Rudi Mathematici
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
Pursuit of Genius: Flexner, Einstein, and the Early Faculty at the Institute
i i i i PURSUIT OF GENIUS i i i i i i i i PURSUIT OF GENIUS Flexner, Einstein,and the Early Faculty at the Institute for Advanced Study Steve Batterson Emory University A K Peters, Ltd. Natick, Massachusetts i i i i i i i i Editorial, Sales, and Customer Service Office A K Peters, Ltd. 5 Commonwealth Road, Suite 2C Natick, MA 01760 www.akpeters.com Copyright ⃝c 2006 by A K Peters, Ltd. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopy- ing, recording, or by any information storage and retrieval system, without written permission from the copyright owner. Library of Congress Cataloging-in-Publication Data Batterson, Steve, 1950– Pursuit of genius : Flexner, Einstein, and the early faculty at the Institute for Advanced Study / Steve Batterson. p. cm. Includes bibliographical references and index. ISBN 13: 978-1-56881-259-5 (alk. paper) ISBN 10: 1-56881-259-0 (alk. paper) 1. Mathematics–Study and teaching (Higher)–New Jersey–Princeton–History. 2. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–History. 3. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–Faculty. I Title. QA13.5.N383 I583 2006 510.7’0749652--dc22 2005057416 Cover Photographs: Front cover: Clockwise from upper left: Hermann Weyl (1930s, cour- tesy of Nina Weyl), James Alexander (from the Archives of the Institute for Advanced Study), Marston Morse (photo courtesy of the American Mathematical Society), Albert Einstein (1932, The New York Times), John von Neumann (courtesy of Marina von Neumann Whitman), Oswald Veblen (early 1930s, from the Archives of the Institute for Advanced Study). -
Downloaded from Brill.Com09/24/2021 10:06:53AM Via Free Access 268 Revue De Synthèse : TOME 139 7E SÉRIE N° 3-4 (2018) Chercheur Pour IBM
REVUE DE SYNTHÈSE : TOME 139 7e SÉRIE N° 3-4 (2018) 267-288 brill.com/rds A Task that Exceeded the Technology: Early Applications of the Computer to the Lunar Three-body Problem Allan Olley* Abstract: The lunar Three-Body problem is a famously intractable problem of Newtonian mechanics. The demand for accurate predictions of lunar motion led to practical approximate solutions of great complexity, constituted by trigonometric series with hundreds of terms. Such considerations meant there was demand for high speed machine computation from astronomers during the earliest stages of computer development. One early innovator in this regard was Wallace J. Eckert, a Columbia University professor of astronomer and IBM researcher. His work illustrates some interesting features of the interaction between computers and astronomy. Keywords: history of astronomy – three body problem – history of computers – Wallace J. Eckert Une tâche excédant la technologie : l’utilisation de l’ordinateur dans le problème lunaire des trois corps Résumé : Le problème des trois corps appliqué à la lune est un problème classique de la mécanique newtonienne, connu pour être insoluble avec des méthodes exactes. La demande pour des prévisions précises du mouvement lunaire menait à des solutions d’approximation pratiques qui étaient d’une complexité considérable, avec des séries tri- gonométriques contenant des centaines de termes. Cela a très tôt poussé les astronomes à chercher des outils de calcul et ils ont été parmi les premiers à utiliser des calculatrices rapides, dès les débuts du développement des ordinateurs modernes. Un innovateur des ces années-là est Wallace J. Eckert, professeur d’astronomie à Columbia University et * Allan Olley, born in 1979, he obtained his PhD-degree from the Institute for the History and Philosophy of Science Technology (IHPST), University of Toronto in 2011. -
Transactions American Mathematical Society
