DOCSLIB.ORG

Reshaping College Mathematics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Reshaping College Mathematics Reshaping College Mathematics Reshaping College Mathematics A project of the Committee on the Undergraduate Program in Mathematics Edited by Lynn Arthur Steen MAA Notes Series The MAA Notes Series, started in 1982, addresses a broad range of topics and themes of interest to all who are involved with undergraduate mathematics. The volumes in this series are readable, informative, and useful, and help the mathematical community keep up with developments of importance to mathematics. Editorial Board Warren Page, Chair Donald W. Bushaw Richard K. Guy Paul J. Campbell Frederick Hoffman Jane M. Day David A. Smith 1. Problem Solving in the Mathematics Curriculum, Committee on the Undergraduate Teaching of Mathematics, Alan Schoenfeld, Editor. 2. Recommendations on the Mathematical Preparation of Teachers, CUPM Panel on Teacher Training. 3. Undergraduate Mathematics Education in the People’s Republic of China, Lynn A. Steen, Editor. 4. Notes on Primality Testing and Factoring, by Carl Pomerance. 5. American Perspectives on the Fifth international Congress in Mathematical Education, Warren Page, Editor: 6. Toward a Lean and Lively Calculus, Ronald Douglas, Editor: 7. Undergraduate Programs in the Mathematical and Computer Sciences: 1985-86, D. J. Albers, R. D.Anderson, D. 0. Loftsgaarden, Editors. 8. Calculus for a New Century, Lynn A. Steen, Editor. 9. Computers and Mathematics: The Use of Computers in Undergraduate instruction, D. A. Smith, G. J. Porter, L. C. Leinbach, R. H. Wenger, Editors. 10. Guidelines for the Continuing Mathematical Education of Teachers, Committee on the Mathematical Education of Teachers. 1 1. Keys to Improved instruction by Teaching Assistants and Part-Time Instructors, Committee on Teaching Assistants and Part-Time Instructors, Bettye Anne Case, Editor. 12. The Use of Calculators in the Standardized Testing of Mathematics, John Kenel/% Editor: 13. Reshaping College Mathematics, Lynn A. Steen, Editor: First Printing 0 1989 by the Mathematical Association of America Library of Congress Number 89-061338 ISBN-0-88385-062-1 Printed in the United States of America Reshaping College Mathematics .. PREFACE............................................................................................... ..vu MATHEMATICALSCIENCES .............................................................................. 1 Curriculum Background 0 Current Issues 0 Curricular Principles 0 Building Mathematical Maturity 0 Core Requirements 0 Teaching Mathematical Reasoning 0 How Much Theory? Sample Majors 0 Mathematical Sciences Minor 0 Examples of Successful Programs 0 IDe- partmental Self-study 0 Discrete Methods 0 Applied Algebra 0 Numerical Analysis. CALCULUS............................................................................................... 19 Rationale 0 First Semester Calculus 0 Second Semester Calculus 0 Intermediate Mathematics Courses 0 Applied Linear Algebra 0 Multivariable Calculus 0 Differential Equations. COREMATHEMATICS ................................................................................... 25 New Roles for Core Mathematics 0 Four Questions 0 Abstract Algebra 0 Analysis. COMPUTERSCIENCE ................................................................................... 29 A Growing Discipline 0 Introductory Courses 0 Intermediate Courses 0 Concentrations and Minors 0 Faculty Training 0 Computer Facilities 0 ACM Curriculum 78. MODELINGAND OPERATIONS RESEARCH.......................................................... .41 Experience in Applications 0 Mathematical Modeling 0 An Undergraduate Modeling Course 0 Operations Research 0 Introductory Operations Research 0 Elementary Modeling 0 Intro- ductory Stochastic Processes 0 References. STATISTICS.............................................................................................. .55 Introductory Course 0 The Place of Probability 0 Alternative Arrangements 0 Instructor Preparation 0 Course Outline 0 Probability and Statistical Theory 0 Applied Statistics 0 Probability and Stochastic Processes 0 Preparation for Graduate Study. DISCRETEMATHEMATICS ............................................................................. 61 Introduction and History 0 Summary of Recommendations 0 General Discussion Needs of Computer Science 0 Syllabus 0 Preparation for Discrete Mathematics 0 Two Year Colleges and High Schools 0 The Impact on Calculus 0 Course Objectives 0 Sample Problems 0 Textbooks 0 References. CALCULUS TRANSITION:FROM HIGH SCHOOL TO COLLEGE ................................... 85 Problem Areas 0 Accelerated Programs 0 High School Calculus 0 Successful Calculus Courses 0 Unsuccessful Calculus Courses 0 College Programs 0 Recommendations 0 References. CURRICULUM FOR GRADES11-13 .................................................................... 