Johan Hoffman, Claes Johnson, Anders Logg

Dreams of Calculus (eBook, PDF)

Perspectives on Mathematics Education

• Format: PDF

Produktbeschreibung

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/

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 162
• Erscheinungstermin: 27. Juni 2011
• Englisch
• ISBN-13: 9783642185861
• Artikelnr.: 53093257

Autorenporträt

Johan Hoffman, Courant Institute of Mathematical Sciences, New York, NY, USA / Anders Logg, Chalmers University of Technology, Göteborg, Sweden

Inhaltsangabe

I Perspectives.- 1 Introduction.- 2 What? How? For Whom? Why?.- 3 A Brief History of Mathematics Education.- 4 What is Mathematics?.- 5 Virtual Reality and the Matrix.- 6 Mountain Climbing.- 7 Scientific Revolutions.- 8 Education is Based on Science.- 9 The Unreasonable Effectiveness of Mathematics the Natural Sciences?.- 10 Do We live in "The Best of Worlds"?.- 11 The Reasonable Effectiveness Computational Mathematics.- 12 Jazz/Pop/Folk vs. Classical Music.- 13 The Right to Not Know.- 14 An Agenda.- II Essence.- 15 A Very Short Calculus Course.- 16 The Solar System.- 17 Turbulence and the Clay Prize.- 18 Do Mathematicians Quarrel?.- III Appendix.- A Comments on the Directives of the Mathematics Delegation.- A.1 The Directives.- A.2 Comments.- A.3 A Sum Up.- B Preface to Body&Soul.- C Public Debate.

Rezensionen

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