Doing Mathematics: Convention, Subject, Calculationnalogy

Doing Mathematics: Convention, Subject, Calculationnalogy

by Martin H Krieger
     
 

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ISBN-10: 9812382062

ISBN-13: 9789812382061

Pub. Date: 04/01/2003

Publisher: World Scientific Publishing Company, Incorporated

This book discusses some ways of doing mathematical work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians — all depend on mathematics, what will work out and what won't. And

Overview

This book discusses some ways of doing mathematical work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians — all depend on mathematics, what will work out and what won't. And the mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, the stability of matter, the Ising model, and the Langlands Program in number theory and representation theory.

Product Details

ISBN-13:
9789812382061
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
04/01/2003
Pages:
472
Product dimensions:
60.00(w) x 85.00(h) x 7.50(d)

Table of Contents

List of Figures and Tablesix
Prefacexiii
1Introduction1
2Convention: How Means and Variances are Entrenched as Statistics18
3Subject: The Fields of Topology44
AppendixThe Two-Dimensional Ising Model of a Ferromagnet95
4Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis106
5Analogy: A Syzygy Between a Research Program in Mathematics and a Research Program in Physics189
6In Concreto: The City of Mathematics231
Epilog264
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
Notes307
Bibliography401
Index435

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