Mathematical Genealogy of the Wellesley College Department of Mathematics in Mathematics Frederic W
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Der Vierfarbensatz. Geschichte, Topologische Grundlagen Und
Der Vierfarbensatz Geschichte, topologische Grundlagen und Beweisidee von Prof. Dr. RudolfjFritsch Universität München unter Mitarbeit von Gerda Fritsch, Gräfelfing Wissenschaftsverlag Mannheim • Leipzig - Wien • Zürich Mathematische Institut dar Universität München Die Deutsche Bibliothek - CIP-Einheitsaufnahme Fritsch, Rudolf: Der Vierfarbensatz: Geschichte, topologische Grundlagen und Beweisidee / von Rudolf Fritsch. Unter Mitarb. von Gerda Fritsch. - Mannheim; Leipzig; Wien; Zürich: BI-Wiss.-Verl., 1994 ISBN 3-411-15141-2 Gedruckt auf säurefreiem Papier mit neutralem pH-Wert (bibliotheksfest) Alle Rechte, auch die der Übersetzung in fremde Sprachen, vorbehalten. Kein Teil dieses Werkes darf ohne schriftliche Einwilligung des Verlages in irgendeiner Form (Fotokopie, Mikrofilm oder ein anderes Verfahren), auch nicht für Zwecke der Unterrichtsgestaltung, reproduziert oder unter Verwendung elektronischer Systeme verarbeitet, vervielfältigt oder verbreitet werden. © Bibliographisches Institut & F. A. Brockhaus AG, Mannheim 1994 Druck: RK Offsetdruck GmbH, Speyer Bindearbeit: Progressdruck GmbH, Speyer Printed in Germany ISBN 3-411-15141-2 Für Dorothee Veronika Bernhard Inhalt s Verzeichnis Statt eines Vorworts 3 Wie man dieses Buch lesen kann 6 1 Geschichte 7 2 (Topologische) Landkarten 45 2.1 Heuristische Vorüberlegungen 45 2.2 Grenzlinien 48 2.3 Formale Definition 61 Ecken 63 Länder 64 Zusammenhang von Landkarten 66 Reduktion auf Landkarten aus Streckenzügen 67 2.4 Grundlegende Beispiele 70 2.5 Landesgrenzen 75 2.6 Gemeinsame Grenzlinien -
Mathematical Genealogy of the Union College Department of Mathematics
Gemma (Jemme Reinerszoon) Frisius Mathematical Genealogy of the Union College Department of Mathematics Université Catholique de Louvain 1529, 1536 The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. Johannes (Jan van Ostaeyen) Stadius http://www.genealogy.math.ndsu.nodak.edu/ Université Paris IX - Dauphine / Université Catholique de Louvain Justus (Joost Lips) Lipsius Martinus Antonius del Rio Adam Haslmayr Université Catholique de Louvain 1569 Collège de France / Université Catholique de Louvain / Universidad de Salamanca 1572, 1574 Erycius (Henrick van den Putte) Puteanus Jean Baptiste Van Helmont Jacobus Stupaeus Primary Advisor Secondary Advisor Universität zu Köln / Université Catholique de Louvain 1595 Université Catholique de Louvain Erhard Weigel Arnold Geulincx Franciscus de le Boë Sylvius Universität Leipzig 1650 Université Catholique de Louvain / Universiteit Leiden 1646, 1658 Universität Basel 1637 Union College Faculty in Mathematics Otto Mencke Gottfried Wilhelm Leibniz Ehrenfried Walter von Tschirnhaus Key Universität Leipzig 1665, 1666 Universität Altdorf 1666 Universiteit Leiden 1669, 1674 Johann Christoph Wichmannshausen Jacob Bernoulli Christian M. von Wolff Universität Leipzig 1685 Universität Basel 1684 Universität Leipzig 1704 Christian August Hausen Johann Bernoulli Martin Knutzen Marcus Herz Martin-Luther-Universität Halle-Wittenberg 1713 Universität Basel 1694 Leonhard Euler Abraham Gotthelf Kästner Franz Josef Ritter von Gerstner Immanuel Kant -
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 -
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 -
A History of Mathematics in America Before 1900.Pdf
