Rudi Mathematici
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Stanisław Zaremba
Danuta Ciesielska*, Krzysztof Ciesielski** Instytut Historii Nauki im. L. i A. Birkenmajerów, PAN Warszawa Instytut Matematyki, Wydział Matematyki i Informatyki, UJ Kraków SSW B (1–192) O DLO K KRTKIE PRZEDSTAWIENIE POLSKIEJ I KRAKOWSKIEJ MATEMATYKI DO POCZTKW XX WIEKU Znaczący rozwój matematyki na świecie datuje się na drugą połowę drugiego tysiąclecia n.e.; przez poprzedzające go półtora tysiąclecia uzyskiwane wyniki były skromne w porównaniu z tym, co uzyskano później. Jednakże do początku XX wieku Polska była z dala od europejskiej, a tym bardziej światowej czołówki. Potęgami ma- tematycznymi były Francja i Niemcy. Ważne rezultaty osiągano w Wielkiej Brytanii i we Włoszech. Sporadycznie pojawiali się słynni matematycy także w innych krajach, jednak w podręcznikach historii matematyki trudno znaleźć wśród nich Polaków. Od XIV wieku Polska miała się czym poszczycić naukowo. Akademia Krakow- ska była drugim uniwersytetem powstałym w środkowej Europie, od początku wy- kładano tu przedmioty kojarzone z matematyką. Na początku XV wieku krakowski mieszczanin Jan Stobner ufundował specjalną katedrę matematyki i astronomii; druga katedra związana z matematyką została ufundowana przez Marcina Króla z Żurawi- cy (ok.1422–ok.1460), pół wieku później. Był to jednak okres istotnie poprzedzający czasy większych osiągnięć matematycznych. Pewne osiągnięcia matematyczne miał ponad wiek później Mikołaj Kopernik (1473–1543), jego nazwisko kojarzone jest jed- nak (oczywiście słusznie) głównie z astronomią. Dopiero w XVII wieku pojawił się w Krakowie matematyk europejskiego formatu – Joannes Broscius (1585–1652; Jan Brożek, znany też jako Brzozek). Był nie tylko mate- matykiem, ale też flozofem, astronomem, teologiem, lekarzem i historykiem nauki. Ma on na swoim koncie znaczące osiągnięcia, głównie związane są z teorią liczb. -
Ernst Abbe 1840-1905: a Social Reformer
We all do not belong to ourselves Ernst Abbe 1840-1905: a Social Reformer Fritz Schulze, Canada Linda Nguyen, The Canadian Press, Wednesday, January 2014: TORONTO – By the time you finish your lunch on Thursday, Canada’s top paid CEO will have already earned (my italics!) the equivalent of your annual salary.* It is not unusual these days to read such or similar headlines. Each time I am reminded of the co-founder of the company I worked for all my active life. Those who know me, know that I worked for the world-renowned German optical company Carl Zeiss. I also have a fine collection of optical instruments, predominantly microscopes, among them quite a few Zeiss instruments. Carl Zeiss founded his business as a “mechanical atelier” in Jena in 1846 and his mathematical consultant, Ernst Abbe, a poorly paid lecturer at the University Jena, became his partner in 1866. That was the beginning of a comet-like rise of the young company. Ernst Abbe was born in Eisenach, Thuringia, on January 23, 1840, as the first child of a spinnmaster of a local textile mill.Till the beginning of the 50s each and every day the Lord made my father stood at his machines, 14, 15, 16 hours, from 5 o’clock in the morning till 7 o’clock in the evening during quiet periods, 16 hours from 4 o’clock in the morning till 8 o’clock in the evening during busy times, without any interruption, not even a lunch break. I myself as a small boy of 5 – 9 years brought him his lunch, alternately with my younger sister, and watched him as he gulped it down leaning on his machine or sitting on a wooden box, then handing me back the empty pail and immediately again tending his machines." Ernst Abbe remembered later. -
List of Members
