You Do the Math. the Newton Fellowship Program Is Looking for Mathematically Sophisticated Individuals to Teach in NYC Public High Schools
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“Gödel's Modernism: on Set-Theoretic Incompleteness,” Revisited
“G¨odel'sModernism: on Set-Theoretic Incompleteness," revisited∗ Mark van Atten and Juliette Kennedy As to problems with the answer Yes or No, the con- viction that they are always decidable remains un- touched by these results. —G¨odel Contents 1 Introduction 1.1 Questions of incompleteness On Friday, November 15, 1940, Kurt G¨odelgave a talk on set theory at Brown University.1 The topic was his recent proof of the consistency of Cantor's Con- tinuum Hypothesis, henceforth CH,2 with the axiomatic system for set theory ZFC.3 His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness:4 (Remarks I planned to make, but did not) Discussion on G¨odel'slecture on the Continuum Hypothesis, November 14,5 1940 There seems to be a difference: between the undecidable propo- sitions of the kind of his example [i.e., 1931] and propositions such as the Axiom of Choice, and the Axiom of the Continuum [CH ]. We used to ask: \When these two have been decided, is then everything decided?" (The Poles, Tarski I think, suspected that this would be the case.) Now we know that (on the basis of the usual finitary rules) there will always remain undecided propositions. ∗An earlier version of this paper appeared as ‘G¨odel'smodernism: on set-theoretic incom- pleteness', Graduate Faculty Philosophy Journal, 25(2), 2004, pp.289{349. Erratum facing page of contents in 26(1), 2005. 1 1. Can we nevertheless still ask an analogous question? I.e. -
Cultural Branding in the Early Modern Period 31 the Literary Author Lieke Van Deinsen and Nina Geerdink
PDF hosted at the Radboud Repository of the Radboud University Nijmegen The following full text is a publisher's version. For additional information about this publication click this link. https://repository.ubn.ru.nl/handle/2066/232945 Please be advised that this information was generated on 2021-09-24 and may be subject to change. Joosten & Steenmeijer(eds) Dera, den Braber, Van Branding Books Across the Ages Strategies and Key Concepts in Literary Branding Branding Books Across the Ages Across the Books Branding Edited by Helleke van den Braber, Jeroen Dera, Jos Joosten and Maarten Steenmeijer Branding Books Across the Ages Branding Books Across the Ages Strategies and Key Concepts in Literary Branding Edited by Helleke van den Braber, Jeroen Dera, Jos Joosten, and Maarten Steenmeijer Amsterdam University Press This volume is supported by the Stichting Frederik Muller Fonds, the Paul Hazard Stichting, the Radboud Institute for Culture and History, and the Department of Modern Languages and Cultures at Radboud University. The authors thank Demi Schoonenberg and Tommie van Wanrooij for their invaluable help during the editorial process of this book. Cover design: Coördesign, Leiden Typesetting: Crius Group, Hulshout isbn 978 94 6372 391 6 e-isbn 978 90 4854 440 0 (pdf) doi 10.5117/9789463723916 nur 621 Creative Commons License CC BY NC ND (http://creativecommons.org/licenses/by-nc-nd/3.0) The authors / Amsterdam University Press B.V., Amsterdam 2021 Some rights reserved. Without limiting the rights under copyright reserved above, any part of this book may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise). -
Calcium: Computing in Exact Real and Complex Fields Fredrik Johansson
Calcium: computing in exact real and complex fields Fredrik Johansson To cite this version: Fredrik Johansson. Calcium: computing in exact real and complex fields. ISSAC ’21, Jul 2021, Virtual Event, Russia. 10.1145/3452143.3465513. hal-02986375v2 HAL Id: hal-02986375 https://hal.inria.fr/hal-02986375v2 Submitted on 15 May 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Calcium: computing in exact real and complex fields Fredrik Johansson [email protected] Inria Bordeaux and Institut Math. Bordeaux 33400 Talence, France ABSTRACT This paper presents Calcium,1 a C library for exact computa- Calcium is a C library for real and complex numbers in a form tion in R and C. Numbers are represented as elements of fields suitable for exact algebraic and symbolic computation. Numbers Q¹a1;:::; anº where the extension numbers ak are defined symbol- ically. The system constructs fields and discovers algebraic relations are represented as elements of fields Q¹a1;:::; anº where the exten- automatically, handling algebraic and transcendental number fields sion numbers ak may be algebraic or transcendental. The system combines efficient field operations with automatic discovery and in a unified way. -