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY EDITED BY A. A. ALBERT OSCAR ZARISKI ANTONI ZYGMUND WITH THE COOPERATION OF RICHARD BRAUER NELSON DUNFORD WILLIAM FELLER G. A. HEDLUND NATHAN JACOBSON IRVING KAPLANSKY S. C. KLEENE M. S. KNEBELMAN SAUNDERS MacLANE C. B. MORREY W. T. REID O. F. G. SCHILLING N. E. STEENROD J. J. STOKER D. J. STRUIK HASSLER WHITNEY R. L. WILDER VOLUME 62 JULY TO DECEMBER 1947 PUBLISHED BY THE SOCIETY MENASHA, WIS., AND NEW YORK 1947 Reprinted with the permission of The American Mathematical Society Johnson Reprint Corporation Johnson Reprint Company Limited 111 Fifth Avenue, New York, N. Y. 10003 Berkeley Square House, London, W. 1 First reprinting, 1964, Johnson Reprint Corporation PRINTED IN THE UNITED STATES OF AMERICA TABLE OF CONTENTS VOLUME 62, JULY TO DECEMBER, 1947 Arens, R. F., and Kelley, J. L. Characterizations of the space of con- tinuous functions over a compact Hausdorff space. 499 Baer, R. Direct decompositions. 62 Bellman, R. On the boundedness of solutions of nonlinear differential and difference equations. 357 Bergman, S. Two-dimensional subsonic flows of a compressible fluid and their singularities. 452 Blumenthal, L. M. Congruence and superposability in elliptic space.. 431 Chang, S. C. Errata for Contributions to projective theory of singular points of space curves. 548 Day, M. M. Polygons circumscribed about closed convex curves. 315 Day, M. M. Some characterizations of inner-product spaces. 320 Dushnik, B. Maximal sums of ordinals. 240 Eilenberg, S. Errata for Homology of spaces with operators. 1. 548 Erdös, P., and Fried, H. On the connection between gaps in power series and the roots of their partial sums. -
J´Ozef Marcinkiewicz
JOZEF¶ MARCINKIEWICZ: ANALYSIS AND PROBABILITY N. H. BINGHAM, Imperial College London Pozna¶n,30 June 2010 JOZEF¶ MARCINKIEWICZ Life Born 4 March 1910, Cimoszka, Bialystok, Poland Student, 1930-33, University of Stefan Batory in Wilno (professors Stefan Kempisty, Juliusz Rudnicki and Antoni Zygmund) 1931-32: taught Lebesgue integration and trigono- metric series by Zygmund MA 1933; military service 1933-34 PhD 1935, under Zygmund 1935-36, Fellowship, U. Lw¶ow,with Kaczmarz and Schauder 1936, senior assistant, Wilno; dozent, 1937 Spring 1939, Fellowship, Paris; o®ered chair by U. Pozna¶n August 1939: in England; returned to Poland in anticipation of war (he was an o±cer in the reserve); already in uniform by 2 September Second lieutenant, 2nd Battalion, 205th In- fantry Regiment Defence of Lwo¶w12 - 21 September 1939; Lwo¶wsurrendered to Red (Soviet) Army Prisoner of war 25 September ("temporary in- ternment" by USSR); taken to Starobielsk Presumed executed Starobielsk, or Kharkov, or Kozielsk, or Katy¶n;Katy¶nMassacre commem- orated on 10 April Work We outline (most of) the main areas in which M's influence is directly seen today, and sketch the current state of (most of) his areas of in- terest { all in a very healthy state, an indication of M's (and Z's) excellent mathematical taste. 55 papers 1933-45 (the last few posthumous) Collaborators: Zygmund 15, S. Bergman 2, B. Jessen, S. Kaczmarz, R. Salem Papers (analysed by Zygmund) on: Functions of a real variable Trigonometric series Trigonometric interpolation Functional operations Orthogonal systems Functions of a complex variable Calculus of probability MATHEMATICS IN POLAND BETWEEN THE WARS K. -
Continuous Nowhere Differentiable Functions
2003:320 CIV MASTER’S THESIS Continuous Nowhere Differentiable Functions JOHAN THIM MASTER OF SCIENCE PROGRAMME Department of Mathematics 2003:320 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 03/320 - - SE Continuous Nowhere Differentiable Functions Johan Thim December 2003 Master Thesis Supervisor: Lech Maligranda Department of Mathematics Abstract In the early nineteenth century, most mathematicians believed that a contin- uous function has derivative at a significant set of points. A. M. Amp`ereeven tried to give a theoretical justification for this (within the limitations of the definitions of his time) in his paper from 1806. In a presentation before the Berlin Academy on July 18, 1872 Karl Weierstrass shocked the mathematical community by proving this conjecture to be false. He presented a function which was continuous everywhere but differentiable nowhere. The function in question was defined by ∞ X W (x) = ak cos(bkπx), k=0 where a is a real number with 0 < a < 1, b is an odd integer and ab > 1+3π/2. This example was first published by du Bois-Reymond in 1875. Weierstrass also mentioned Riemann, who apparently had used a similar construction (which was unpublished) in his own lectures as early as 1861. However, neither Weierstrass’ nor Riemann’s function was the first such construction. The earliest known example is due to Czech mathematician Bernard Bolzano, who in the years around 1830 (published in 1922 after being discovered a few years earlier) exhibited a continuous function which was nowhere differen- tiable. Around 1860, the Swiss mathematician Charles Cell´erieralso discov- ered (independently) an example which unfortunately wasn’t published until 1890 (posthumously). -