LIST OF MEMBERS, ALFRED BAKER, M.A., Professor of Mathematics, University of Toronto, Toronto, Canada. ARTHUR LATHAM BAKER, C.E., Ph.D., Professor of Mathe matics, Stevens School, Hpboken., N. J. MARCUS BAKER, U. S. Geological Survey, Washington, D.C. JAMES MARCUS BANDY, B.A., M.A., Professor of Mathe matics and Engineering, Trinit)^ College, N. C. EDGAR WALES BASS, Professor of Mathematics, U. S. Mili tary Academy, West Point, N. Y. WOOSTER WOODRUFF BEMAN, B.A., M.A., Member of the London Mathematical Society, Professor of Mathe matics, University of Michigan, Ann Arbor, Mich. R. DANIEL BOHANNAN, B.Sc, CE., E.M., Professor of Mathematics and Astronomy, Ohio State University, Columbus, Ohio. CHARLES AUGUSTUS BORST, M.A., Assistant in Astronomy, Johns Hopkins University, Baltimore, Md. EDWARD ALBERT BOWSER, CE., LL.D., Professor of Mathe matics, Rutgers College, New Brunswick, N. J. JOHN MILTON BROOKS, B.A., Instructor in Mathematics, College of New Jersey, Princeton, N. J. ABRAM ROGERS BULLIS, B.SC, B.C.E., Macedon, Wayne Co., N. Y. WILLIAM ELWOOD BYERLY, Ph.D., Professor of Mathematics, Harvard University, Cambridge*, Mass. WILLIAM CAIN, C.E., Professor of Mathematics and Eng ineering, University of North Carolina, Chapel Hill, N. C. CHARLES HENRY CHANDLER, M.A., Professor of Mathe matics, Ripon College, Ripon, Wis. ALEXANDER SMYTH CHRISTIE, LL.M., Chief of Tidal Division, U. S. Coast and Geodetic Survey, Washington, D. C. JOHN EMORY CLARK, M.A., Professor of Mathematics, Yale University, New Haven, Conn. FRANK NELSON COLE, Ph.D., Assistant Professor of Mathe matics, University of Michigan, Ann Arbor, Mich. -
Bernhard Riemann 1826-1866
Modern Birkh~user Classics Many of the original research and survey monographs in pure and applied mathematics published by Birkh~iuser in recent decades have been groundbreaking and have come to be regarded as foun- dational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain ac- cessible to new generations of students, scholars, and researchers. BERNHARD RIEMANN (1826-1866) Bernhard R~emanno 1826 1866 Turning Points in the Conception of Mathematics Detlef Laugwitz Translated by Abe Shenitzer With the Editorial Assistance of the Author, Hardy Grant, and Sarah Shenitzer Reprint of the 1999 Edition Birkh~iuser Boston 9Basel 9Berlin Abe Shendtzer (translator) Detlef Laugwitz (Deceased) Department of Mathematics Department of Mathematics and Statistics Technische Hochschule York University Darmstadt D-64289 Toronto, Ontario M3J 1P3 Gernmany Canada Originally published as a monograph ISBN-13:978-0-8176-4776-6 e-ISBN-13:978-0-8176-4777-3 DOI: 10.1007/978-0-8176-4777-3 Library of Congress Control Number: 2007940671 Mathematics Subject Classification (2000): 01Axx, 00A30, 03A05, 51-03, 14C40 9 Birkh~iuser Boston All rights reserved. This work may not be translated or copied in whole or in part without the writ- ten permission of the publisher (Birkh~user Boston, c/o Springer Science+Business Media LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de- veloped is forbidden. -
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 . -
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 -
View Front and Back Matter from The
TRANSACTIONS OF THE American Mathematical Society EDITED BY ElilAKIM HASTINGS MOOBE EDWARD BURR VAN VLECK HENRY SEELY WHITE WITH THE COOPERATION OF CHARLES LEONARD BOTJTON LEONARD EUGENE DICKSON JOHN IHWIN HUTCHINSON EDWARD KASNEH EDWIN BLDWELL WILSON J'UBLIWHEll QCABTEILT BI THE tSOCIKTT WITH THB BUPPOBT OF Yale University Nobthwestekn University Columbia University The University of Illinois Wesleyan University Cornell University ilavehfobd college the university of chicago The University of Missouri Stanford University Volume 8 1907 Lancaster, Pa., and New Yobk THE MACMIIXAN COMPANY Agents fob the Society 1907 Reprinted with the permission of The American Mathematical Society Johnson Reprint Corporation 111 Fifth Avenue, New York 3, N. Y. Johnson Reprint Company Limited Berkeley Square House, London, W. 1 First