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The History and Development of Numerical Analysis in Scotland: a Personal Perspective∗
The history and development of numerical analysis in Scotland: a personal perspective∗ G. A. Watson, Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland. Abstract An account is given of the history and development of numerical analysis in Scotland. This covers, in particular, activity in Edinburgh in the first half of the 20th century, the collaboration between Edinburgh and St Andrews in the 1960s, and the role played by Dundee from the 1970s. I will give some reminiscences from my own time at both Edinburgh and Dundee. 1 Introduction To provide a historical account of numerical analysis (or of anything else), it is necessary to decide where to begin. If numerical analysis is defined to be the study of algorithms for the problems of continuous mathematics [16], then of course it has a very long history (see, for example, [6], [13]). But \modern" numerical analysis is inextricably linked with computing machines. It is usually associated with programmable electronic computers, and is often said to have its origins in the 1947 paper by von Neumann and Goldstine [10]. The name apparently was first used around that time, and was given formal recognition in the setting up of the Institute for Numerical Analysis, located on the campus of the University of California at Los Angeles [3]. This was a section of the National Applied Mathematics Laboratories of the National Bureau of Standards, headed by J. H. Curtiss, who is often given credit for the name. Others consider modern numerical analysis to go back further than this; for example Todd [15] suggests it begins around 1936, and cites papers by Comrie and Turing. -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
Vectors and Beyond: Geometric Algebra and Its Philosophical
dialectica Vol. 63, N° 4 (2010), pp. 381–395 DOI: 10.1111/j.1746-8361.2009.01214.x Vectors and Beyond: Geometric Algebra and its Philosophical Significancedltc_1214 381..396 Peter Simons† In mathematics, like in everything else, it is the Darwinian struggle for life of ideas that leads to the survival of the concepts which we actually use, often believed to have come to us fully armed with goodness from some mysterious Platonic repository of truths. Simon Altmann 1. Introduction The purpose of this paper is to draw the attention of philosophers and others interested in the applicability of mathematics to a quiet revolution that is taking place around the theory of vectors and their application. It is not that new math- ematics is being invented – on the contrary, the basic concepts are over a century old – but rather that this old theory, having languished for many decades as a quaint backwater, is being rediscovered and properly applied for the first time. The philosophical importance of this quiet revolution is not that new applications for old mathematics are being found. That presumably happens much of the time. Rather it is that this new range of applications affords us a novel insight into the reasons why vectors and their mathematical kin find application at all in the real world. Indirectly, it tells us something general but interesting about the nature of the spatiotemporal world we all inhabit, and that is of philosophical significance. Quite what this significance amounts to is not yet clear. I should stress that nothing here is original: the history is quite accessible from several sources, and the mathematics is commonplace to those who know it. -
The Royal Society Medals and Awards
The Royal Society Medals and Awards Table of contents Overview and timeline – Page 1 Eligibility – Page 2 Medals open for nominations – Page 8 Nomination process – Page 9 Guidance notes for submitting nominations – Page 10 Enquiries – Page 20 Overview The Royal Society has a broad range of medals including the Premier Awards, subject specific awards and medals celebrating the communication and promotion of science. All of these are awarded to recognise and celebrate excellence in science. The following document provides guidance on the timeline and eligibility criteria for the awards, the nomination process and our online nomination system Flexi-Grant. Timeline • Call for nominations opens 30 November 2020 • Call for nominations closes on 15 February 2021 • Royal Society contacts suggested referees from February to March if required. • Premier Awards, Physical and Biological Committees shortlist and seek independent referees from March to May • All other Committees score and recommend winners to the Premier Awards Committee by April • Premier Awards, Physical and Biological Committees score shortlisted nominations, review recommended winners from other Committees and recommend final winners of all awards by June • Council reviews and approves winners from Committees in July • Winners announced by August Eligibility Full details of eligibility can be found in the table. Nominees cannot be members of the Royal Society Council, Premier Awards Committee, or selection Committees overseeing the medal in question. More information about the selection committees for individual medals can be found in the table below. If the award is externally funded, nominees cannot be employed by the organisation funding the medal. Self-nominations are not accepted. -
Recent Books on Vector Analysis. 463
