The Scottish Irish Mathematical Trail: People, Places, Practices
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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. -
From Counting to Quaternions -- the Agonies and Ecstasies of the Student Repeat Those of D'alembert and Hamilton
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Keck Graduate Institute Journal of Humanistic Mathematics Volume 1 | Issue 1 January 2011 From Counting to Quaternions -- The Agonies and Ecstasies of the Student Repeat Those of D'Alembert and Hamilton Reuben Hersh University of New Mexico Follow this and additional works at: https://scholarship.claremont.edu/jhm Recommended Citation Hersh, R. "From Counting to Quaternions -- The Agonies and Ecstasies of the Student Repeat Those of D'Alembert and Hamilton," Journal of Humanistic Mathematics, Volume 1 Issue 1 (January 2011), pages 65-93. DOI: 10.5642/jhummath.201101.06 . Available at: https://scholarship.claremont.edu/jhm/vol1/ iss1/6 ©2011 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. From Counting to Quaternions { The Agonies and Ecstasies of the Student Repeat Those of D'Alembert and Hamilton Reuben Hersh Department of Mathematics and Statistics, The University of New Mexico [email protected] Synopsis Young learners of mathematics share a common experience with the greatest creators of mathematics: \hitting a wall," meaning, first frustration, then strug- gle, and finally, enlightenment and elation. -
Chesterfield Wfa
CHESTERFIELD WFA Newsletter and Magazine issue 53 Co-Patrons -Sir Hew Strachan & Prof. Peter Simkins Welcome to Issue 53 - the May 2020 Newsletter and Magazine of President - Professor Gary Sheffield MA PhD FRHistS Chesterfield WFA. FRSA Vice-Presidents In view of the current public health Andre Colliot pandemic engulfing the globe, your Professor John Bourne BA PhD committee took the prudent FRHistS decision, before the introduction of The Burgomaster of Ypres Government legislation, to cancel the The Mayor of Albert April, May and June Meetings of the Lt-Col Graham Parker OBE Branch. Christopher Pugsley FRHistS Lord Richard Dannat GCB CBE MC Meetings and other activities will be DL restarted as and when the authorities Roger Lee PhD jssc deem it safe for us to do so. Dr Jack Sheldon In the interim this Newsletter / Magazine will Branch contacts continue Tony Bolton (Chairman) We would urge all our members to adopt all the anthony.bolton3@btinternet .com government`s regulations that way we can keep safe Mark Macartney (Deputy Chairman) and hopefully this crisis will be controlled, the virus [email protected] defeated, and a degree of normality restored. Jane Lovatt (Treasurer) Grant Cullen (Secretary) Stay safe everybody – we are all – in the meantime - [email protected] Facebook `Confined to Barracks` http://www.facebook.com/g roups/157662657604082/ Grant Cullen – Branch Secretary http://www.wfachesterfield.com/ Western Front Association Chesterfield Branch – Meetings 2020 Meetings start at 7.30pm and take place at the Labour Club, Unity House, Saltergate, Chesterfield S40 1NF January 7th . AGM and Members Night – presentations by Jane Ainsworth, Ed Fordham, Judith Reece, Edwin Astill and Alan Atkinson February 4th Graham Kemp `The Impact of the economic blockage of Germany AFTER the armistice and how it led to WW2` March 3rd Peter Hart Après la Guerre Post-war blues, demobilisation and a home fit for very few. -
Elizabeth F. Lewis Phd Thesis
PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS Elizabeth Faith Lewis A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6330 This item is protected by original copyright PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS ELIZABETH FAITH LEWIS This thesis is submitted in partial fulfilment for the degree of Ph.D. at the University of St Andrews. 2014 1. Candidate's declarations: I, Elizabeth Faith Lewis, hereby certify that this thesis, which is approximately 59,000 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2010 and as a candidate for the degree of Ph.D. in September 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2010 and 2014. Signature of candidate ...................................... Date .................... 2. Supervisor's declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Ph.D. -
Aspects of the Life and Work of Peter Guthrie Tait, FRSE1
Aspects of the Life and Work of Peter Guthrie Tait, FRSE1 An essay by Dr. Chris Pritchard, PhD, FIMA, McLaren High School, Callander, Scotland. Peter Guthrie Tait was born in Dalkeith in 1831. Upon the death of his father when he was just six his mother took him and his two sisters to live in Edinburgh with her brother. Here in his uncle’s house he was encouraged to dabble in photography and astronomy. We know that at the age of thirteen he was making nightly observations of the positions of Jupiter's satellites. By this time he had entered the Edinburgh Academy. Fleeming Jenkin2 was a member of the same class, James Clerk Maxwell in the class above. The friendship which developed between Maxwell and Tait during their school days would last throughout Maxwell’s relatively short life. If there was a competitive element to that friendship, encouraged by the school’s awarding of the mathematics prize to Tait in 1846 and to Maxwell the following year then it was certainly not apparent. They exchanged drafts of papers they were writing in their teens and we know that Tait retained his annotated copies of Maxwell’s early geometrical papers for many years. At sixteen both young men went up to their local university but after just one session Tait moved on to Peterhouse, Cambridge, from where he graduated as Senior Wrangler in 1852. When Maxwell eventually moved to Cambridge it was in Tait’s college that he initially enrolled despite being advised by Forbes3 to enter Trinity. Within a couple of years of graduation Tait had been offered a mathematics chair at Queen’s College, Belfast. -