Landscapes of Korean and Korean American Biblical Interpretation
BIBLICAL INTERPRETATION AMERICAN AND KOREAN LANDSCAPES OF KOREAN International Voices in Biblical Studies In this first of its kind collection of Korean and Korean American Landscapes of Korean biblical interpretation, essays by established and emerging scholars reflect a range of historical, textual, feminist, sociological, theological, and postcolonial readings. Contributors draw upon ancient contexts and Korean American and even recent events in South Korea to shed light on familiar passages such as King Manasseh read through the Sewol Ferry Tragedy, David and Bathsheba’s narrative as the backdrop to the prohibition against Biblical Interpretation adultery, rereading the virtuous women in Proverbs 31:10–31 through a Korean woman’s experience, visualizing the Demilitarized Zone (DMZ) and demarcations in Galatians, and introducing the extrabiblical story of Eve and Norea, her daughter, through story (re)telling. This volume of essays introduces Korean and Korean American biblical interpretation to scholars and students interested in both traditional and contemporary contextual interpretations. Exile as Forced Migration JOHN AHN is AssociateThe Prophets Professor Speak of Hebrew on Forced Bible Migration at Howard University ThusSchool Says of Divinity.the LORD: He Essays is the on author the Former of and Latter Prophets in (2010) Honor ofand Robert coeditor R. Wilson of (2015) and (2009). Ahn Electronic open access edition (ISBN 978-0-88414-379-6) available at http://ivbs.sbl-site.org/home.aspx Edited by John Ahn LANDSCAPES OF KOREAN AND KOREAN AMERICAN BIBLICAL INTERPRETATION INTERNATIONAL VOICES IN BIBLICAL STUDIES Jione Havea Jin Young Choi Musa W. Dube David Joy Nasili Vaka’uta Gerald O. West Number 10 LANDSCAPES OF KOREAN AND KOREAN AMERICAN BIBLICAL INTERPRETATION Edited by John Ahn Atlanta Copyright © 2019 by SBL Press All rights reserved. -
NEWSLETTER Issue: 491 - November 2020
i “NLMS_491” — 2020/10/28 — 11:56 — page 1 — #1 i i i NEWSLETTER Issue: 491 - November 2020 COXETER THE ROYAL INSTITUTION FRIEZES AND PROBABILIST’S CHRISTMAS GEOMETRY URN LECTURER i i i i i “NLMS_491” — 2020/10/28 — 11:56 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Eleanor Lingham (Sheeld Hallam University) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or David Chillingworth (University of Southampton) photographer for the rights to reproduce. Jessica Enright (University of Glasgow) The LMS cannot accept responsibility for the Jonathan Fraser (University of St Andrews) accuracy of information in the Newsletter. Views Jelena Grbic´ (University of Southampton) expressed do not necessarily represent the Cathy Hobbs (UWE) views or policy of the Editorial Team or London Christopher Hollings (Oxford) Mathematical Society. Stephen Huggett Adam Johansen (University of Warwick) ISSN: 2516-3841 (Print) Susan Oakes (London Mathematical Society) ISSN: 2516-385X (Online) Andrew Wade (Durham University) DOI: 10.1112/NLMS Mike Whittaker (University of Glasgow) Early Career Content Editor: Jelena Grbic´ NEWSLETTER WEBSITE News Editor: Susan Oakes Reviews Editor: Christopher Hollings The Newsletter is freely available electronically at lms.ac.uk/publications/lms-newsletter. CORRESPONDENTS AND STAFF MEMBERSHIP LMS/EMS Correspondent: David Chillingworth Joining the LMS is a straightforward process. For Policy Digest: John Johnston membership details see lms.ac.uk/membership. -
New Bern in Fiction: Works of Fiction About Or Mentioning the New Bern Area Compiled by Victor T
New Bern in Fiction: Works of fiction about or mentioning the New Bern area Compiled by Victor T. Jones, Jr. Arthur, Donald. The River Basin (Victoria, B.C. : Trafford Publishing, 2004, 250 p.) Location: R NC F ART (also copy at Pamlico NC F ART)—Time seemed to stand still in the sleepy little town of New Bern. The river that flowed through this peaceful place was a life source for its residents; however, something lay beneath its depths that would change their lives forever. (Cover) Boyd, James. Drums (New York: Scribner’s, 1925, 490 p.). Location: NC F BOY—Johnny Fraser, the piney-woods hero of this classic novel of the Revolution in N.C., goes from Edenton to London, and in sentiment from Toryism to supporting John Paul Jones in his great sea battle. Boyd’s historical realism and dimensional