91 Issues of Apparent Consensus 0 Recommendation 0 Issues Requiring Further Study 0 Gifted Students 0 Greater Integration 0 Statistics & Discrete Mathematics 0 Twelfth Grade Math- ematics 0 Calculus Review 0 Deductive Reasoning 0 Calculators 0 Alternatives to Remedial Courses 0 Use of Standardized Test Scores 0 Geometry 0 Collaborative Efforts. MINIMALMATHEMATICAL COMPETENCIES FOR COLLEGE GRADUATES..................... .lo3 Recommendations 0 Mathematics for Coping with Life 0 Mathematics Appreciation. MATHEMATICSAPPRECIATION COURSES .......................................................... 109 Philosophy 0 Things to Stress 0 Things to Avoid 0 Course Organization 0 Examples of Topics 0 Two-Year Colleges 0 Films 0 Classroom Aids 0 Survey Monographs 0 Collections of Essays 0 Bibliography & References. Preface Calls for Change Background CUPM was established in 1953 to “modernize and For over 35 years the Committee on the Undergrad- upgrade” the mathematics curriculum arnd to halt what uate Program in Mathematics (CUPM) has helped pro- was even then decried as “the pessimislk retreat to re- vide coherence to the mathematics major by monitor- medial mathematics.” At that time total enrollment in ing practice, advocating goals, and suggesting model college mathematics courses in the United States was curricula. This volume brings together various curricu- approximately 800,000; each year about 4,000 students lum reports issued during the decade of the 1980’s. received a bachelor’s degree in mathematics, and about It provides a convenient reference for the mathe- 200 received Ph.D. degrees. matical community as it begins to reshape college In its early years CUPM concentrated on proposals mathematics in response to mounting demands for to strengthen undergraduate preparation for graduate change. study in mathematics. Spurred on by Sputnik and as- Many of the calls for reform have been expressed in sisted by significant support from the National Science published reports, for example: Foundation, the mathematical community in the United 1989 Curriculum and Evaluation Standards for School States matured rapidly from a servant discipline inden- Mathematics, published by the National Council tured to science and engineering to vigorous world lead- of Teachers of Mathematics. ership. By 1970 U.S. mathematics dlepartments pro- duced 24,000 bachelor’s and 1,200 doctoral degrees-a 1989 Everybody Counts: A Report to the Nation on the Future of Mathematics Education, published six-fold increase in less than twenty years. by the National Research Council. Then the bubble burst. As student, interest shifted from personal goals to financial security, and as com- 1988 Changing America: The New Face of Science puter science began to attract increasing numbers of and Engineering, published by the White House students who in earlier years might have studied math- Task Force on Women, Minorities, and the ematics, the numbers of mathematics bachelor’s degrees Handicapped in Science and Technology. dropped by over 50% in ten years, as did the number 1987 The Underachieving Curriculum, published by of U.S. students who went on to a Ph.D. in mathemat- the Second International Mathematics Study. ics. In 1981, at the nadir of B.A. productivity, CUPM published a comprehensive report entitled Recommen- 1986 Towards a Lean and Lively Calculus, published dations for a General Mathematical Sciences Program. by the Mathematical Association of America. Significantly, this report advocated not a strengthened 1985 Integrity in the College Curriculum: A Report program in traditional (pre-doctoral) mathematics, but to the Academic Community, published by the a broad, innovative program in mathematical sciences. Association of American Colleges. Although CUPM did not create the movement to- wards mathematical sciences, its 1981 report helped le- 1984 Renewing US. Mathematics: Critical Resource gitimize a process that was well under way. As a con- for the Future, published by the National Re- sequence, mathematics programs in 1J.S. colleges and search Council. universities are now dominated by variations on two Other pressures for change are expressed in articles paradigms that reflect the two phases of CUPM activ- diffused throughout the literature on a wide range of is- ity. The first, a fading image of the CUPM recommen- sues, from remediation (too much) through Ph.D. pro- dations of the 1960’~~focuses on core mathematics as duction (too little), from students (greater diversity) to preparation for graduate study in mathematics. The mathematics (greater applicability), and from technol- second, reflecting the broader objectives of CUPM’s ogy (under-utilized) to pedagogy (too passive). What 1981 mathematical sciences report, focuses on
Load more

Recommended publications
  • Using Concrete Scales: a Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, Guia Gali
    Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, Guia Gali To cite this version: Fanny Chevalier, Romain Vuillemot, Guia Gali. Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures. IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers, 2013, 19 (12), pp.2426-2435. 10.1109/TVCG.2013.210. hal-00851733v1 HAL Id: hal-00851733 https://hal.inria.fr/hal-00851733v1 Submitted on 8 Jan 2014 (v1), last revised 8 Jan 2014 (v2) 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. Using Concrete Scales: A Practical Framework for Effective Visual Depiction of Complex Measures Fanny Chevalier, Romain Vuillemot, and Guia Gali a b c Fig. 1. Illustrates popular representations of complex measures: (a) US Debt (Oto Godfrey, Demonocracy.info, 2011) explains the gravity of a 115 trillion dollar debt by progressively stacking 100 dollar bills next to familiar objects like an average-sized human, sports fields, or iconic New York city buildings [15] (b) Sugar stacks (adapted from SugarStacks.com) compares caloric counts contained in various foods and drinks using sugar cubes [32] and (c) How much water is on Earth? (Jack Cook, Woods Hole Oceanographic Institution and Howard Perlman, USGS, 2010) shows the volume of oceans and rivers as spheres whose sizes can be compared to that of Earth [38].
    [Show full text]
  • Of the American Mathematical Society August 2017 Volume 64, Number 7
    ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves
    [Show full text]
  • The Warped Ways of Cosmic Light
    BIOLOGIE & MEDIZIN_Infektionsbiologie “Around that area there are indeed numerous small nebulous patches so close together that, upon seeing the region, one is positively startled by the strange appearance of this ‘nebula cluster’.” This was the sentiment expressed by Heidelberg-based astronomer Max Wolf in 1901 about the galaxy cluster in the constellation Coma Berenices. The cluster Abell 2218 presents a similar appearance to the viewer today on this image from the Hubble Space Telescope. The “strange appearance” – the many blue and orange arcs – owes, in this case, to the effect of a gravitational lens. PHYSICS & ASTRONOMY_Gravitational Lenses The Warped Ways of Cosmic Light Albert Einstein predicted them, modern giant telescopes detected them – and Klaus Dolag simulates them on a computer: gravitational lenses. The academic staff member at the Max Planck Institute for Astrophysics in Garching and at the University Observatory Munich uses this physical phenomenon to such ends as weighing galaxy clusters and probing that ominous substance known as dark matter. TEXT HELMUT HORNUNG he sky over Principe was a total eclipse of the Sun. The test was More recent analyses of Eddington’s cloudy and the mood in the simple: if a massive object bends space, findings show that the values measured camp on the coconut plan- then the Sun must also cause the pass- at that time did, indeed, correspond to tation had hit rock bottom. ing light from stars to deviate from its the prediction, but that they are appar- Having set out from Eng- straight course. In other words, the ently the result of an instrument error T land, the men had been traveling for points of light in the immediate vicin- of, as it so happens, the very same mag- weeks to reach the volcanic island in ity of the black Sun should be shifted nitude.
    [Show full text]
  • List of Mathematics, Statistics E Books
    Copyright Sr No Book Title Author Year English Package Name OpenURL An Introduction to the Mathematical 1 Theory of the Navier-Stokes Equations Giovanni Galdi 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-09620-9 2 The Proof is in the Pudding Steven G. Krantz 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-48744-1 Inequalities: Theory of Majorization and 3 Its Applications Albert W. Marshall, Ingram Olkin, Barry C. Arnold 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-68276-1 Functional Analysis, Sobolev Spaces and 4 Partial Differential Equations Haim Brezis 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-70914-7 Neutral and Indifference Portfolio Pricing, 5 Hedging and Investing Srdjan Stojanovic 2012 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-71418-9 6 The Real Numbers and Real Analysis Ethan D. Bloch 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-72177-4 7 An Introduction to Hopf Algebras Robert G. Underwood 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-72766-0 8 It's a Nonlinear World Richard H. Enns 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-75340-9 The Colorado Mathematical Olympiad and 9 Further Explorations Alexander Soifer 2011 Mathematics and Statistics http://link.springer.com/openurl?genre=book&isbn=978-0-387-75472-7
    [Show full text]
  • Remembering Sofia Kovalevskaya
    Remembering Sofia Kovalevskaya Michèle Audin Remembering Sofia Kovalevskaya Michèle Audin Institut de recherche mathématique avancée Université de Strasbourg et CNRS 7 rue René-Descartes 67084 Strasbourg Cedex France [email protected] Whilst we have made considerable efforts to contact all holders of copyright material contained in this book. We have failed to locate some of them. Should holders wish to contact the Publisher, we will make every effort to come to some arrangement with them ISBN 978-0-85729-928-4 e-ISBN 978-0-85729-929-1 DOI 10.1007/978-0-85729-929-1 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2011935730 Mathematics Subject Classification: 01-00, 01455, 14H70, 70Hxx, 70Exx, 35A10 Translation from the French language edition: ‘Souvenirs sur Sofia Kovalevskaya’ by Michèle Audin Copyright © 2008 Calvage et Mounet, France http://www.calvage-et-mounet.fr/ All Rights Reserved Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copy- right, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use.
