81. Integrazione E Misura come quelli di Hermann Henkel, paul du Bois - Reymond, Henry Smith http://www2.math.unifi.it/~archimede/archimede/mostra_calcolo/pannelli/9.html

Il giardino di Archimede Un museo per la matematica L'integrazione e la misura opere della sezione Giuseppe Peano, Applicazioni geometriche del calcolo infinitesimale, Torino-Firenze-Roma-Napoli, Fratelli Bocca editori, 1887. vedi anche Integrazione e misura Nel Résumé des leçons données à l'École Royale Polytechnique del 1823 Cauchy dà quella che viene indicata come la prima definizione moderna di integrale. Egli considera il caso di funzioni continue su un intervallo, estendendosi poi al caso di funzioni con una o con un numero finito di discontinuità. In un articolo del 1829 sul "Journal für die reine und angewandte Mathematik", trattando il problema della rappresentazione delle funzioni in serie di Fourier, Dirichlet solleva il problema del caso di funzioni con un numero infinito di discontinuità, portando anche l'esempio della funzione che porta il suo nome. Nel 1854 Bernhard Riemann (1826-1866) scrive la tesi di abilitazione per ottenere la libera docenza intitolata Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe , ossia "sulla rappresentabilità di una funzione mediante una serie trigonometrica", che resta sconosciuta fino al 1867 quando è pubblicata a cura di Dedekind. Qui viene introdotto l'integrale che porta il suo nome corredato da esempi di funzioni che pur avendo un numero infinito di discontinuità risultano integrabili. Sulla nuova definizione si innestano numerose ricerche riguardanti le proprietà dei sottoinsiemi della retta, prime tra tutte quelle di Cantor, e si aggiungono via via contributi sulla caratterizzazione dell'integrabilità in relazione all'insieme dei punti di discontinuità come quelli di Hermann Henkel, Paul Du Bois - Reymond, Henry Smith, Axel Harnack, Vito Volterra.

82. References For Du_Bois-Reymond Books GH Hardy, Orders of infinity the Infinitärcalcül of Pauldu boisreymond (Cambridge, 1910, reprinted 1971). Articles http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ7584.htm

References for Paul David Gustav Du Bois-Reymond Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: G H Hardy, (Cambridge, 1910, reprinted 1971). Articles: G Fisher, The infinite and infinitesimal quantities of du Bois-Reymond and their reception, Arch. Hist. Exact Sci. Ju F Kosolapov and V S Sologub, Du Bois-Reymond's works on the theory of partial differential equations (Ukrainian), Narisi Istor. Prirodoznav. i Tekhn. H Weber, Paul du Bois-Reymond, Mathematische Annalen Close this window or click this link to go back to du Bois-Reymond Welcome page Biographies Index History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Du_Bois-Reymond.html

83. Infinity -- From MathWorld 7788, 1996. Hardy, G. H. Orders of Infinity, the infinitarcalcul of paul DuBois-Reymond, 2nd ed. Cambridge, England Cambridge University Press, 1924. http://mathworld.wolfram.com/Infinity.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Set Theory Cardinal Numbers ... Commands Infinity An unbounded quantity greater than every real number , most often denoted as The symbol had been used as an alternative to M ( ) in Roman numerals until 1655, when John Wallis suggested it be used instead for infinity. Infinity is a very tricky concept to work with, as evidenced by some of the counterintuitive results which follow from Georg Cantor's treatment of infinite sets Informally, a statement which can be made rigorous using the limit concept, Similarly, where the notation indicates that the limit is taken from the positive side of the real line In Mathematica is represented using the symbol Infinity Aleph Aleph-0 Aleph-1 ... search Conway, J. H. and Guy, R. K. The Book of Numbers.