1921.] RECENT BOOKS ON VECTOR ANALYSIS. 463 RECENT BOOKS ON VECTOR ANALYSIS. Einführung in die Vehtoranalysis, mit Anwendungen auf die mathematische Physik. By R. Gans. 4th edition. Leip zig and Berlin, Teubner, 1921. 118 pp. Elements of Vector Algebra. By L. Silberstein. New York, Longmans, Green, and Company, 1919. 42 pp. Vehtor analysis. By C. Runge. Vol. I. Die Vektoranalysis des dreidimensionalen Raumes. Leipzig, Hirzel, 1919. viii + 195 pp. Précis de Calcul géométrique. By R. Leveugle. Preface by H. Fehr. Paris, Gauthier-Villars, 1920. lvi + 400 pp. The first of these books is for the most part a reprint of the third edition, which has been reviewed in this BULLETIN (vol. 21 (1915), p. 360). Some small condensation of results has been accomplished by making deductions by purely vector methods. The author still clings to the rather common idea that a vector is a certain triple on a certain set of coordinate axes, so that his development is rather that of a shorthand than of a study of expressions which are not dependent upon axes. The second book is a quite brief exposition of the bare fundamentals of vector algebra, the notation being that of Heaviside, which Silberstein has used before. It is designed primarily to satisfy the needs of those studying geometric optics. However the author goes so far as to mention a linear vector operator and the notion of dyad. The exposition is very simple and could be followed by high school students who had had trigonometry. The third of the books mentioned is an elementary exposition of vectors from the standpoint of Grassmann. -
William Robertson Smith, Solomon Schechter and Contemporary Judaism
https://doi.org/10.14324/111.444.jhs.2016v48.026 William Robertson Smith, Solomon Schechter and contemporary Judaism bernhard maier University of Tübingen, Germany* During Solomon Schechter’s first years in the University of Cambridge, one of his most illustrious colleagues was the Scottish Old Testament scholar and Arabist William Robertson Smith (1846–1894), who is today considered to be among the founding fathers of comparative religious studies. Smith was the son of a minister of the strongly evangelical Free Church of Scotland, which had constituted itself in 1843 as a rival to the state-controlled established Church of Scotland. Appointed Professor of Old Testament Exegesis in the Free Church College Aberdeen at the early age of twenty-four, Smith soon came into conflict with the conservative theologians of his church on account of his critical views. After a prolonged heresy trial, he was finally deprived of his Aberdeen chair in 1881. In 1883 he moved to Cambridge, where he served, successively, as Lord Almoner’s Reader in Arabic, University Librarian, and Thomas Adams’s Professor of Arabic. Discussing Schechter’s relations with Robertson Smith, one has to bear in mind that direct contact between Schechter and Smith was confined to a relatively short period of less than five years (1890–94), during which Smith was frequently ill and consequently not resident in Cambridge at all.1 Furthermore, there is not much written evidence, so that several hints and clues that have come down to us are difficult to interpret, our understanding being sometimes based on inference and reasoning by analogy rather than on any certain knowledge. -
Former Fellows Biographical Index Part
Former Fellows of The Royal Society of Edinburgh 1783 – 2002 Biographical Index Part Two ISBN 0 902198 84 X Published July 2006 © The Royal Society of Edinburgh 22-26 George Street, Edinburgh, EH2 2PQ BIOGRAPHICAL INDEX OF FORMER FELLOWS OF THE ROYAL SOCIETY OF EDINBURGH 1783 – 2002 PART II K-Z C D Waterston and A Macmillan Shearer This is a print-out of the biographical index of over 4000 former Fellows of the Royal Society of Edinburgh as held on the Society’s computer system in October 2005. It lists former Fellows from the foundation of the Society in 1783 to October 2002. Most are deceased Fellows up to and including the list given in the RSE Directory 2003 (Session 2002-3) but some former Fellows who left the Society by resignation or were removed from the roll are still living. HISTORY OF THE PROJECT Information on the Fellowship has been kept by the Society in many ways – unpublished sources include Council and Committee Minutes, Card Indices, and correspondence; published sources such as Transactions, Proceedings, Year Books, Billets, Candidates Lists, etc. All have been examined by the compilers, who have found the Minutes, particularly Committee Minutes, to be of variable quality, and it is to be regretted that the Society’s holdings of published billets and candidates lists are incomplete. The late Professor Neil Campbell prepared from these sources a loose-leaf list of some 1500 Ordinary Fellows elected during the Society’s first hundred years. He listed name and forenames, title where applicable and national honours, profession or discipline, position held, some information on membership of the other societies, dates of birth, election to the Society and death or resignation from the Society and reference to a printed biography. -
Meeting Reports
AUGUST 2014 MEETING Speaker: Andrew Conacher Topic: Sir Humphry Davy – The Davy Lamp Andrew’s talk on Sir Humphry Davy was most engaging and enjoyable. He firstly spoke on Sir Humphry’s background and life and then focused on the Davy Lamp, its context and importance. Andrew indicated that he has an ancestral family connection to Sir Humphry. The following is a brief extract from Andrew’s paper. Sir Humphry was born on 17 December 1778 in Penzance, Cornwall, England and died 29 May 1829 in Geneva, Switzerland aged 50 years. A statue stands in Penzance with him holding his safety lamp. Andrew Conacher holds up miner’s safety lamps. He was both a chemist and inventor Picture: KIRK GILMOUR, Wollongong Advertiser 6 August 2014 and was also a poet and painter. He enthusiastically turned to science and later became a professor at the Royal Institution and flame (acting as a flame arrestor) presented a series of lectures which were later published. thus preventing the methane gas burning inside the lamp to pass out He worked with a number of scientists of the day (for into the atmosphere. The lamp also example, Sir Joseph Banks, who interviewed Davy for his provided a test for the presence of role at the Royal Institution and Michael Faraday who was gases. If flammable gases were a co-worker with him) and was a popular public figure. present the flame of the lamp He made a number of scientific discoveries (for example, burnt higher and with a blue tinge. electrolysis, sodium, potassium, barium) and was knighted The lamp saved lives and helped in1812 and awarded a baronetcy in 1819. -