An Idle, Unpopular Student
CHAPTER THREE An Idle, Unpopular Student SLEEPLESS he lay beneath a blanket in the cockpit of the yacht, under the wide and starry sky spread seamlessly from horizon to horizon. Nothing obtruded to betray the presence of 19th‐century man, beyond the small wooden island with sails carrying the 37‐year‐old Louis across the greatness of the Pacific towards the archipelago of the Paumotus. In the glow of the binnacle lamp he could see the silhouette of the helmsman, guiding them towards a tiny tuft of palms and a coastline so low it was almost submerged, like the islands in the milk of Louis’s porridge all those years ago. The Pacific night around him now was warm as milk . and all of a sudden I had a vision of ‐ Drummond Street. It came on me like a flash of lightning: I simply returned thither, and into the past. And when I remember all I hoped and feared as I pickled about Rutherford’s in the rain and the east wind; how I feared I should make a mere shipwreck, and yet timidly hoped not; how I feared I should never have a friend, far less a wife, and yet passionately hoped I might; how I hoped (if I did not take to drink) I should possibly write one little book, etc. etc. And then now ‐ what a change! I feel somehow as if I should like the incident set upon a brass plate at the corner of that dreary thoroughfare for all students to read, poor devils, when their hearts are down.1 THE officious clanging of the bell summoned students from the Pump, as they called Rutherford’s tavern in Drummond Street, a stone’s throw from the great Playfair arch that gave access to the quadrangle of the university. -
Medical News
769 emphatically so the thing you have never seen or heard of before. The thing you cannot get a pigeon- hole for is the finger point showing the way to Medical News. discovery." His own scientific hypotheses had a knack of turning out right-for example, his forecast of the life-history of Schistosoma hcematobium in the UNIVERSITY OF CAMBRIDGE : DIPLOMA IN PSYCHO- edition of his manual of Diseases in LOGICAL MEDICINE.-A short course of instruction for the fourth Tropical D.P.M. also his in 1903 of the two of examination will be held in Cambridge from July 12th 1907, suggestion species to August 17th. The course will include lectures and true in 1915. prac- schistosoma proved by Leiper Younger tical work on psychology, the anatomy and physiology of men who came under Manson’s influence remarked the nervous system, morbid psychology, mental diseases, always that in outlook and in knowledge he remained dreams, mental deficiency, &c. The fee for the full course is eager and enthusiastic to the end. His interest in his twelve guineas. Further particulars may be obtained from the work never flagged. Only 14 days before his death Secretary, D.P.M. Committee, Psychological Laboratory, he visited the London School of Tropical Medicine Cambridge. and critically examined some microscopical prepara- UNIVERSITY OF DUBLIN, SCHOOL OF PIIYSIC, tions, showing his usual perspicacity in picking out the TRINITY COLLEGE.-At examinations held recently the important points in each specimen and emphasising following candidates were successful :- the lessons they taught. Almost the last words he FINAL MEDICAL EXAMINATION. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
Quaternions: a History of Complex Noncommutative Rotation Groups in Theoretical Physics
QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS by Johannes C. Familton A thesis submitted in partial fulfillment of the requirements for the degree of Ph.D Columbia University 2015 Approved by ______________________________________________________________________ Chairperson of Supervisory Committee _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Program Authorized to Offer Degree ___________________________________________________________________ Date _______________________________________________________________________________ COLUMBIA UNIVERSITY QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS By Johannes C. Familton Chairperson of the Supervisory Committee: Dr. Bruce Vogeli and Dr Henry O. Pollak Department of Mathematics Education TABLE OF CONTENTS List of Figures......................................................................................................iv List of Tables .......................................................................................................vi Acknowledgements .......................................................................................... vii Chapter I: Introduction ......................................................................................... 1 A. Need for Study ........................................................................................ -