THE BOOK WAS DRENCHED 00 S< OU_1 60514 > CD CO THE CARUS MATHEMATICAL MONOGRAPHS Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Publication Committee GILBERT AMES BLISS DAVID RAYMOND CURTISS AUBREY JOHN KEMPNER HERBERT ELLSWORTH SLAUGHT CARUS MATHEMATICAL MONOGRAPHS are an expression of THEthe desire of Mrs. Mary Hegeler Carus, and of her son, Dr. Edward H. Carus, to contribute to the dissemination of mathe- matical knowledge by making accessible at nominal cost a series of expository presenta- tions of the best thoughts and keenest re- searches in pure and applied mathematics. The publication of these monographs was made possible by a notable gift to the Mathematical Association of America by Mrs. Carus as sole trustee of the Edward C. Hegeler Trust Fund. The expositions of mathematical subjects which the monographs will contain are to be set forth in a manner comprehensible not only to teach- ers and students specializing in mathematics, but also to scientific workers in other fields, and especially to the wide circle of thoughtful people who, having a moderate acquaintance with elementary mathematics, wish to extend their knowledge without prolonged and critical study of the mathematical journals and trea- tises. The scope of this series includes also historical and biographical monographs. The Carus Mathematical Monographs NUMBER FIVE A HISTORY OF MATHEMATICS IN AMERICA BEFORE 1900 By DAVID EUGENE SMITH Professor Emeritus of Mathematics Teacliers College, Columbia University and JEKUTHIEL GINSBURG Professor of Mathematics in Yeshiva College New York and Editor of "Scripta Mathematica" Published by THE MATHEMATICAL ASSOCIATION OF AMERICA with the cooperation of THE OPEN COURT PUBLISHING COMPANY CHICAGO, ILLINOIS THE OPEN COURT COMPANY Copyright 1934 by THE MATHEMATICAL ASSOCIATION OF AMKRICA Published March, 1934 Composed, Printed and Bound by tClfe QlolUgUt* $Jrr George Banta Publishing Company Menasha, Wisconsin, U. -
Some Comments on Multiple Discovery in Mathematics
Journal of Humanistic Mathematics Volume 7 | Issue 1 January 2017 Some Comments on Multiple Discovery in Mathematics Robin W. Whitty Queen Mary University of London Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the History of Science, Technology, and Medicine Commons, and the Other Mathematics Commons Recommended Citation Whitty, R. W. "Some Comments on Multiple Discovery in Mathematics," Journal of Humanistic Mathematics, Volume 7 Issue 1 (January 2017), pages 172-188. DOI: 10.5642/jhummath.201701.14 . Available at: https://scholarship.claremont.edu/jhm/vol7/iss1/14 ©2017 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Some Comments on Multiple Discovery in Mathematics1 Robin M. Whitty Queen Mary University of London [email protected] Synopsis Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical com- puter science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. -
Mathematics in the Austrian-Hungarian Empire
Mathematics in the Austrian-Hungarian Empire Christa Binder The appointment policy in the Austrian-Hungarian Empire In: Martina Bečvářová (author); Christa Binder (author): Mathematics in the Austrian-Hungarian Empire. Proceedings of a Symposium held in Budapest on August 1, 2009 during the XXIII ICHST. (English). Praha: Matfyzpress, 2010. pp. 43–54. Persistent URL: http://dml.cz/dmlcz/400817 Terms of use: © Bečvářová, Martina © Binder, Christa Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz THE APPOINTMENT POLICY IN THE AUSTRIAN- -HUNGARIAN EMPIRE CHRISTA BINDER Abstract: Starting from a very low level in the mid oft the 19th century the teaching and research in mathematics reached world wide fame in the Austrian-Hungarian Empire before World War One. How this was complished is shown with three examples of careers of famous mathematicians. 1 Introduction This symposium is dedicated to the development of mathematics in the Austro- Hungarian monarchy in the time from 1850 to 1914. At the beginning of this period, in the middle of the 19th century the level of teaching and researching mathematics was very low – with a few exceptions – due to the influence of the jesuits in former centuries, and due to the reclusive period in the first half of the 19th century. But even in this time many efforts were taken to establish a higher education. -
