Skip to main content
SpringerLink
Log in

Dreams of Calculus

Perspectives on Mathematics Education

  • Textbook
  • © 2004

Overview

Authors:
  1. Johan Hoffman

    1. Courant Institute of Mathematical Sciences, New York University, New York, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Claes Johnson

    1. Department of Computational Mathematics, Chalmers University of Technology, Göteborg, Sweden

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Anders Logg

    1. Department of Computational Mathematics, Chalmers University of Technology, Göteborg, Sweden

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • A first-class debate book on the crucial issues of current mathematics teaching

  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Perspectives

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 3-5

    3. What? How? For Whom? Why?

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 7-14

    4. A Brief History of Mathematics Education

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 15-18

    5. What is Mathematics?

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 19-33

    6. Virtual Reality and the Matrix

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 35-37

    7. Mountain Climbing

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 39-40

    8. Scientific Revolutions

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 41-44

    9. Education is Based on Science

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 45-47

    10. The Unreasonable Effectiveness of Mathematics in the Natural Sciences?

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 49-55

    11. Do We live in “The Best of Worlds”?

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 57-58

    12. The Reasonable Effectiveness of Computational Mathematics

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 59-65

    13. Jazz/Pop/Folk vs. Classical Music

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 67-68

    14. The Right to Not Know

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 69-70

    15. An Agenda

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 71-72

  3. Essence

    1. Front Matter

      Pages 73-73
      Download chapter PDF

    2. A Very Short Calculus Course

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 75-87

    3. The Solar System

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 89-99

    4. Turbulence and the Clay Prize

      • Johan Hoffman, Claes Johnson, Anders Logg
      Pages 101-119
Back to top

Keywords

About this book

The purpose of this book is to stimulate a much needed debate on ma- ematics education reform. We do not claim that we present anything near the whole truth, and that there are not many other points of view. We thus invite to debate and urge other people to express their views. As scientists we believe that it is our duty to present our own standpoints and conc- sions as clearly as possible, to open for scrutiny and discussion, rather than ambiguous politically correct views, which are di?cult to question. This book may be viewed as an introduction to our mathematics e- cation reform project Body&Soul based on a synthesis of Body (com- tational mathematics) and Soul (analytical mathematics). We do make a case for computational mathematics, which is the new world of mathem- ics opened by the computer, now waiting to enter mathematics education. But we do also propose a synthesis of this new world, with the kernel being computational algorithms, and the traditional world of analytical ma- ematics, with analytical formulas as the kernel. In fact, algorithms are expressed using analytical formulas before being translated into computer code, and good analytical formulas are necessary for understanding and insight.

Reviews

From the reviews:

"[...] this book fills a gap in the literature of mathematics education although the analysis and conclusions in it are not constraining (but very interesting!)."

St.Götz, Monatshefte für Mathematik 148, Issue 3, 2006

"The object of this book is to make a case for computational mathematics to be treated as a subject in its own right. … The text is copiously illustrated with diagrams associated with the topic discussed and portraits of some of the mathematicians mentioned. … The printing and format are pleasing and the book will be of interest to those in university departments contemplating revision of syllabi."

Ll. G. Chambers, Zentralblatt MATH, Vol. 1079, 2006

Authors and Affiliations

  • Courant Institute of Mathematical Sciences, New York University, New York, USA

    Johan Hoffman

  • Department of Computational Mathematics, Chalmers University of Technology, Göteborg, Sweden

    Claes Johnson, Anders Logg

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation