CSHPM Bulletin, May 2013
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Egyptian Mathematics
Egyptian Mathematics Dr. Carmen Bruni David R. Cheriton School of Computer Science University of Waterloo November 1st, 2017 Three Part Series • Egyptian Mathematics • Diophantus and Alexandria • Tartaglia, Cardano and the Renaissance Age Egypt and Babylon Egypt circa 1500 BCE • Egyptian civilization established on the shores of the Nile about 5000 years ago • The yearly flood of the Nile brings sediments and nutriments that enriched the surrounding soils in the valley • The Nile becomes a method of transportation for both material and people and with the flood allowing for crops to grow, Egypt becomes a self-sufficient country (unlike other civilizations) Papyrus • Egyptians were the first known source of papyrus, a writing surface made from the pith (tissue in the stems) of a papyrus plant. • A lot of what we know from Egyptian mathematics originates from papyri. • We will be discussing content from two main papyri: the Rhind Mathematical Papyrus and the Moscow Mathematical Papyrus. Rhind Papyrus Written by the scribe Ahmes (also known as Ahmose or A'hmos`e). (Source: Wikimedia Commons) Moscow Papyrus (Source: Wikimedia Commons) Mathematics Arising Out of Necessity For Egyptians, mathematics was used as a tool to solve many of the problems they encountered. • Areas • Taxes • Calendars • Food • Volumes Areas Common units of measurement: • Cubit: length from the tip of the middle finger to the bottom of the elbow. Approximately 52cm. • Khet: 100 cubits • Setat/Arura/Aroura: A square khet. (About 2.7 square km or 2=3 of an acre). • Digit, palm, hand, fist: Other smaller units of measurement. This allowed them to give parcels of land to people and to keep track of these lands for taxes. -
Simply-Riemann-1588263529. Print
Simply Riemann Simply Riemann JEREMY GRAY SIMPLY CHARLY NEW YORK Copyright © 2020 by Jeremy Gray Cover Illustration by José Ramos Cover Design by Scarlett Rugers All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. For permission requests, write to the publisher at the address below. [email protected] ISBN: 978-1-943657-21-6 Brought to you by http://simplycharly.com Contents Praise for Simply Riemann vii Other Great Lives x Series Editor's Foreword xi Preface xii Introduction 1 1. Riemann's life and times 7 2. Geometry 41 3. Complex functions 64 4. Primes and the zeta function 87 5. Minimal surfaces 97 6. Real functions 108 7. And another thing . 124 8. Riemann's Legacy 126 References 143 Suggested Reading 150 About the Author 152 A Word from the Publisher 153 Praise for Simply Riemann “Jeremy Gray is one of the world’s leading historians of mathematics, and an accomplished author of popular science. In Simply Riemann he combines both talents to give us clear and accessible insights into the astonishing discoveries of Bernhard Riemann—a brilliant but enigmatic mathematician who laid the foundations for several major areas of today’s mathematics, and for Albert Einstein’s General Theory of Relativity.Readable, organized—and simple. Highly recommended.” —Ian Stewart, Emeritus Professor of Mathematics at Warwick University and author of Significant Figures “Very few mathematicians have exercised an influence on the later development of their science comparable to Riemann’s whose work reshaped whole fields and created new ones. -
Henri Poincaré. a Scientific Biography
Book Review Henri Poincaré. A Scientific Biography Reviewed by John Stillwell Henri Poincaré. A Scientific Biography Jeremy Gray Princeton University Press, 2013 248 pp., US$16.55 ISBN-13: 978-0691151007 I think I can say, without fear of contradiction, that it takes a brave mathematician to write a scientific biography of Poincaré. It is remarkable that Jeremy Gray has dared to do it and even more remarkable that he has succeeded so brilliantly. Poincaré was, with the possible exception of Hilbert, the deepest, most prolific, and most Figure 1. The modular tessellation. versatile mathematician of his time. His collected works fill eleven large volumes, and that does not include several volumes on mathematical physics and philosophy. Gray, who has written and edited and another several volumes of essays on science many books on nineteenth-century mathematics, and philosophy for the educated reader. For most particularly geometry and complex analysis, is the people it would be a life’s work simply to read ideal guide to this big picture. his output, let alone understand it well enough to write a clear and absorbing account. We are very Non-Euclidean Geometry fortunate to have this book. How did Poincaré find himself in non-Euclidean Poincaré is probably best known to modern geometry? Bolyai and Lobachevskii developed non- mathematicians for his contributions to non- Euclidean geometry in the 1820s, and Beltrami Euclidean geometry, his discovery of chaos (in put it on a firm foundation (using Riemann’s celestial mechanics), and his creation of algebraic differential geometry) in 1868. So non-Euclidean topology (in which the “Poincaré conjecture” was geometry was already old news, in some sense, the central unsolved problem for almost a century). -
