Doing Mathematics: Convention ~ Subject ~ Calculation ~ Analogy (Softcover)
Doing Mathematics: Convention ~ Subject ~ Calculation ~ Analogy (Softcover)
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From the back cover: "Doing Mathematics 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 the 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."BRIEF CONTENTS
- List of Figures and Tables
- Preface
- ONE: Introduction
- TWO: Convention: How Means and Variances are Entrenched as Statistics
- THREE: Subject: The Fields of Topology Appendix: The Two-Dimensional Ising Model of a Ferromagnet
- FOUR: Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis
- FIVE: Analogy: A Syzygy Between a Research Program in Mathematics and a Research Program in Physics
- SIX: In Concreto: The City of Mathematics Epilog
- C.N. Yang, "The Spontaneous Magnetization of a Two-Dimensional Ising Model" (1952)
- C. Fefferman and L.A. Seco, "On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom" (1994, pp. 1-15)
- J. Leray, "Sur la forme des espaces topologiques et sur les points fixes des représentations" (1945, pp. 96-99)
- A. Weil, "Une lettre à Simone Weil" (1940)
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PUBLISHER: World Scientific Publishing
ISBN-13: 9789812382061
ISBN-10: 9812382062