Papers of John Todd and Olga Taussky-Todd
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On the Similarity Transformation Between a Matirx and Its Transpose
Pacific Journal of Mathematics ON THE SIMILARITY TRANSFORMATION BETWEEN A MATIRX AND ITS TRANSPOSE OLGA TAUSSKY AND HANS ZASSENHAUS Vol. 9, No. 3 July 1959 ON THE SIMILARITY TRANSFORMATION BETWEEN A MATRIX AND ITS TRANSPOSE OLGA TAUSSKY AND HANS ZASSENHAUS It was observed by one of the authors that a matrix transforming a companion matrix into its transpose is symmetric. The following two questions arise: I. Does there exist for every square matrix with coefficients in a field a non-singular symmetric matrix transforming it into its transpose ? II. Under which conditions is every matrix transforming a square matrix into its transpose symmetric? The answer is provided by THEOREM 1. For every n x n matrix A — (aik) with coefficients in a field F there is a non-singular symmetric matrix transforming A into its transpose Aτ'. THEOREM 2. Every non-singular matrix transforming A into its transpose is symmetric if and only if the minimal polynomial of A is equal to its characteristic polynomial i.e. if A is similar to a com- panion matrix. Proof. Let T = (ti1c) be a solution matrix of the system Σ(A) of the linear homogeneous equations. (1) TA-ATT=O ( 2 ) T - Tτ = 0 . The system Σ(A) is equivalent to the system (3) TA-ATTT = 0 ( 4 ) T - Tτ = 0 which states that Γand TA are symmetric. This system involves n2 — n equations and hence is of rank n2 — n at most. Thus there are at least n linearly independent solutions of Σ(A).1 On the other hand it is well known that there is a non-singular matrix To satisfying - A* , Received December 18, 1958. -
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 -
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 -
Scientific References for Nobel Physics Prizes
1 Scientific References for Nobel Physics Prizes © Dr. John Andraos, 2004 Department of Chemistry, York University 4700 Keele Street, Toronto, ONTARIO M3J 1P3, CANADA For suggestions, corrections, additional information, and comments please send e-mails to [email protected] http://www.chem.yorku.ca/NAMED/ 1901 - Wilhelm Conrad Roentgen "in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him." Roentgen X-ray Roentgen, W.C. Ann. Physik 1898, 64 , 1 Stanton, A. Science 1896, 3 , 227; 726 (translation) 1902 - Hendrik Antoon Lorentz and Pieter Zeeman "in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena." Zeeman effect Zeeman, P., Verhandlungen der Physikalischen Gesellschaft zu Berlin 1896, 7 , 128 Zeeman, P., Nature 1897, 55 , 347 (translation by A. Stanton) 1903 - Antoine Henri Becquerel "in recognition of the extraordinary service he has rendered by his discovery of spontaneous radioactivity." Becquerel, A.H. Compt. Rend. 1896, 122 , 420; 501; 559; 689; 1086 Becquerel, A.H. Compt. Rend. 1896, 123 , 855 Becquerel, A.H. Compt. Rend. 1897, 124 , 444; 800 Becquerel, A.H. Compt. Rend. 1899, 129 , 996; 1205 Becquerel, A.H. Compt. Rend. 1900, 130 , 327; 809; 1583 Becquerel, A.H. Compt. Rend. 1900, 131 , 137 Becquerel, A.H. Compt. Rend. 1901, 133 , 977 1903 - Pierre Curie and Marie Curie, nee Sklodowska "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel." Curie unit of radiation Curie, P; Desains, P., Compt. Rend. -
Historical Notes on Loop Theory
Comment.Math.Univ.Carolin. 41,2 (2000)359–370 359 Historical notes on loop theory Hala Orlik Pflugfelder Abstract. This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s. Keywords: quasigroup theory, loop theory, history Classification: Primary 01A60; Secondary 20N05 This paper is an attempt to map, to fit together not only in a geographical and a chronological sense but also conceptually, the various areas where loop theory originated and through which it moved during the early part of its 70 years of history. 