September 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 439 September 2014 Society Meetings HIGHEST HONOUR FOR UK and Events MATHEMATICAN Professor Martin Hairer, FRS, 2014 University of Warwick, has become the ninth UK based Saturday mathematician to win the 6 September prestigious Fields Medal over Mathematics and the its 80 year history. The medal First World War recipients were announced Meeting, London on Wednesday 13 August in page 15 a ceremony at the four-year- ly International Congress for 1 Wednesday Mathematicians, which on this 24 September occasion was held in Seoul, South Korea. LMS Popular Lectures See page 4 for the full report. Birmingham page 12 Friday LMS ANNOUNCES SIMON TAVARÉ 14 November AS PRESIDENT-DESIGNATE LMS AGM © The University of Cambridge take over from the London current President, Professor Terry Wednesday Lyons, FRS, in 17 December November 2015. SW & South Wales Professor Tavaré is Meeting a versatile math- Plymouth ematician who has established a distinguished in- ternational career culminating in his current role as The London Mathematical Director of the Cancer Research Society is pleased to announce UK Cambridge Institute and Professor Simon Tavaré, Professor in DAMTP, where he NEWSLETTER FRS, FMedSci, University of brings his understanding of sto- ONLINE: Cambridge, as President-Des- chastic processes and expertise newsletter.lms.ac.uk ignate. Professor Tavaré will in the data science of DNA se- (Cont'd on page 3) LMS NEWSLETTER http://newsletter.lms.ac.uk Contents No. 439 September 2014 15 44 Awards Partial Differential Equations..........................37 Collingwood Memorial Prize..........................11 Valediction to Jeremy Gray..............................33 Calendar of Events.......................................50 News LMS Items European News.................................................16 HEA STEM Strategic Project........................... -
An Amazing Race
THE MATHEMATICAL THE COMMON ASSOCIATION OF VICTORIA DENOMINATOR 2/15 AN AMAZING RACE Students are totally absorbed in Lumen Christi’s mathematics challenge: The Amazing Race. INSIDE As children darted from stage to stage eagerly chatting about strategies, encouraging and praising each other’s mathematical eforts it was clear that this of all school days was one that Pattern and would be remembered. A day from which we could establish interest and engagement, a day structure from which we could raise both the profile of mathematics in our school community and in the 7 minds of the students that we teach. What had started as an ambition to host a competition Problem solving challenges had quickly permeated through the school and taken on a life of its own. Indeed, from little high ability students ideas big things grow or in this case from MAV Games Days whole school engagement grows. 8 Games: In early September 2014, our school, Lumen Christi Catholic Primary School, was fortunate just trivial pursuits? enough to host a Year 6 MAV Games Day. The day was a great success and really helped 11 students apply their knowledge of mathematics in a supportive team environment, where the Mathematica and the focus was less about getting the ‘right’ answer but more about enjoying everything that maths 14Australian Curriculum has to ofer. Continued on page 4 FROM THE PRESIDENT Associate Professor Marj Horne - Faculty of Education, Australian Catholic University THE COMMON SOAK UP MATHS DURING THE REVISED VCE MATHEMATICS DENOMINATOR SUMMER STUDY IMPLEMENTATION The MAV’s magazine SUPPORT WORKSHOPS published for its members. -
JPBM Communications Award
JPBM Communications Award The 2010 Communications Award of the Joint the Riemann hypothesis, entitled The Music of the Policy Board for Mathematics (JPBM) was presented Primes, is a best seller which has been translated at the Joint Mathematics Meetings in San Francisco, into ten languages. In his 2008 book, Symmetry: California, in January 2010. A Journey into the Patterns of Nature, du Sautoy The JPBM Communications Award is presented guides the reader through groups and symmetry, annually to reward and encourage journalists from Babylonia to Moonshine theory, while at the and other communicators who, on a same time giving an engaging glimpse into math- sustained basis, bring mathematical ematicians’ minds. His four-part television series, ideas and information to nonmathe- The Story of Maths, presents a fascinating look at matical audiences. JPBM represents the the development of mathematics from the design American Mathematical Society, the of the pyramids in Egypt to Perelman’s proof of American Statistical Association, the Poincaré’s conjecture. Whether it is talking about Mathematical Association of America, Beckham’s choice of number on a sports radio pro- and the Society for Industrial and Ap- gram, explaining the work of the Abel prize winner plied Mathematics. The award carries on Norwegian television, writing a weekly math a cash prize of US$1,000. column for the London Times, hosting a television Previous recipients of the JPBM game show based on math puzzles, or delivering Communications Award are: James the Royal Institution Christmas Lectures, Marcus Gleick (1988), Hugh Whitemore (1990), du Sautoy invariably seizes opportunities to make Ivars Peterson (1991), Joel Schneider mathematics more accessible and more appealing. -