A Beautiful Approach: Transformational Optics
A beautiful approach: “Transformational optics” [ several precursors, but generalized & popularized by Ward & Pendry (1996) ] warp a ray of light …by warping space(?) [ figure: J. Pendry ] Euclidean x coordinates transformed x'(x) coordinates amazing Solutions of ordinary Euclidean Maxwell equations in x' fact: = transformed solutions from x if x' uses transformed materials ε' and μ' Maxwell’s Equations constants: ε0, μ0 = vacuum permittivity/permeability = 1 –1/2 c = vacuum speed of light = (ε0 μ0 ) = 1 ! " B = 0 Gauss: constitutive ! " D = # relations: James Clerk Maxwell #D E = D – P 1864 Ampere: ! " H = + J #t H = B – M $B Faraday: ! " E = # $t electromagnetic fields: sources: J = current density E = electric field ρ = charge density D = displacement field H = magnetic field / induction material response to fields: B = magnetic field / flux density P = polarization density M = magnetization density Constitutive relations for macroscopic linear materials P = χe E ⇒ D = (1+χe) E = ε E M = χm H B = (1+χm) H = μ H where ε = 1+χe = electric permittivity or dielectric constant µ = 1+χm = magnetic permeability εµ = (refractive index)2 Transformation-mimicking materials [ Ward & Pendry (1996) ] E(x), H(x) J–TE(x(x')), J–TH(x(x')) [ figure: J. Pendry ] Euclidean x coordinates transformed x'(x) coordinates J"JT JµJT ε(x), μ(x) " ! = , µ ! = (linear materials) det J det J J = Jacobian (Jij = ∂xi’/∂xj) (isotropic, nonmagnetic [μ=1], homogeneous materials ⇒ anisotropic, magnetic, inhomogeneous materials) an elementary derivation [ Kottke (2008) ] consider× -
Preview 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press Is a Department of the University of Oxford
JAMES CLERK MAXWELL Perspectives on his Life and Work Material Edited by raymond flood mark mccartney and andrew whitaker Copyrighted - Preview 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on anyMaterial acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
Acta Technica Jaurinensis
Acta Technica Jaurinensis Győr, Transactions on Engineering Vol. 3, No. 1 Acta Technica Jaurinensis Vol. 3. No. 1. 2010 The Historical Development of Thermodynamics D. Bozsaky “Széchenyi István” University Department of Architecture and Building Construction, H-9026 Győr, Egyetem tér 1. Phone: +36(96)-503-454, fax: +36(96)-613-595 e-mail: [email protected] Abstract: Thermodynamics as a wide branch of physics had a long historical development from the ancient times to the 20th century. The invention of the thermometer was the first important step that made possible to formulate the first precise speculations on heat. There were no exact theories about the nature of heat for a long time and even the majority of the scientific world in the 18th and the early 19th century viewed heat as a substance and the representatives of the Kinetic Theory were rejected and stayed in the background. The Caloric Theory successfully explained plenty of natural phenomena like gas laws and heat transfer and it was impossible to refute it until the 1850s when the Principle of Conservation of Energy was introduced (Mayer, Joule, Helmholtz). The Second Law of Thermodynamics was discovered soon after that explanation of the tendency of thermodynamic processes and the heat loss of useful heat. The Kinetic Theory of Gases motivated the scientists to introduce the concept of entropy that was a basis to formulate the laws of thermodynamics in a perfect mathematical form and founded a new branch of physics called statistical thermodynamics. The Third Law of Thermodynamics was discovered in the beginning of the 20th century after introducing the concept of thermodynamic potentials and the absolute temperature scale. -
Maxwell Discovers That Light Is Electromagnetic Waves in 1862
MAXWELL DISCOVERS LIGHT IS ELECTROMAGNETIC WAVES James Clerk Maxwell was a Scottish scientist. He worked in the mid-nineteenth century in Scotland and England. At that time, electricity and magnetism had been extensively studied, and it was known since 1831 that electric current produces magnetism. Maxwell added the idea that changing magnetism could produce electricity. The term that Maxwell added to the known equations (called Ampere's law) for magnetism allowed Maxwell to see that there were wave-like solutions, that is, solutions that look like a sine wave (as a function of time). The numbers in Maxwell's equations all came from laboratory experiments on electric- ity and magnetism. There was nothing in those equations about light, and radio waves were completely unknown at the time, so the existence of electromagnetic waves was also completely unknown. But mathematics showed that Maxwell's equations had wave-like solutions. What did that mean? Maxwell proceeded to calculate the speed of those waves, which of course depended on the numbers that came from lab experiments with electricity and magnetism (not with light!). He got the answer 310,740,000 meters per second. Maxwell must have had an \aha moment" when he recognized that number. He did recognize that number: it was the speed of light! He was lecturing at King's College, London, in 1862, and there he presented his result that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, and commented: \We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." 1 2 MAXWELL DISCOVERS LIGHT IS ELECTROMAGNETIC WAVES He published his work in his 1864 paper, A dynamical theory of the electromagnetic field.