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Doing Mathematics: Convention, Subject, Calculationnalogy

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Overview

The conventions mathematicians adopt, the subject areas they delimit, what they can prove and calculate about the physical world, and the analogies that work for mathematicians all depend on what will and will not work in the mathematics itself, argues Krieger (planning, U. of Southern California). What is more, he says, the mathematics itself is shaped and supported, or not, by the other factors as well. His goal is to encourage mathematicians to think more closely about what they are doing, but also hopes lay readers might be intrigued by a glimpse into the field. Annotation ©2003 Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9789812382009
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 3/28/2003
  • Pages: 472
  • Product dimensions: 6.30 (w) x 8.80 (h) x 1.10 (d)

Table of Contents

List of Figures and Tables ix
Preface xiii
1 Introduction 1
2 Convention: How Means and Variances are Entrenched as Statistics 18
3 Subject: The Fields of Topology 44
Appendix The Two-Dimensional Ising Model of a Ferromagnet 95
4 Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis 106
5 Analogy: A Syzygy Between a Research Program in Mathematics and a Research Program in Physics 189
6 In Concreto: The City of Mathematics 231
Epilog 264
Appendices
A "The Spontaneous Magnetization of a Two-Dimensional Ising Model" (1952) 266
B "On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom," (1994, pp. 1-15) 275
C "Sur la forme des espaces topologiques et sur les points fixes des representations" (1945, pp. 96-99) 290
D "Une lettre a Simone Weil" (1940) 293
Notes 307
Bibliography 401
Index 435
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