Resource Pack for Level 3 Preparation Programmes for Entry to Numeracy Teacher Training
SkillsSkills for for LifeLife Support Programme Support Programme Resource pack for Level 3 preparation programmes for entry to numeracy teacher training The Skills for Life Support Programme CfBT Education Trust T: 0118 902 1920 is delivered on behalf of the Learning 60 Queens Road F: 0845 838 1207 and Skills Improvement Service by Reading E: [email protected] CfBT Education Trust and partners RG1 4BS W: www.excellencegateway.org.uk/sflsp Skills for Life Support Programme Acknowledgements This pack is the result of input and work from a range of individuals including the participants at the three events run by the Skills for Life Support Programme in 2010 and the members of CfBT, LLU+ at London South Bank University, LSN, NIACE and NRDC. The authors wish to thank these individuals for their input into this resource. Skills for Life Support Programme Contents Chapter 1 Introduction and rationale 3 1.1 Introduction and rationale 4 Chapter 2 Self assessment, number and geometry 8 2.1 Level 3 Self assessment carousel activity 9 2.2 Checklist of level 3 personal skills 49 2.3 Group summary checklist 53 2.4 Number systems and place value 59 2.5 Number systems 63 2.6 Egyptian multiplication 65 2.7 The commutative, associative and distributive laws 66 2.8 Approaches for dividing fractions 70 2.9 Pythagoras’ theorem 71 2.10 Discovering ratios in right angled triangles 72 2.11 Trigonometry 76 Chapter 3 Algebra and its applications 78 3.1 Kinaesthetic equations 79 3.2 Algebra carousel activity 82 3.3 I think of a number 105 3. -
2009 Whiteman Prize
2009 Whiteman Prize Jeremy J. Gray received the 2009 AMS Albert His publications Leon Whiteman Memorial Prize at the 115th An- have taken a great many nual Meeting of the AMS in Washington, DC, in forms and have cov- January 2009. ered very wide areas. He has edited and writ- Citation ten introductions to In awarding the Albert Leon Whiteman Prize to works of Janos Bolyai Jeremy J. Gray of the Open University and the and Julian Coolidge. University of Warwick, the American Mathematical He has produced, with Society recognizes the value of his many histori- John Fauvel, a compen- cal works, which have not only shed great light on dious book of readings the history of modern mathematics but also have in the history of math- ematics, originally for given an example of the ways in which historical the Open University scholarship can contribute to the understanding Jeremy J. Gray but since published by of mathematics and its philosophy. In addition, Macmillan. In addition Gray’s work as an editor, teacher, translator, and to his undergraduate textbook on the history of organizer of forums for historical work has helped geometry in the nineteenth century, Worlds Out invigorate the study of the history of modern of Nothing (2007), he has been co-editor of two mathematics internationally. volumes of scholarly contributions to the study of Gray’s book Ideas of Space (1979) deals with history of mathematics, Episodes in the History of geometrical studies through history, from the Modern Algebra (1800–1950) with Karen Parshall, Babylonians to Einstein. His fascination with non- and The Architecture of Modern Mathematics with Euclidean geometry is evident in much of his work, José Ferreirós. -
History of Mathematics in the Higher Education Curriculum
History of Mathematics in the Higher Education Curriculum Mathematical Sciences HE Curriculum Innovation Project Innovation Curriculum HE Sciences Mathematical Edited by Mark McCartney History of Mathematics in the Higher Education Curriculum Edited by Mark McCartney A report by the working group on History of Mathematics in the Higher Education Curriculum, May 2012. Supported by the Maths, Stats and OR Network, as part of the Mathematical Sciences Strand of the National HE STEM Programme, and the British Society for the History of Mathematics (BSHM). Working group members: Noel-Ann Bradshaw (University of Greenwich; BSHM Treasurer); Snezana Lawrence (Bath Spa University; BSHM Education Officer); Mark McCartney (University of Ulster; BSHM Publicity Officer); Tony Mann (University of Greenwich; BSHM Immediate Past President); Robin Wilson (Pembroke College, Oxford; BSHM President). History of Mathematics in the Higher Education Curriculum Contents Contents Introduction 5 Teaching the history of mathematics at the University of St Andrews 9 History in the undergraduate mathematics curriculum – a case study from Greenwich 13 Teaching History of Mathematics at King’s College London 15 History for learning Analysis 19 History of Mathematics in a College of Education Context 23 Teaching the history of mathematics at the Open University 27 Suggested Resources 31 History of Mathematics in the Higher Education Curriculum Introduction Introduction Mathematics is usually, and of course correctly, presented ‘ready-made’ to students, with techniques and applications presented systematically and in logical order. However, like any other academic subject, mathematics has a history which is rich in astonishing breakthroughs, false starts, misattributions, confusions and dead-ends. This history gives a narrative and human context which adds colour and context to the discipline. -