    [Show full text]
  • Shining the Spotlight on Movie Microbes
    THE MICROSCOPE • Vol. 61:2, pp 63–73 (2013) C R I T I C A L FOCUS Brian J. Ford Shining the Spotlight on Movie Microbes arilyn Monroe Spielberg who created the “M was a confused, Movie stars don’t have to be human to be most unusual film stars of sweet angel,” said our visi- memorable. The microscopic realm offers all: microbes. His epic tor, as the sun sparkled on movie “War of the Worlds” his crystal glass of orange the most exciting images for filmmakers, features free-swimming juice. “And Cary — did but almost everyone ignores it. microorganisms in the you know he was born in opening scenes. We zoom Britain? Cary Grant was out from the nucleus of a so muddled in his mind. He and I became such good ciliated microbe to find a water droplet on a leaf that is friends. Archibald Leach, he was called originally. Poor swarming with protists swimming eagerly about. It chap ran away to become a performer when his mother is a memorable scene. The film, released in 2005, is one was locked up in a mental institution in Bristol and of the few to show microbes as part of the story. nobody told him about it. It’s strange what makes In narrating the closing moments of the film, Mor- people into movie stars.” My dear friend Charles gan Freeman muses that “humans have suffered bil- Bennett had been born in 1899, and stayed with us in lions of lives to earn the right to live with these tiny Cambridgeshire when he was 94.
    [Show full text]
  • Butterflies Are Free to Fly
    BUTTERFLIES ARE FREE TO FLY A New and Radical Approach To Spiritual Evolution By Stephen Davis Smashwords Edition, License Notes Thank you for downloading this free ebook. You are welcome to share it with your friends. This book may be reproduced, copied and distributed for non-commercial purposes, provided the book remains in its complete original form. Copyright 2010 by L & G Productions, LLC Table of Contents Chapter 0 – Introduction PART ONE – The Movie Theater Metaphor Preface to Part One Chapter 1 – Plato‟s Cave Chapter 2 – Joining Together Chapter 3 – What‟s Wrong with This Picture? Chapter 4 – The Library Chapter 5 – The Field Chapter 6 – The Hologram Chapter 7 – There is No “Out There” Out There Chapter 8 – The Breakout PART TWO – Inside the Cocoon Preface to Part Two Chapter 9 – The Consciousness Model Chapter 10 – The Player Model Chapter 11 – The Human Game Model Chapter 12 – The Two Halves Chapter 13 – The Process Chapter 14 – Spiritual Autolysis Chapter 15 – Detaching & “Desirelessness” Chapter 16 – Judgment Chapter 17 – Beliefs & Opinions Chapter 18 – Resistance Chapter 19 – Fear Chapter 20 – Who Am I? Chapter 21 – On Becoming a Butterfly PART THREE – Questions & Answers Preface to Part Three Chapter 22 – One Big Hologram? Chapter 23 – Other People Chapter 24 – The “Earth Environment” Template Chapter 25 – Are We All One? Chapter 26 – One Player per Infinite I? Chapter 27 – Past Lives? Chapter 28 – Karma, Cause & Effect Chapter 29 – Trust Chapter 30 – Money Chapter 31 – The Ego Chapter 32 – Compassion Chapter 33 – Robert Scheinfeld Chapter 34 – Jed McKenna Chapter 35 – U.G. Krishnamurti Chapter 36 – The Future You are invited to write a book review, or offer comments, or download the free audio book version of this ebook by visiting: ButterfliesFree.com CHAPTER 0 INTRODUCTION Back to the Table of Contents Sweet freedom whispered in my ear You're a butterfly And butterflies are free to fly Fly away, high away, bye bye ~ from Someone Saved my Life Tonight, music by Elton John, lyrics by Bernie Taupin George had a problem.