70 years is not very much compared to, say, over 300 years of differential calculus. But it is precisely because loop theory is a relatively young subject that it is often misinterpreted. Therefore, it is extremely important for us to acknowledge its distinctive origins. To give an example, when somebody asks, “What is a loop?”, the simplest way to explain is to say, “it is a group without associativity”. This is true, but it is not the whole truth. It is essential to emphasize that loop theory is not just a generalization of group theory but a discipline of its own, originating from and still moving within four basic research areas — algebra, geometry, topology, and combinatorics. Looking back on the first 50 years of loop history, one can see that every decade initiated a new and important phase in its development. These distinct periods can be summarized as follows: I. 1920s the first glimmerings of non-associativity II. 1930s the defining period (Germany) III. 1940s-60s building the basic algebraic frame and new approaches to projective geometry (United States) IV. -
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. -
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]. -
Microfilms International 300 N /EE B ROAD
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The other two groups deal with a variety of plane situa tions: measures of approximation of a convex set by another convex set of some given class (symmetric sets, sets of con stant width etc*)» extremal properties of triangles inscribed in and circumscribed about convex sets, properties of curves of constant width, and so on. Although the general level and workmanship are inferior to those of the author1 s Cambridge Tract on convexity, the present collection contains some interesting and important things and will be of interest to the specialist, Z« A* Melzak, McGill University Fallacies in Mathematics» by E.A. Maxwell, Cambridge University Press, Macmillan Company of Canada L»td. $2*75, In this book the author, a Fellow of Queen1 s College, Cambridge, is acquainting his readers (College and High School teachers as well as interested pupils) in an often amusing and always interesting way with the fallacies a mathematician is apt to meet in the fields of elementary geometry, algebra and trigonometry and calculus* He distinguishes between mistakes (not discussed in the book), howlers and fallacies in the proper sense like this gem: 1= <JT = J(-l){-l) = V-l J-l = i.i = -1. The first 10 serious chapters presenting a choice selection of fallacies in each of the fields with subsequent detailed discussion are followed by a chapter on miscellaneous howlers, e.g., the following. Solve (x+3)(2-x) = 4* Answer: Either x -I- 3 = 4 „ a • x = 1 or 2 - x = 4 / , x = «2, correct» The book is most instructive for any mathematics teacher, Hans Zassenhaus, California Institute of Technology Some Aspects of Analysis and- Probability, by Irving Kaplansky, Marshall Hall Jre , Edwin Hewitt and Robert Fortet* Surveys in Applied Mathematics IV. -
Emil Artin Lecture Hall.”
Emil - Artin - Lecture Ladies and Gentlemen, on behalf of the Mathematics Center Heidelberg, MATCH, and on behalf of the faculty of mathematics and computer science I would like to welcome all of you to the Emil-Artin-Lecture. The idea of this lecture series, which is organised once a year by MATCH, is to appreciate significant developments and ground breaking contributions in mathematics and to present it to a broader public interested in mathematics. Why do we call it in honour of Emil Artin? Let me say it straight away: Artin does not seem to have any special, close relationship to Heidelberg at all, it is not clear to me, whether he has ever been here! Apart from his fundamental contributions to number theory it is his way of doing and thinking about mathematics, which is a source of inspiration to us and which we consider as a impressive example. Therefore we would like to bear in remembrance Emil Artin and his work. Let me say a few words about Artin before going over to todays lecture: Emil Artin was born in 1898 in Vienna where he grew up before moving to Reichenberg (now Liberec in the Czech Republic) in 1907 where he attended the Realschule. His academic performance then was barely satisfactory and rather irregular. About his mathematical inclination at that early period he later wrote: ªMy own predilection for mathematics manifested itself only in my sixteenth year, whereas earlier there was absolutely no question of any particular aptitude for it.º But after spending a school year in France his marking improved considerably.