Reprinting, 1963, Johnson Reprint Corporation TABLE OF CONTENTS VOLUME 8 1907 PAGES Blichfeldt, H. F., of Stanford University, Cal. On modular groups isomorphic with a given linear group.30- 32 Bliss, Gilbert Ames, of Princeton, N. J. A new form of the simplest problem of the calculus of variations.405—414 Bolza, Oskar, of Chicago, 111. Existence proof for a field of extremals tangent to a given curve.399-404 Dickson, Leonard Eugene, of Chicago, 111. Invariants of binary forms under modular transformations.205-232 _Modular theory of group-matrices.389—398 Eisenhart, Luther Pfahler, of Princeton, N. J. Applicable surfaces with asymptotic lines of one surface corresponding to a conjugate system of another.113—134 Fite, William Benjamin, of Ithaca, N. Y. Irreducible linear homogeneous groups whose orders are powers of a prime . 107—112 Fréchet, Maurice, of Paris, France. -
Mcshane-E-J.Pdf
NATIONAL ACADEMY OF SCIENCES EDWARD JAMES MCSHANE 1904–1989 A Biographical Memoir by LEONARD D. BERKOVITZ AND WENDELL H. FLEMING Any opinions expressed in this memoir are those of the authors and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoirs, VOLUME 80 PUBLISHED 2001 BY THE NATIONAL ACADEMY PRESS WASHINGTON, D.C. EDWARD JAMES MCSHANE May 10, 1904–June 1, 1989 BY LEONARD D. BERKOVITZ AND WENDELL H. FLEMING URING HIS LONG CAREER Edward James McShane made D significant contributions to the calculus of variations, integration theory, stochastic calculus, and exterior ballistics. In addition, he served as a national leader in mathematical and science policy matters and in efforts to improve the undergraduate mathematical curriculum. McShane was born in New Orleans on May 10, 1904, and grew up there. His father, Augustus, was a medical doctor and his mother, Harriet, a former schoolteacher. He gradu- ated from Tulane University in 1925, receiving simultaneously bachelor of engineering and bachelor of science degrees, as well as election to Phi Beta Kappa. He turned down an offer from General Electric and instead continued as a student instructor of mathematics at Tulane, receiving a master’s degree in 1927. In the summer of 1927 McShane entered graduate school at the University of Chicago, from which he received his Ph.D. in 1930 under the supervision of Gilbert Ames Bliss. He interrupted his studies during 1928-29 for financial reasons to teach at the University of Wichita. It was at Chicago that McShane’s long-standing interest in the calculus of variations began. -
RM Calendar 2017
Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
TOWARDS a HISTORY of the GEOMETRIC FOUNDATIONS of MATHEMATICS LATE Xixth CENTURY*
ARTICLES TOWARDS A HISTORY OF THE GEOMETRIC FOUNDATIONS OF MATHEMATICS LATE XIXth CENTURY* Rossana TAZZIOLI RÉSUMÉ : Beaucoup de « géomètres » du XIXe siècle – Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres – ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d’Euclide, ils n’ont pas identifié « l’espace physique » avec « l’espace de nos sens ». Partant de notre expérience dans l’espace, ils ont cherché à identifier les propriétés les plus importantes de l’espace et les ont posées à la base de la géométrie. C’est sur la connaissance active de l’espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens – De Paolis, Gino Fano, Pieri, et autres – ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l’arithmétique sur la géométrie et non l’inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. MOTS-CLÉS : Riemann, Helmholtz, fondements des mathématiques, géométrie, espace. ABSTRACT : Many XIXth century « geometers » – such as Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, and others – played an important role in the discussion about the founda- tions of mathematics. But in contrast to Euclid’s ideas, they did not simply identify « physical space » with the « space of the senses ».