    [Show full text]
  • A Russian Childhood Sofya Kovalevskaya a Russian Childhood
    A Russian Childhood Sofya Kovalevskaya A Russian Childhood TRANSLATED, EDITED AND INTRODUCED BY BEATRICE STILLMAN With an Analysis of Kovalevskaya' s Mathematics by P. Y. Kochina USSR Academy of Sciences Springer Science+Business Media New York This book has been selected for inclusion in the Sources and Translation Series of the Russian Institute, Columbia University. AMS'classification 01A70 Library of Congress Cataloging in Publication Data Kovalevskafa, Sof; Vasil'evna Korvin-Krukovskafa, 1850-1891. A Russian childhood. Translation of Vospominanifa detstva. Bibliography: p. Includes index. 1. Kovalevskai';, Sofi; Vasil'evna Korvin-Krukovskai-;, 1850- 1891. 2. Mathematicians-Russia-Biography. I. Title. QA29.K67A3513 510'.92'4 [B] 78-12955 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag. © 1978 by Beatrice Stillman Originally published by Springer-Verlag New York in 197R. Softcover reprint of the hardcover 1st edition 1978 ISBN 978-1-4419-2808-5 ISBN 978-1-4757-3839-1 (eBook) DOI 10.1007/978-1-4757-3839-1 For Pelageya Y akovlevna Kochina, untiring scholar and generous spirit, in admiration and friendship Contents Pre/ace tX Introduction 1 CHAPTER ONE Earliest Memories 47 CHAPTER TWO The Thief 59 CHAPTER THREE Metamorphosis 77 CHAPTER FOUR Palibino 82 CHAPTER FIVE Mzss Smith 98 vii Contents CHAPTER SIX Uncle Pyotr V asil£evich Krukovsky 111 CHAPTER SEVEN Uncle Fyodor Fyodorovich Shubert 124 CHAPTER EIGHT My Sister 133 CHAPTER NINE Anyuta's Nihilism 145 CHAPTER TEN Anyuta's First Literary Experiments 155 CHAPTER ELEVEN Our Friendship with Fyodor Mikhailovich Dostoevsky 173 Notes 201 An Autobiographical Sketch 213 On the Scientific Work of Sofya Kovalevskaya, by P.
    [Show full text]
  • Founded in 1939 Under the Aegis of Scotsman John Grierson, Pioneering Theorist and Practitioner of the Documentary Form, The
    Founded in 1939 under the aegis of Scotsman John Grierson , pioneering theorist and practitioner of the documentary form, the National Film Board was initially put in the service of war propaganda. Two years later, the addition to its ranks of Grierson’s countryman Norman McLaren would instigate the NFB’s second elemental thrust: technically adventurous, audaciously whimsical animation. These two interwoven threads have permeated the Film Board’s productions ever since, giving us formally innovative works that nonetheless edify. NFB films are fun, entertaining, and favor the dramatic over the didactic. We present, drawn from the shelves of Oddball Archives, what can only pretend at a cross-section of NFB’s voluminous output: explorations from the subatomic to the outer reaches of space, with a dose of human-scale drama and sheer flights of fancy. Pas de deux (1968) B+W 13 min. by Norman McLaren Set against a black ground, two graceful dancers become pure embodiments of light. Using optical superimposition, McLaren multiplies the figures, transforming live action into his own brand of kinetics. Beautifully choreographed and shot, hauntingly scored (featuring the United Folk Orchestra of Romania ), hypnotic and unforgettable. Cosmic Zoom (1968) Color 8 min. by Eva Szasz A fantastic, “continuous” voyage from a rowboat on the Ottawa river, upward and outward to a grand view of galactic flotsam, then back inwards through a rivulet of blood in the tip of a mosquito’s proboscis, to examine an atomic nucleus. Remade a decade later by Charles and Ray Eames (Powers of Ten ) with narration (and its jumping-off point moved to Chicago), then again as an Imax movie ( Cosmic Voyage ) with Morgan Freeman , Cosmic Zoom is where it all began.