characters make this a great novel of its genre. (North Carolina Fiction). Carroll, Ruth. Tough Enough's Pony (New York: H. Z. Walck, 1957, 64 p.). Location: NC J CAR—Beanie's little dog Tough Enough finds one of grandfather's ponies injured on the beach (Shackleford Banks, Carteret County), and when the little horse is well he follows Beanie, the family, and his good friend Tough to their home in the Smoky Mountains. (North Carolina Fiction) Carter, Jimmy. The Hornet’s Nest (New York: Simon & Schuster, 2003, 480 p.). Location: F CAR (also Book on CD, CD F CAR)—A novel of the American South during the Revolutionary War follows Ethan Pratt, his wife Epsey, and their neighbors, Kindred and Mavis Morris, as they become caught up in the conflict and the problems confronting local Indian tribes. -
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. -
Georg Kreisel Papers SC0136
http://oac.cdlib.org/findaid/ark:/13030/kt4k403759 No online items Guide to the Georg Kreisel Papers SC0136 Daniel Hartwig & Jenny Johnson Department of Special Collections and University Archives October 2010 Green Library 557 Escondido Mall Stanford 94305-6064 [email protected] URL: http://library.stanford.edu/spc Note This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0.This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0. Guide to the Georg Kreisel Papers SC0136 1 SC0136 Language of Material: English Contributing Institution: Department of Special Collections and University Archives Title: Georg Kreisel papers creator: Kreisel, Georg Identifier/Call Number: SC0136 Physical Description: 24.75 Linear Feet Date (inclusive): 1957-1984 Language of Material: English Language of Material: English Abstract: Correspondence with professional colleagues, collaborators, students, and others, primarily from 1962 to 1984, lecture notes, manuscripts and other writings. Ownership & Copyright All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94304-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner. Such permission must be obtained from the copyright owner, heir(s) or assigns. See: http://library.stanford.edu/depts/spc/pubserv/permissions.html. Restrictions also apply to digital representations of the original materials. Use of digital files is restricted to research and educational purposes. Biographical/Historical Sketch Professor of Logic and the Foundations of Mathematics at Stanford University. -
Statistics Making an Impact
John Pullinger J. R. Statist. Soc. A (2013) 176, Part 4, pp. 819–839 Statistics making an impact John Pullinger House of Commons Library, London, UK [The address of the President, delivered to The Royal Statistical Society on Wednesday, June 26th, 2013] Summary. Statistics provides a special kind of understanding that enables well-informed deci- sions. As citizens and consumers we are faced with an array of choices. Statistics can help us to choose well. Our statistical brains need to be nurtured: we can all learn and practise some simple rules of statistical thinking. To understand how statistics can play a bigger part in our lives today we can draw inspiration from the founders of the Royal Statistical Society. Although in today’s world the information landscape is confused, there is an opportunity for statistics that is there to be seized.This calls for us to celebrate the discipline of statistics, to show confidence in our profession, to use statistics in the public interest and to champion statistical education. The Royal Statistical Society has a vital role to play. Keywords: Chartered Statistician; Citizenship; Economic growth; Evidence; ‘getstats’; Justice; Open data; Public good; The state; Wise choices 1. Introduction Dictionaries trace the source of the word statistics from the Latin ‘status’, the state, to the Italian ‘statista’, one skilled in statecraft, and on to the German ‘Statistik’, the science dealing with data about the condition of a state or community. The Oxford English Dictionary brings ‘statistics’ into English in 1787. Florence Nightingale held that ‘the thoughts and purpose of the Deity are only to be discovered by the statistical study of natural phenomena:::the application of the results of such study [is] the religious duty of man’ (Pearson, 1924). -
From Singularities to Graphs
