Jakob Milich Albert-Ludwigs-Universität Freiburg Im Breisgau / Universität Wien Nicoló Fontana Tartaglia 1520
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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. -
Interview of Albert Tucker
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange About Harlan D. Mills Science Alliance 9-1975 Interview of Albert Tucker Terry Speed Evar Nering Follow this and additional works at: https://trace.tennessee.edu/utk_harlanabout Part of the Mathematics Commons Recommended Citation Speed, Terry and Nering, Evar, "Interview of Albert Tucker" (1975). About Harlan D. Mills. https://trace.tennessee.edu/utk_harlanabout/13 This Report is brought to you for free and open access by the Science Alliance at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in About Harlan D. Mills by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. The Princeton Mathematics Community in the 1930s (PMC39)The Princeton Mathematics Community in the 1930s Transcript Number 39 (PMC39) © The Trustees of Princeton University, 1985 ALBERT TUCKER CAREER, PART 2 This is a continuation of the account of the career of Albert Tucker that was begun in the interview conducted by Terry Speed in September 1975. This recording was made in March 1977 by Evar Nering at his apartment in Scottsdale, Arizona. Tucker: I have recently received the tapes that Speed made and find that these tapes carried my history up to approximately 1938. So the plan is to continue the history. In the late '30s I was working in combinatorial topology with not a great deal of results to show. I guess I was really more interested in my teaching. I had an opportunity to teach an undergraduate course in topology, combinatorial topology that is, classification of 2-dimensional surfaces and that sort of thing. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
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 . -
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. -
“A Valuable Monument of Mathematical Genius”\Thanksmark T1: the Ladies' Diary (1704–1840)
Historia Mathematica 36 (2009) 10–47 www.elsevier.com/locate/yhmat “A valuable monument of mathematical genius” ✩: The Ladies’ Diary (1704–1840) Joe Albree ∗, Scott H. Brown Auburn University, Montgomery, USA Available online 24 December 2008 Abstract Our purpose is to view the mathematical contribution of The Ladies’ Diary as a whole. We shall range from the state of mathe- matics in England at the beginning of the 18th century to the transformations of the mathematics that was published in The Diary over 134 years, including the leading role The Ladies’ Diary played in the early development of British mathematics periodicals, to finally an account of how progress in mathematics and its journals began to overtake The Diary in Victorian Britain. © 2008 Published by Elsevier Inc. Résumé Notre but est de voir la contribution mathématique du Journal de Lady en masse. Nous varierons de l’état de mathématiques en Angleterre au début du dix-huitième siècle aux transformations des mathématiques qui a été publié dans le Journal plus de 134 ans, en incluant le principal rôle le Journal de Lady joué dans le premier développement de périodiques de mathématiques britanniques, à finalement un compte de comment le progrès dans les mathématiques et ses journaux a commencé à dépasser le Journal dans l’Homme de l’époque victorienne la Grande-Bretagne. © 2008 Published by Elsevier Inc. Keywords: 18th century; 19th century; Other institutions and academies; Bibliographic studies 1. Introduction Arithmetical Questions are as entertaining and delightful as any other Subject whatever, they are no other than Enigmas, to be solved by Numbers; . -
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. -
Life and Work of Friedrich Hirzebruch
Jahresber Dtsch Math-Ver (2015) 117:93–132 DOI 10.1365/s13291-015-0114-1 HISTORICAL ARTICLE Life and Work of Friedrich Hirzebruch Don Zagier1 Published online: 27 May 2015 © Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2015 Abstract Friedrich Hirzebruch, who died in 2012 at the age of 84, was one of the most important German mathematicians of the twentieth century. In this article we try to give a fairly detailed picture of his life and of his many mathematical achievements, as well as of his role in reshaping German mathematics after the Second World War. Mathematics Subject Classification (2010) 01A70 · 01A60 · 11-03 · 14-03 · 19-03 · 33-03 · 55-03 · 57-03 Friedrich Hirzebruch, who passed away on May 27, 2012, at the age of 84, was the outstanding German mathematician of the second half