Transnational Mathematics and Movements: Shiing- Shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1
Chinese Annals of History of Science and Technology 3 (2), 118–165 (2019) doi: 10.3724/SP.J.1461.2019.02118 Transnational Mathematics and Movements: Shiing- shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1 Zuoyue Wang 王作跃,2 Guo Jinhai 郭金海3 (California State Polytechnic University, Pomona 91768, US; Institute for the History of Natural Sciences, Chinese Academy of Sciences, Beijing 100190, China) Abstract: This paper reconstructs, based on American and Chinese primary sources, the visits of Chinese mathematicians Shiing-shen Chern 陈省身 (Chen Xingshen) and Hua Luogeng 华罗庚 (Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s, especially their interactions with Oswald Veblen and Hermann Weyl, two leading mathematicians at the IAS. It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts, and that socio-political factors combined with professional-personal ones to shape their decisions. The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China, the US, and elsewhere in the twentieth century. Keywords: Shiing-shen Chern, Chen Xingshen, Hua Luogeng, Loo-Keng Hua, Institute for 1 This article was copy-edited by Charlie Zaharoff. 2 Research interests: History of science and technology in the United States, China, and transnational contexts in the twentieth century. He is currently writing a book on the history of American-educated Chinese scientists and China-US scientific relations. -
8. Gram-Schmidt Orthogonalization
Chapter 8 Gram-Schmidt Orthogonalization (September 8, 2010) _______________________________________________________________________ Jørgen Pedersen Gram (June 27, 1850 – April 29, 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark. Important papers of his include On series expansions determined by the methods of least squares, and Investigations of the number of primes less than a given number. The process that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883. http://en.wikipedia.org/wiki/J%C3%B8rgen_Pedersen_Gram ________________________________________________________________________ Erhard Schmidt (January 13, 1876 – December 6, 1959) was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905. His doctoral dissertation was entitled Entwickelung willkürlicher Funktionen nach Systemen vorgeschriebener and was a work on integral equations. Together with David Hilbert he made important contributions to functional analysis. http://en.wikipedia.org/wiki/File:Erhard_Schmidt.jpg ________________________________________________________________________ 8.1 Gram-Schmidt Procedure I Gram-Schmidt orthogonalization is a method that takes a non-orthogonal set of linearly independent function and literally constructs an orthogonal set over an arbitrary interval and with respect to an arbitrary weighting function. Here for convenience, all functions are assumed to be real. un(x) linearly independent non-orthogonal un-normalized functions Here we use the following notations. n un (x) x (n = 0, 1, 2, 3, …..). n (x) linearly independent orthogonal un-normalized functions n (x) linearly independent orthogonal normalized functions with b ( x) (x)w(x)dx i j i , j . -
The History of the Abel Prize and the Honorary Abel Prize the History of the Abel Prize