Presentation of the Austrian Mathematical Society - E-Mail: [email protected] La Rochelle University Lasie, Avenue Michel Crépeau B
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features S E European A Problem for the 21st/22nd Century M M Mathematical Euler, Stirling and Wallis E S Society History Grothendieck: The Myth of a Break December 2019 Issue 114 Society ISSN 1027-488X The Austrian Mathematical Society Yerevan, venue of the EMS Executive Committee Meeting New books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Todd Fisher (Brigham Young University, Provo, USA) and Boris Hasselblatt (Tufts University, Medford, USA) Hyperbolic Flows (Zürich Lectures in Advanced Mathematics) ISBN 978-3-03719-200-9. 2019. 737 pages. Softcover. 17 x 24 cm. 78.00 Euro The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consulta- tion with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. -
Solomon Lefschetz
NATIONAL ACADEMY OF SCIENCES S O L O M O N L EFSCHETZ 1884—1972 A Biographical Memoir by PHILLIP GRIFFITHS, DONALD SPENCER, AND GEORGE W HITEHEAD Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1992 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. SOLOMON LEFSCHETZ September 3, 1884-October 5, 1972 BY PHILLIP GRIFFITHS, DONALD SPENCER, AND GEORGE WHITEHEAD1 OLOMON LEFSCHETZ was a towering figure in the math- Sematical world owing not only to his original contribu- tions but also to his personal influence. He contributed to at least three mathematical fields, and his work reflects throughout deep geometrical intuition and insight. As man and mathematician, his approach to problems, both in life and in mathematics, was often breathtakingly original and creative. PERSONAL AND PROFESSIONAL HISTORY Solomon Lefschetz was born in Moscow on September 3, 1884. He was a son of Alexander Lefschetz, an importer, and his wife, Vera, Turkish citizens. Soon after his birth, his parents left Russia and took him to Paris, where he grew up with five brothers and one sister and received all of his schooling. French was his native language, but he learned Russian and other languages with remarkable fa- cility. From 1902 to 1905, he studied at the Ecole Centrale des Arts et Manufactures, graduating in 1905 with the de- gree of mechanical engineer, the third youngest in a class of 220. His reasons for entering that institution were com- plicated, for as he said, he had been "mathematics mad" since he had his first contact with geometry at thirteen. -
Academic Genealogy of Peh Hoon Ng the Mathematics Genealogy
Erhard Weigel Universität Leipzig 1650 Otto Mencke Gottfried Wilhelm Leibniz Universität Leipzig 1668 Universität Altdorf 1666 Johann Christoph Wichmannshausen Jacob Bernoulli Universität Leipzig 1685 Christian August Hausen Johann Bernoulli Martin-Luther-Universität Halle-Wittenberg 1713 1694 Abraham Gotthelf Kaestner Leonhard Euler Universität Leipzig 1739 Universität Basel 1726 Friedrich Anton Justus Thibaut Johann Tobias Meyer d.J. Johann Friedrich Pfaff Joseph Louis Lagrange Christian-Albrechts-Universität zu Kiel 1796 Georg-August-Universität Göttingen 1773 Georg-August-Universität Göttingen 1786 Enno Heeren Dirksen Carl Friedrich Gauß Simeon Denis Poisson Jean-Baptiste Joseph Fourier Karl Christian von Langsdorf Georg-August-Universität Göttingen 1820 Universität Helmstedt 1799 Universität Erfurt 1781 Karl Gustav Jacob Jacobi