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Dreams of Calculus

Perspectives on Mathematics Education

  • Johan Hoffman
  • Claes Johnson
  • Anders Logg

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Perspectives

    1. Front Matter
      Pages 1-1
    2. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 3-5
    3. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 7-14
    4. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 15-18
    5. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 19-33
    6. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 35-37
    7. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 39-40
    8. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 41-44
    9. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 45-47
    10. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 49-55
    11. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 57-58
    12. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 59-65
    13. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 67-68
    14. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 69-70
    15. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 71-72
  3. Essence

    1. Front Matter
      Pages 73-73
    2. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 75-87
    3. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 89-99
    4. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 101-119
    5. Johan Hoffman, Claes Johnson, Anders Logg
      Pages 121-139
  4. Back Matter
    Pages 141-158

About this book

Introduction

Dreams of Calculus presents evidence that mathematics education today is in a process of change of paradigm, caused by the revolutionary new possibilities offered by the computer. The authors complement the physicist Eugene Wigner's famous statement concerning "the unreasonable effectiveness of mathematics in the natural sciences", by presenting evidence of "the reasonable effectiveness of computational mathematics". The book may also serve as an introduction to the Body&Soul mathematics education reform project reflecting the new paradigm.

Dreams of Calculus is directed to a large audience of teachers, students and users of mathematics. In a first part the authors present a brief history leading into applications of computational mathematics today. In a second part, they present key applications of computational mathematics for simulation of the motion of the planets in our solar system by solving Newton's equation, and turbulence by solving the Navier--Stokes equations.

This book is stimulated by the work of the Mathematics Delegation created by the Swedish Minister of Education in 2003 with the task of analyzing the current crisis in mathematics education on all levels.

The authors are leading researchers in computational mathematics.

Further information can be found at http://www.phi.chalmers.se/bodysoul/

Keywords

analysis applied mathematics calculus computational mathematics differential equation evolution mathematics virtual reality

Authors and affiliations

  • Johan Hoffman
    • 1
  • Claes Johnson
    • 2
  • Anders Logg
    • 2
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of Computational MathematicsChalmers University of TechnologyGöteborgSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18586-1
  • Copyright Information Springer Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21976-7
  • Online ISBN 978-3-642-18586-1
  • Buy this book on publisher's site
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