84. Elementary Function -- From MathWorld 512519, 1992. Hardy, G. H. Orders of Infinity, the infinitarcalcul of paul DuBois-Reymond, 2nd ed. Cambridge, England Cambridge University Press, 1924. http://mathworld.wolfram.com/ElementaryFunction.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Functions Calculus and Analysis ... Miscellaneous Special Functions Elementary Function A function built up of a finite combination of constant functions, field operations ( addition multiplication division , and root extractions the elementary operations )and algebraic, exponential, and logarithmic functions and their inverses under repeated compositions (Shanks 1993, p. 145; Chow 1999). Among the simplest elementary functions are the logarithm exponential function (including the hyperbolic functions power function, and trigonometric functions Following Liouville (1837, 1838, 1839), Watson (1966, p. 111) defines the elementary transcendental functions as and lets etc. Not all functions are elementary. For example, the normal distribution function is a notorious example of a nonelementary function, where

85. Contributed Papers dvi). History of Logic of the 20th century Michel Bourdeau PaulDu boisreymond et l idée de logique empirique (ps, dvi); Manuel http://lc2000.logique.jussieu.fr/abstracta.html

LC 2000 and ELSS 2000 Contributed Papers The deadline for submission of abstracts of contributed talks was on April 18, and we do not accept any new contributions. The abstracts of talks accepted for presentation will appear in a volume handed out to the participants of the Colloquium. The abstracts of members of the ASL will also appear later in the BSL. A few sessions of contributed papers will be reserved for participants of ELSS 2000. Here is a (provisional) list of contributions, listed by themes. At the end you will find the list of contributions presented by title. You can view the abstracts in format dvi or ps. You can view the provisional schedule of the contributed talks by clicking here . (It has not yet been updated to reflect what really happened - our apologies). A (*) indicates that the participant presented his/her contributed talk in the special session of Contributed talks of ELSS 2000, on Thursday July 27. Applications of Logic to Cognitive Sciences Nicholas Asher, Yi Mao:

86. Borel Translate this page Mais, d’un point de vue historique, la réponse pointe sans conteste vers PaulDu bois-reymond (1831-1889), et attire ainsi l’attention sur une oeuvre qui http://www.univ-lille3.fr/set/col/BOREL.html

Michel Bourdeau (Paris) intuitionniste empirique in adjecto Au plan proprement mathématique, Brunschvicg et Cavaillès accordaient à Du Bois-Reymond une place non négligeable dans la genèse de la théorie des ensembles. Son influence est très sensible dans l’oeuvre de Borel. Il est en effet l’inventeur du raisonnement diagonal, souvent attribué à Cantor et, avec son "théorème fondamental" il nous a, le premier, montré l’existence de l’indénombrable. Les pré-intuitionnistes ne cachaient pas leur sympathie pour un point de vue où, à la différence de chez Cantor, le transfini repose non sur un principe posé a priori, a priori, ou mieux des reconstructions a posteriori

87. Berichte Und Rezensionen: Berichte Und Rezensionen Translate this page Der Mathematikhistoriker wird hier so bekannte Mathematiker finden wie paul duBois-Reymond (1831–1889), die Weierstraß-Schüler Emil Lampe (1840–1918 http://www.luise-berlin.de/bms/bmstext/9810reza.htm

Hellmut Lorenz (Hrsg.) Berliner Baukunst der Barockzeit Die Zeichnungen und Notizen aus dem Reisetagebuch des Architekten Christoph Pitzler Nicolaische Verlagsbuchhandlung, Berlin 1998 Helmut Caspar Eberhard Knobloch Annette Vogt Laurenz Demps Parthas, Berlin 1998 Kurt Wernicke www.luise-berlin.de

88. © 1998-2002 Sommerfeld-Projekt. Ausgelesen Am 29. Dezember 2002 Kirchhoff, Gustav (1824-1887); Klein, Felix (1849-1925); Maxwell, James Clerk http://www.lrz-muenchen.de/~Sommerfeld/BriefDat/00436.html

