Doing Mathematics: Convention, Subject, Calculationnalogy

Doing Mathematics: Convention, Subject, Calculationnalogy

by Martin H. Krieger
     
 

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,… See more details below

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

Product Details

ISBN-13:
9789812382009
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
03/28/2003
Pages:
472
Product dimensions:
6.30(w) x 8.80(h) x 1.10(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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