INTRODUCTION I.1 Opening Remarks I.1.1
© Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. INTRODUCTION I.1 Opening Remarks I.1.1. Mathematical Modernism In this book I argue that the period from 1890 to 1930 saw mathematics go through a modernist transformation. Here, modernism is defined as an autonomous body of ideas, having little or no outward reference, placing considerable emphasis on formal aspects of the work and maintaining a complicated—indeed, anxious—rather than a naı¨ve relationship with the day-to-day world, which is the de facto view of a coherent group of people, such as a professional or discipline-based group that has a high sense of the seriousness and value of what it is trying to achieve. This brisk definition is certainly compatible with what many creators of the ar tistic modernisms thought they were doing. Consider, for example, these remarks by Guillaume Apollinaire from his The Beginnings of Cubism, published in 1912, where, speaking of many young painters, he said: These painters, while they still look at nature, no longer imitate it, and carefully avoid any representation of natural scenes which they may have observed, and then re constructed from preliminary studies. Real resemblance no longer has any importance, since everything is sacrificed by the artist to truth, to the necessities of a higher na ture whose existence he assumes, but does not lay bare. The subject has little or no importance any more. Thus we are moving towards an entirely new art which will stand, with respect to painting as envisaged heretofore, as music stands to literature. -
Finnish Mathematical Society
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 32 DK2800 Lyngby, Denmark e-mail: [email protected] June 1999 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University Reymonta 4 30-059 Krakow, Poland EMS News .......................................................................................................... 2 e-mail: [email protected] KATHLEEN QUINN Editorial by EMS Vice-President, Luc Lemaire ............................................. 3 Open University [address as above] Note from the Editor ........................................................................................ 4 e-mail: [email protected] SPECIALIST EDITORS Introducing the Committee : part 2 ................................................................ 5 INTERVIEWS Steen Markvorsen [address as above] EMS Executive Committee Meeting ................................................................ 6 SOCIETIES Krzysztof Ciesielski [address as above] Ian Stewart: Making the Magical Maze ........................................................... 7 EDUCATION Vinicio Villani Interview with Helmut Neunzert (Kaiserslautern) ....................................... 10 Dipartimento di Matematica EMS Summer Schools : Call for proposals .................................................. -
Mathematics in India
TRADITIONSKnowledg & PRACTICES OF INDIA e Textbook for Class XI Module 7 Mathematics in India CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India TRADITIONSKnowledg & PRACTICESe OF INDIA Textbook for Class XI Module 7 Mathematics in India CENTRAL BOARD OF SECONDARY EDUCATION Shiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 India No part of this publication may be reproduced or stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical photocopying, recording or otherwise, without the prior permission of the Central Board of Secondary Education (CBSE). Preface India has a rich tradition of intellectual inquiry and a textual heritage that goes back to several hundreds of years. India was magnificently advanced in knowledge traditions and practices during the ancient and medieval times. The intellectual achievements of Indian thought are found across several fields of study in ancient Indian texts ranging from the Vedas and the Upanishads to a whole range of scriptural, philosophical, scientific, technical and artistic sources. As knowledge of India's traditions and practices has become restricted to a few erudite scholars who have worked in isolation, CBSE seeks to introduce a course in which an effort is made to make it common knowledge once again. Moreover, during its academic interactions and debates at key meetings with scholars and experts, it was decided that CBSE may introduce a course titled ‘Knowledge Traditions and Practices of India’ as a new Elective for classes XI - XII from the year 2012-13. It has been felt that there are many advantages of introducing such a course in our education system.