Christian Ludwig Gerling Gustav Peter Lejeune Dirichlet Martin Ohm Humboldt-Universität zu Berlin 1825 Georg-August-Universität Göttingen 1812 Rheinische Friedrich-Wilhelms-Universität Bonn 1827 Friedrich-Alexander-Universität Erlangen-Nürnberg 1811 Otto Hesse Friedrich Julius Richelot Julius Plücker Rudolf Otto Sigismund Lipschitz Universität Königsberg 1840 Universität Königsberg 1831 Philipps-Universität Marburg 1823 Universität Berlin 1853 Carl Gottfried Neumann C. Felix (Christian) Klein Universität Königsberg 1856 Rheinische Friedrich-Wilhelms-Universität Bonn 1868 William Edward Story Universität Leipzig 1875 Solomon Lefschetz Clark University 1911 Albert William Tucker Paul Althaus Smith Princeton -
Algebraic Properties of Groups
Summer Research Summary Saman Gharib∗ properties came from Artin’s genius approach to organize group ele- ments into some special intuitive form, known as Artin’s combing. Now During my discussions with Prof.Rolfsen we studied mostly on algebraic the general property is if you remove bunch of hyperplane in R2n and properties of groups1. We encountered many interesting groups. To compute the first homotopy group of this space, it can be shown that it name a few, Artin and Coxeter groups, Thompson group, group of ori- decomposes into semi-direct product of bunch of free groups . entation preserving homeomorphisms of the real line or [0,1], group of germs of orientation preserving homeomorphisms of real line fixing one fact. F1 o F2 o ... o Fn is locally indicable [ where Fi ’s are free groups ] . specific point. Moreover if the semi-direct products acts nicely you can prove that the resulting group is bi-orderable. Let G be a weighted graph ( to every edge of a graph there is an associ- ated number, m(ex,y ) that can be in f2,3,4,...,1g ) Related to these game-theory-like playing in high dimensions are 2 in- tuitive papers Configuration Spaces[10] and Braid Groups[1] . Artin(G ) = hv 2 VG : v w v ... = w v w ...8v,w 2 VG i Next topic which we worked on was about space of ordering of a group. Coxeter(G ) = hv 2 V : v w v ... = w v w ...8v,w 2 V ,v 2 = 18v 2 V i G G G There are good papers of Sikora[2] , Navas[5] and Tatarin[32]. -
Odd Primary Exponents of Moore Spaces
Contemporary Mathematics Odd primary exponents of Moore spaces Joseph Neisendorfer Dedicated to the memory of John Coleman Moore Contents 1. Introduction 1 2. Tools for odd primary exponent theory 5 3. Decompositions of suspensions into bouquets 7 4. Splittings which lead to exponents for odd primary Moore spaces 9 5. Proof of the geometric exponent theorems for odd primary Moore spaces 12 6. An exponent for the odd primary Moore spaces which works for all odd primes 14 7. The adjoint form of the semi-splitting 15 8. A cofibration sequence 16 9. Acyclic envelopes 17 10. Geometric acyclic envelopes 18 11. Proof of the semi-splitting 20 References 22 1. Introduction If p is a prime and A is an abelian group, then A is said to have exponent pn at the prime p if pn annihilates the p torsion of A and it is the least such power. A topological space X has exponent pn if if this is the least power which annihilates the p torsion in all the homotopy groups of X. The proof of the exact result for the homotopy exponent of an odd primary Moore space is one which always made me feel uneasy. You know you are on dangerous ground when you have trouble recalling why some of things you have written are true. It was with some trepidation that I dealt with Brayton Gray's questions about this work. Some serious mistakes were found. But they were not fatal, except for the 3-primary case. Modulo the 3-primary case, the proof has survived this test and it has even improved under Brayton's insightful questioning.