of the twentieth century, not only because of his beautiful and influential discoveries within mathematics itself, but also, and perhaps even more importantly, for his role in reshaping German math- ematics and restoring the country’s image after the devastations of the Nazi years. The field of his scientific work can best be summed up as “Topological methods in algebraic geometry,” this being both the title of his now classic book and the aptest de- scription of an activity that ranged from the signature and Hirzebruch-Riemann-Roch theorems to the creation of the modern theory of Hilbert modular varieties. Highlights of his activity as a leader and shaper of mathematics inside and outside Germany in- clude his creation of the Arbeitstagung, -
E. T. Bell and Mathematics at Caltech Between the Wars Judith R
E. T. Bell and Mathematics at Caltech between the Wars Judith R. Goodstein and Donald Babbitt E. T. (Eric Temple) Bell, num- who was in the act of transforming what had been ber theorist, science fiction a modest technical school into one of the coun- novelist (as John Taine), and try’s foremost scientific institutes. It had started a man of strong opinions out in 1891 as Throop University (later, Throop about many things, joined Polytechnic Institute), named for its founder, phi- the faculty of the California lanthropist Amos G. Throop. At the end of World Institute of Technology in War I, Throop underwent a radical transformation, the fall of 1926 as a pro- and by 1921 it had a new name, a handsome en- fessor of mathematics. At dowment, and, under Millikan, a new educational forty-three, “he [had] be- philosophy [Goo 91]. come a very hot commodity Catalog descriptions of Caltech’s program of in mathematics” [Rei 01], advanced study and research in pure mathematics having spent fourteen years in the 1920s were intended to interest “students on the faculty of the Univer- specializing in mathematics…to devote some sity of Washington, along of their attention to the modern applications of with prestigious teaching mathematics” and promised “to provide defi- stints at Harvard and the nitely for such a liaison between pure and applied All photos courtesy of the Archives, California Institute of Technology. of Institute California Archives, the of courtesy photos All University of Chicago. Two Eric Temple Bell (1883–1960), ca. mathematics by the addition of instructors whose years before his arrival in 1951. -
Mathematical Genealogy of the Wellesley College Department Of
Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe -
ACTA UNIVERSITATIS UPSALIENSIS Uppsala Studies in History of Ideas 48
ACTA UNIVERSITATIS UPSALIENSIS Uppsala Studies in History of Ideas 48 ANDREAS RYDBERG Inner Experience An Analysis of Scientific Experience in Early Modern Germany Dissertation presented at Uppsala University to be publicly examined in Geijersalen (Eng6-1023), Engelska Parken, Humanistiskt centrum, Thunbergsvägen 3P, Uppsala, Friday, 9 June 2017 at 10:00 for the degree of Doctor of Philosophy. The examination will be conducted in Swedish. Faculty examiner: Kristiina Savin (Lunds universitet, Institutionen för kulturvetenskaper). Abstract Rydberg, A. 2017. Inner Experience. An Analysis of Scientific Experience in Early Modern Germany. Uppsala Studies in History of Ideas 48. 245 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9926-6. In the last decades a number of studies have shed light on early modern scientific experience. While some of these studies have focused on how new facts were forced out of nature in so-called experimental situations, others have charted long-term transformations. In this dissertation I explore a rather different facet of scientific experience by focusing on the case of the Prussian university town Halle in the period from the late seventeenth till the mid-eighteenth century. At this site philosophers, theologians and physicians were preoccupied with categories such as inner senses , inner experience, living experience, psychological experiments and psychometrics. In the study I argue that these hitherto almost completely overlooked categories take us away from observations of external things to the internal organisation of experience and to entirely internal objects of experience. Rather than seeing this internal side of scientific experience as mere theory and epistemology, I argue that it was an integral and central part of what has been referred to as the cultura animi tradition, that is, the philosophical and medical tradition of approaching the soul as something in need of cultivation, education, disciplination and cure.