The History of the Abel Prize and the Honorary Abel Prize The History of the Abel Prize Arild Stubhaug On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Govern- ment decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003. That is the history in brief of the Abel Prize as we know it today. Behind this government decision to commemorate and honor the country’s great mathematician, however, lies a more than hundred year old wish and a short and intense period of activity. Volumes of Abel’s collected works were published in 1839 and 1881. The first was edited by Bernt Michael Holmboe (Abel’s teacher), the second by Sophus Lie and Ludvig Sylow. Both editions were paid for with public funds and published to honor the famous scientist. The first time that there was a discussion in a broader context about honoring Niels Henrik Abel’s memory, was at the meeting of Scan- dinavian natural scientists in Norway’s capital in 1886. These meetings of natural scientists, which were held alternately in each of the Scandinavian capitals (with the exception of the very first meeting in 1839, which took place in Gothenburg, Swe- den), were the most important fora for Scandinavian natural scientists. The meeting in 1886 in Oslo (called Christiania at the time) was the 13th in the series. -
Marshall Stone Y Las Matemáticas
MARSHALL STONE Y LAS MATEMÁTICAS Referencia: 1998. Semanario Universidad, San José. Costa Rica. Marshall Harvey Stone nació en Nueva York el 8 de abril de 1903. A los 16 años entró a Harvard y se graduó summa cum laude en 1922. Antes de ser profesor de Harvard entre 1933 y 1946, fue profesor en Columbia (1925-1927), Harvard (1929-1931), Yale (1931-1933) y Stanford en el verano de 1933. Aunque graduado y profesor en Harvard University, se conoce más por haber convertido el Departamento de Matemática de la University of Chicago -como su Director- en uno de los principales centros matemáticos del mundo, lo que logró con la contratación de los famosos matemáticos Andre Weil, S. S. Chern, Antoni Zygmund, Saunders Mac Lane y Adrian Albert. También fueron contratados en esa época: Paul Halmos, Irving Seal y Edwin Spanier. Para Saunders Mac Lane, el Departamento de Matemática que constituyó Stone en Chicago fue en su momento “sin duda el departamento de matemáticas líder en el país”., y probablemente, deberíamos añadir, en el mundo. Los méritos científicos de Stone fueron muchos. Cuando llegó a Chicago en 1946, por recomendación de John von Neumann al presidente de la Universidad de Chicago, ya había realizado importantes trabajos en varias áreas matemáticas, por ejemplo: la teoría espectral de operadores autoadjuntos en espacios de Hilbert y en las propiedades algebraicas de álgebras booleanas en el estudio de anillos de funciones continuas. Se le conoce por el famoso teorema de Stone Weierstrass, así como la compactificación de Stone Cech. Su libro más influyente fue Linear Transformations in Hilbert Space and their Application to Analysis. -
On the Origin and Early History of Functional Analysis
U.U.D.M. Project Report 2008:1 On the origin and early history of functional analysis Jens Lindström Examensarbete i matematik, 30 hp Handledare och examinator: Sten Kaijser Januari 2008 Department of Mathematics Uppsala University Abstract In this report we will study the origins and history of functional analysis up until 1918. We begin by studying ordinary and partial differential equations in the 18th and 19th century to see why there was a need to develop the concepts of functions and limits. We will see how a general theory of infinite systems of equations and determinants by Helge von Koch were used in Ivar Fredholm’s 1900 paper on the integral equation b Z ϕ(s) = f(s) + λ K(s, t)f(t)dt (1) a which resulted in a vast study of integral equations. One of the most enthusiastic followers of Fredholm and integral equation theory was David Hilbert, and we will see how he further developed the theory of integral equations and spectral theory. The concept introduced by Fredholm to study sets of transformations, or operators, made Maurice Fr´echet realize that the focus should be shifted from particular objects to sets of objects and the algebraic properties of these sets. This led him to introduce abstract spaces and we will see how he introduced the axioms that defines them. Finally, we will investigate how the Lebesgue theory of integration were used by Frigyes Riesz who was able to connect all theory of Fredholm, Fr´echet and Lebesgue to form a general theory, and a new discipline of mathematics, now known as functional analysis. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
Academic Genealogy of the Oakland University Department Of
Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università