Doing mathematics : convention, subject, calculation, analogy / Martin H. Krieger.

Format:

Book

Author/Creator:

Krieger, Martin H.

Language:

English

Subjects (All):

Mathematics--Research.

Mathematics.

Physical Description:

1 online resource (472p. ) illustrations

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2003.

Language Note:

English

Summary:

A discussion of ways of doing mathematical work. 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.

A discussion of 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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 401-433) and index.

ISBN:

9786611935856

9781281935854

1281935859

9789812795489

9812795480

OCLC:

815752567