Doing mathematics : convention subject calculation analogy
著者
書誌事項
Doing mathematics : convention subject calculation analogy
World Scientific, c2003
- : pbk
大学図書館所蔵 全7件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- Convention: How Means and Variances are Entrenched as Statistics
- Subject: The Fields of Topology
- Appendix: The Two-Dimensional Ising Model of a Ferromagnet
- Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis
- Analogy: A Syzygy Between a Research Program in Mathematics and a Research Program in Physics, Each of Which is Itself an Analogy
- Mathematics in Concreto.
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