Dreams of Calculus: Perspectives on Mathematics Education

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/

A first-class debate book on the crucial issues of current mathematics teaching The authors offer startling evidence that computers are changing mathematics in a profound way Raises the question of how to alter teaching in mathermatics as a result of the computer's influence on the field      

What is the relationship between modern mathematics - more precisely computational mathematics - and mathematical education? It is this controversal topic that the authors address with an in-depth analysis. In fact, what they present is an extremely well-reasoned account of the development of mathematics and its culture giving concrete recommendation for a much-needed reform of the teaching of mathematics. The book is essential reading for everybody involved in mathematics and science, and mathematics teaching.

I. Perspectives.- 1 Introduction.- 2 What? How? For Whom? Why?- 3 A Brief History of Mathematics Education.- 4 What is Mathematics?- 5 Mountain Climbing.- 6 Jazz/Pop/Folk vs Classical Music.- 7 Virtual Reality and the Matrix.- 8 Scientific Revolutions.- 9 Education is based on Science.- 10 The Unreasonable Effectiveness of Mathematics in the Natural Sciences?- 11 Do we live in "The Best of Worlds"?- 12 The Reasonable Effectiveness of Computational Mathematics!- 13 The Need of Mathematics according to the Mathematics Delegation.- 14 An Agenda.- II. Essence.- 15 A Very Short Calculus Course.- 16 The Solar System.- 17 Turbulence and the Clay Prize.- III. Appendix.- 18 Appendix: The Mathematics Delegation and its Task.- 19 Preface to Body&Soul.- 20 Do Mathematicians Quarrel?