The Vortex Theory of Atoms — Pinnacle of Classical Physics —
The Vortex Theory of Atoms — pinnacle of classical physics — Thesis for the master’s degree in History and Philosophy of Science, by Steven van der Laan1 Supervisor: Dr. Jeroen van Dongen Institute for History and Foundations of Science Utrecht University December 2012 [email protected] i Abstract Investigation into a nineteenth century atomic theory that assumed atoms to be vortices in an ether. Originally an idea of Kelvin, the vortex atom theory enjoyed great popularity in England, roughly form 1870 to 1890. In this thesis, the popular- ity of the vortex atom theory is explained through four values in nineteenth century English physics. Furthermore, it will be argued that the (surprising) fact that the theory was virtually ignored by German scientists can be explained by a German critical attitude towards scientific theories. An attitude that was a reaction to the Romantic philosophy of Naturphilosophie. Acknowledgements Without the support of my supervisor, Jeroen van Dongen, this masterthesis would have been nothing of what it is in its current form. Not only did he teach me a lot about doing history of science and writing academic texts in general, he also broke my habit of cutting corners while doing research. I am furthermore always thankful for Sylvia and Arjo, for they made everything possible. ii Contents 1 Introduction to the vortex theory of atoms 1 1.1 Etherandatoms ................................... 1 1.2 ThevortextheoryofKelvin ............................ 2 1.3 Historyofthevortextheoryofatoms . ..... 3 1.4 Researchquestion.................................. 10 2 The Vortex Theory of Atoms 12 2.1 Propertiesofgasesandmolecules . ... 12 2.2 Requirementsmadetoatoms . .. .. 13 2.3 Vortextheoryofgases .............................. .. 16 2.4 Vortextheoryforchemistry . -
The Culture of Quaternions the Phoenix Bird of Mathematics
The Culture of Quaternions The Phoenix Bird of Mathematics Herb Klitzner June 1, 2015 Presentation to: New York Academy of Sciences, Lyceum Society © 2015, Herb Klitzner http://quaternions.klitzner.org The Phoenix Bird CONTENTS 1. INTRODUCTION - new uses after a long period of neglect 2. HISTORY AND CONTROVERSIES – perceptions of quaternions 3. APPLICATIONS – advantages; how quaternions operate 4. MATH – nature of quaternions 5. MUSIC COGNITION AND 4D – potential for new uses of quaternions Introduction The Word “Quaternion” • The English word quaternion comes from a Latin word quaterni which means grouping things “four by four.” • A passage in the New Testament (Acts 12:4) refers to a Roman Army detachment of four quaternions – 16 soldiers divided into groups of four, who take turns guarding Peter after his arrest by Herod. So a quaternion was a squad of four soldiers. • In poetry, a quaternion is a poem using a poetry style in which the theme is divided into four parts. Each part explores the complementary natures of the theme or subject. [Adapted from Wikipedia] • In mathematics, quaternions are generated from four fundamental elements (1, i, j, k). • Each of these four fundamental elements is associated with a unique dimension. So math quaternions are, by nature, a 4D system. Introduction The Arc of Dazzling Success and Near-Total Obscurity Quaternions were created in 1843 by William Hamilton. Today, few contemporary scientists are familiar with, or have even heard the word, quaternion. (Mathematical physics is an exception.) And yet -- • During the 19th Century quaternions became very popular in Great Britain and in many universities in the U.S. -
Regelation: Why Does Ice Melt Under Pressure?
Regelation: why does ice melt under pressure? Phase-boundary reversible dispersivity and hydrogen-bond extraordinary recoverability Chang Q Sun [email protected] Nanyang Technological University, Singapore Unlike other unusual materials whose bonds contract under compression, the O:H nonbond undergoes contraction and the H-O bond elongation towards O:H and H-O length symmetry in water and ice. The energy drop of the H-O bond dictates the melting point Tm depression of ice. Once the pressure is relieved, the O:H-O bond fully recovers its initial state, resulting in Regelation. Ref: [1] Anomaly 2: Floating ice, http://arxiv.org/abs/1501.04171 [2] Anomaly 1: Mpemba effect, http://arxiv.org/abs/1501.00765 [3] Hydrogen-bond relaxation dynamics: resolving mysteries of water ice. Coord. Chem. Rev., 2015. 285: 109-165. 1 Anomaly: Ice Regelation Observations in Figure 1 revealed the following: 1) Ice melts under pressure and freezes again when the pressure is relieved [1-4]Error! Bookmark not defined.. An ice block remains a solid after a weighted wire cutting it through [5]. 2) Ice melts at a limit temperature of -22C under 210 MPa pressure but a -95 MPa pressure (tension) raises the melting point up to +6.5C [6, 7]. a b 280 270 (K) Quasi-solid Liquid m T 260 V pdvH TP() V C 110 TPCH()00 E 250 -100 -50 0 50 100 150 200 P(MPa) Figure 1 Regelation of ice. (a) A weighted wire cuts a block of ice through without severing it [5]. (b) Theoretical formulation [8] of the pressure dependence of the ice melting temperature Tm(P) or the phase boundary between the liquid and quasi-solid [6, 7] indicates that the H-O bond energy relaxation dictates the Tm(P).