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.

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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