Green's Formula, Proc. Nat. Acad. Sci. 26 (1940), 660--664	41	(6)
The Behavior of a Complex Function at Infinity, Proc. Nat. Acad. Sci. 41 (1955), 512--513	47	(2)
A Characterization of Weierstrass Analytic Functions, Proc. Nat. Acad. Sci. 54 (1965), 1025--1026	49	(2)
Analytische Funktionen, Wissenschaftliche Abhandlungen der Arbeitsgemeinschaft fur Forschung des Landes Nordrhein-Westfalen, Vol. 33, Koln (1965), 609--612	51	(4)
Une caracterisation des fonctions analytiques, Comptes Rendus Acad. Paris 261 (1965), 4968--4969	55	(2)
Weierstrass Analytic Functions, Mathematische Annalen 167 (1966), 177--194	57	(18)
Selected Papers on Length	75	(34)
Commentary on Menger's Path Length Papers	77	(4)
Senechal, L.
On Shortest Polygonal Approximations to a Curve, Reports of Math. Colloq. Notre Dame, Indiana 2 (1940), 33--38	81	(6)
Definition intrinseque de la notion de chemin, Comptes Rendus Acad. Paris 221 (1945), 739--741	87	(4)
Stieltjes Integrals Considered as Lengths, Annales Societe Polonaise Math. 21 (1948), 173--175	91	(4)
What Paths Have Length?, Fundamenta Mathematicae 36 (1949), 109--118	95	(10)
A Topological Characterization of the Length of Paths, Proc. Nat. Acad. Sci. 38 (1952), 66--69	105	(4)
Selected Papers on Algebra of Analysis	109	(192)
Commentary on the Algebra of Analysis and Algebra of Functions	111	(16)
Sklar, A.
The Influence of Menger's Ideas on the Work of Nobauer and His School	127	(8)
Kaiser, H.
Algebra of Analysis, Report Notre Dame Mathematical Lectures, Vol. 3, 1944 (pp. I--II, 1--44)	135	(46)
Tri-Operational Algebra, Reports of Math. Colloq. Notre Dame, Indiana 5/6 (1944), 3--10	181	(8)
General Algebra of Analysis, Reports of Math. Colloq. Notre Dame, Indiana 7 (1946), 46--60	189	(16)
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	(20)
The Algebra of Functions: Past, Present, Future, Rendiconti di Matematica 20 (1961), 409--430	225	(22)
On Substitutive Algebra and Its Syntax, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 10 (1964), 81--104	247	(24)
Superassociative Systems and Logical Functors, Mathematische Annalen 157 (1964), 278--295	271	(18)
Two Theorems on the Generation of Systems of Functions (with H. I. Whitlock), Fundamenta Mathematicae 58 (1966), 229--240	289	(12)
Selected Papers on Didactics, Variables, and Fluents	301	(106)
Commentary on Didactics, Variables, Fluents	303	(14)
Schweizer, B.
Sklar, A.
A Mengerian Tour Along Caratheodory's Royal Road	317	(8)
Senechal, L
Schweizer, B.
Calculus -- A Modern Approach, Introduction and Chapter 1, Ginn and Co., Boston, 1955, xi--xvii and 1--18	325	(26)
The Mathematics of Elementary Thermodynamics, American Journal of Physics 18 (1950), 89--103	351	(16)
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	(16)
What are x and y? The Mathematical Gazette 40 (1956), 246--255	383	(10)
Rates of Change and Derivatives, Fundamenta Mathematicae 46 (1958), 89--102	393	(14)
Selected Papers on Probabilistic Geometry	407	(42)
Commentary on Probabilistic Geometry	409	(24)
Schweizer, B.
Statistical Metrics, Proc. Nat. Acad. Sci. 28 (1942), 535--537	433	(4)
Probabilistic Theories of Relations, Proc. Nat. Acad. Sci. 37 (1951), 178--180	437	(4)
Probabilistic Geometry, Proc. Nat. Acad. Sci. 37 (1951), 226--229	441	(4)
Ensembles flous et fonctions aleatoires, Comptes Rendus Acad. Paris 232 (1951), 2001--2003	445	(4)
Selected Papers on Group Theory and Algebra	449	(42)
Commentary on Menger's Work on Algebra	451	(12)
Lausch, H.
Beitrage zur Gruppentheorie I. Uber eine Gruppenmetrik, Mathematische Zeitschrift 33 (1931), 396--418	463	(24)
Une theorie axiomatique generale des determinants, Comptes Rendus Acad. Paris 234 (1952), 1941--1943	487	(4)
Selected Papers on Sociology	491	(34)
Commentary on Menger's Work on Sociology	493	(8)
Leonard, R.
An Exact Theory of Social Groups and Relations, American Journal of Sociology 43 (1938), 790--798	501	(10)
On Social Groups and Relations, Mathematical Social Sciences 6 (1983), 13--25	511	(14)
Menger's Work on Economics	525	(30)
Commentary on Menger's `Austrian Marginalism and Mathematical Economics'	527	(4)
Sigmund, K.
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	(24)
Miscellaneous	555	(108)
Editors Comments	557	(2)
Otto Schreier, Nachruf, Monatshefte fur Mathematik 37 (1930), 1--6	559	(6)
Hans Hahn †, Fundamenta Mathematicae 24 (1935), 317--320	565	(4)
Memories of Moritz Schlick, in: Rationality and Science, ed. by E. T. Gadol, Springer, Wien-New York, 1982, 83--103	569	(22)
Introduction to: Ernst Mach: The Science of Mechanics, 6th American Edition, Open Court. La Salle, Illinois 1960, v--xxi	591	(18)
Introduction to: Hans Hahn: Empiricism, Logic and Mathematics, Vienna Circle Collection Vol. 13, Reidel, Dordrecht, 1980, ix--xviii	609	(10)
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	(36)
Table of Contents -- Vol. I	655	(4)
Table of Contents of Karl Menger: ``Selected Papers in Logic and Foundations, Didactics, Economics''	659	(4)
List of Publications	663
Karl Menger