Paul Volkmann an Arnold Sommerfeld, 17. Oktober 1899 Archiv: (Archiv HS 1977-28/A,348) Stichworte Personen: Bois-Reymond, Paul du (1831-1889); Kelvin, Lord (1824-1907); Kirchhoff, Gustav (1824-1887); Klein, Felix (1849-1925); Maxwell, James Clerk (1831-1879); Reiff, Richard (1855-1908); Sommerfeld, Johanna (1874-1955); Volkmann, [Ehefrau Paul]; Waals, Johannes D. van der (1837-1923); Wangerin, Albert (1844-1933); Weinstein, Bernhard (1852-1918) Wissenschaft: Reihen: Promotion Reiff Institution: Start Biographie Projekt Online-Suche

89. Mehmke (1857 - 1944) Grassmann schen Ausdehnungslehre auf die Geometrie der Kreise in der Ebene . http://www.kk.s.bw.schule.de/mathge/mehmke.htm

Rudolf Mehmke (1857 - 1944) Lauterberg, Harz 1875 - SS 1877 WS 1977 - WS 1878/79 SS 1879 - WS 1879/80 Studium der Mathematik am Polytechnikum Stuttgart Studium der Architekt am Polytechnikum in Stuttgart Anwendung der Grassmann'schen Ausdehnungslehre auf die Geometrie der Kreise in der Ebene C. W. Baur Stuttgart angewandten Mathematiker reiner Mathematik Othmar Baier Baier und Lotze S. 31 Mehmke war ein engagierter Pazifist und politisch aktiver Mensch. Sein Sohn schrieb 1946: Bausteine Schriftenverzeichnis: Siehe Karin Reich: Der Mathematiker Rudolf Mehmke: Bausteine zu Leben und Werk. Briefwechsel von Mehmke Liste der Briefe Literatur zu Mehmke: Othmar Baier und Alfred Lotze: Rudolf Mehmke zum Gedenken. Rudolf Fritsch in: Neue Deutsche Biographie. Bd 16, S. 621-623 Karin Reich: Der Mathematiker Rudolf Mehmke: Bausteine zu Leben und Werk Karin Reich: Die Rolle Arnold Sommerfelds bei der Diskussion um dieVektorrechnung In: History of Mathematics: states of the art. Hrsg. Joseph W. Dauben [et al]. San Diego et al 1996, S. 319 - 341 Bertram Maurer. 1/1998

90. Résultat De La Recherche http://gallica.bnf.fr/scripts/Catalog.asp?Sujet=Fonctions

91. Naturwissenschaft Und Technik In Der Geschichte Mathematisches Seminar analytische Übungen (WS 1878/79); Siegmund http://www.gnt-verlag.de/programm/15/p263-285_reich.shtml

Weitere Informationen Helmuth Albrecht (Hrsg.) Naturwissenschaft und Technik in der Geschichte 400 Seiten, Pb., 40.00 DM ISBN 3-928186-15-9 Der Titel ist vergriffen! Rezensionen Der Mathematiker Rudolf Mehmke: Bausteine zu Leben und Werk. Karin Reich 2 Materialien in Stuttgart In Stuttgart befinden sich die Originalmanuskripte Mehmkes 2.1 Vorlesungsmitschriften I. Werkmanuskripte, II. Korrespondenzen (1 Brief), III. Lebensdokumente: 1. Vorlesungsmitschriften, Weitere bemerkenswerte Vorlesungsmitschriften Mehmkes sind: Albert Wangerin: Conforme Abbildungen (Berlin SS 1879); Ernst Eduard Kummer: Mathematisches Seminar, Aufgaben (Berlin WS 1879/80. Mehmke war auch Mitglied des Berliner mathematischen Vereins. 2.2 Mehmkes gedrucktes Werk Mehmke selbst teilte seine Schriften ein in: I. Schriften, IV. Mathematische Apparate und Instrumente, V. Abhandlungen und kleinere Mitteilungen. I. Schriften, III. Aufgaben, IV. Besprechungen, V. Sonstiges 2.4 Modelle, Apparate, Instrumente In der Tat hatte Mehmke 18 eigene, selbst entworfene und gebaute Objekte ausgestellt und beschrieben Nr. 11: Weber's Rechenkreis (Dyck I, 142)

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