    [Show full text]
  • Arxiv:Hep-Th/0212169V1 15 Dec 2002
    LPT–Orsay–02–111 RUB–TP2–17/02 hep-th/0212169 Noncompact Heisenberg spin magnets from high-energy QCD III. Quasiclassical approach ´ 1 2 3 S.E. Derkachov , G.P. Korchemsky and A.N. Manashov ∗ 1 Department of Mathematics, St.-Petersburg Technology Institute, 198013 St.-Petersburg, Russia 2 Laboratoire de Physique Th´eorique†, Universit´ede Paris XI, 91405 Orsay C´edex, France 3 Institut f¨ur Theoretische Physik II, Ruhr–Universit¨at Bochum, 44780 Bochum, Germany Abstract: The exact solution of the noncompact SL(2, C) Heisenberg spin magnet reveals a hidden sym- metry of the energy spectrum. To understand its origin, we solve the spectral problem for arXiv:hep-th/0212169v1 15 Dec 2002 the model within quasiclassical approach. In this approach, the integrals of motion satisfy the Bohr-Sommerfeld quantization conditions imposed on the orbits of classical motion. In the rep- resentation of the separated coordinates, the latter wrap around a Riemann surface defined by the spectral curve of the model. A novel feature of the obtained quantization conditions is that they involve both the α and β periods of the action differential on the Riemann surface, thus allowing us to find their− solutions− by exploring the full modular group of the spectral curve. We demonstrate that the quasiclassical energy spectrum is in a good agreement with the exact results. ∗ Permanent address: Department of Theoretical Physics, Sankt-Petersburg State University, 199034 St.- Petersburg, Russia †Unite Mixte de Recherche du CNRS (UMR 8627) Contents 1. Introduction 2 2. Noncompact Heisenberg spin magnet 6 2.1. Classicalmodel .................................... 6 2.2.
    [Show full text]
  • Remarkable Russian Women in Pictures, Prose and Poetry
    University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Zea E-Books Zea E-Books 11-2013 Remarkable Russian Women in Pictures, Prose and Poetry Marcelline Hutton [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/zeabook Part of the European History Commons, European Languages and Societies Commons, Slavic Languages and Societies Commons, Women's History Commons, and the Women's Studies Commons Recommended Citation Hutton, Marcelline, "Remarkable Russian Women in Pictures, Prose and Poetry" (2013). Zea E-Books. 21. https://digitalcommons.unl.edu/zeabook/21 This Book is brought to you for free and open access by the Zea E-Books at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Zea E-Books by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Remarkable Russian Women in Pictures, Prose and Poetry N Marcelline Hutton Many Russian women of the late 19th and early 20th centuries tried to find happy marriages, authentic religious life, liberal education, and ful- filling work as artists, doctors, teachers, and political activists. Some very remarkable ones found these things in varying degrees, while oth- ers sought unsuccessfully but no less desperately to transcend the genera- tions-old restrictions imposed by church, state, village, class, and gender. Like a Slavic “Downton Abbey,” this book tells the stories, not just of their outward lives, but of their hearts and minds, their voices and dreams, their amazing accomplishments against overwhelming odds, and their roles as feminists and avant-gardists in shaping modern Russia and, in- deed, the twentieth century in the West.
    [Show full text]
  • S. Kovalevsky: a Mathematical Lesson Author(S): Karen D
    S. Kovalevsky: A Mathematical Lesson Author(s): Karen D. Rappaport Reviewed work(s): Source: The American Mathematical Monthly, Vol. 88, No. 8 (Oct., 1981), pp. 564-574 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/2320506 . Accessed: 25/02/2013 16:08 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The American Mathematical Monthly. http://www.jstor.org This content downloaded on Mon, 25 Feb 2013 16:08:52 PM All use subject to JSTOR Terms and Conditions S. KOVALEVSKY: A MATHEMATICAL LESSON KAREN D. RAPPAPORT MathemcaticsDepartmenit, Essex CounitvCollege, Newark, NJ 07102 SofyaKovalevsky was a notedwriter whose works include both fiction and nonfiction.She was also a politicalactivist and a public advocate of feminism.In addition,she was a brilliant mathematicianwho made significant contributions despite the enormous educational and political obstaclesthat she had to overcome.Somehow her manyachievements have been forgotten.In thosefew instances where her work has not been lostit has been denigratedby such studiesas FelixKlein's history of nineteenth-centurymathematics. Klein dismisses Kovalevsky's work in the followingmanner: "Her worksare done in thestyle of Weierstrassand so one doesn'tknow how muchof herown ideas are in them."'He findssomething wrong with all herresearch and credits her withonly one positiveaccomplishment, drawing Weierstrass out of his shell throughtheir correspondence.It is timeto set thisrecord straight and to let thefacts speak for themselves.
    [Show full text]