FROM SINGULARITIES TO GRAPHS PATRICK POPESCU-PAMPU Abstract. In this paper I analyze the problems which led to the introduction of graphs as tools for studying surface singularities. I explain how such graphs were initially only described using words, but that several questions made it necessary to draw them, leading to the elaboration of a special calculus with graphs. This is a non-technical paper intended to be readable both by mathematicians and philosophers or historians of mathematics. Contents 1. Introduction 1 2. What is the meaning of those graphs?3 3. What does it mean to resolve a surface singularity?4 4. Representations of surface singularities around 19008 5. Du Val's singularities, Coxeter's diagrams and the birth of dual graphs 10 6. Mumford's paper on the links of surface singularities 14 7. Waldhausen's graph manifolds and Neumann's calculus on graphs 17 8. Conclusion 19 References 20 1. Introduction Nowadays, graphs are common tools in singularity theory. They mainly serve to represent morpholog- ical aspects of surface singularities. Three examples of such graphs may be seen in Figures1,2,3. They are extracted from the papers [57], [61] and [14], respectively. Comparing those figures we see that the vertices are diversely depicted by small stars or by little circles, which are either full or empty. These drawing conventions are not important. What matters is that all vertices are decorated with numbers. We will explain their meaning later. My aim in this paper is to understand which kinds of problems forced mathematicians to associate graphs to surface singularities. -
Academic and Professional Publishing Catalogue
Services for Booksellers Make use of the wide range of services which Cambridge offers: NewNEW! Batch Academic and Professional http://www.batch.co.uk • Standard batch service is free of charge for Booksellers Publishing Catalogue • Make a single payment for all your suppliers, saving time, bank and postage charges • See invoices on the batch system before delivery arrives New books • No more copy invoices- view invoices online and print your own • Advanced notification that deliveries are on the way • Make claims online, saving telephone calls, faxes and e-mails Bookseller website http://www.booksellers.cambridge.org • Secure online ordering • Manage your account settings and dues / backorders • Price and Availability checks and data downloads • New Title Information and Bestseller lists • Contacts and further information • Coming soon: Hotline and E-mail alerting PubEasy http://www.PubEasy.com • Cambridge is now a PubEasy affiliate! • Online ordering across multiple publishers • Online real time price and availability checks • Dues management Datashop and Catalogshop http://datashop.cambridge.org • Free, online data delivery • Define your own reports and update them online • File Formats from simple text price and availability to Onix • Delivery by e-mail or FTP • Automatic updates daily, weekly, monthly, yearly • Download all Cambridge publicity material in PDF and other formats from Catalogshop www.cambridge.org/booksellers Cambridge University Press The Edinburgh Building www.cambridge.org/booksellers JANUARY–JUNE 2006 Cambridge CB2 -
Computability on the Real Numbers
4. Computability on the Real Numbers Real numbers are the basic objects in analysis. For most non-mathematicians a real number is an infinite decimal fraction, for example π = 3•14159 ... Mathematicians prefer to define the real numbers axiomatically as follows: · (R, +, , 0, 1,<) is, up to isomorphism, the only Archimedean ordered field satisfying the axiom of continuity [Die60]. The set of real numbers can also be constructed in various ways, for example by means of Dedekind cuts or by completion of the (metric space of) rational numbers. We will neglect all foundational problems and assume that the real numbers form a well-defined set R with all the properties which are proved in analysis. We will denote the R real line topology, that is, the set of all open subsets of ,byτR. In Sect. 4.1 we introduce several representations of the real numbers, three of which (and the equivalent ones) will survive as useful. We introduce a rep- n n resentation ρ of R by generalizing the definition of the main representation ρ of the set R of real numbers. In Sect. 4.2 we discuss the computable real numbers. Sect. 4.3 is devoted to computable real functions. We show that many well known functions are computable, and we show that partial sum- mation of sequences is computable and that limit operator on sequences of real numbers is computable, if a modulus of convergence is given. We also prove a computability theorem for power series. Convention 4.0.1. We still assume that Σ is a fixed finite alphabet con- taining all the symbols we will need.